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NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations

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NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations

Edited By Saumya.Srivastava | Updated on Sep 05, 2023 07:24 PM IST

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations

Here students will get NCERT Solutions For Quadratic Equation class 10 which are created by expert team at Careers360 keeping in mind of latest syllabus of CBSE 2023-24. These solutions are very helpful for students to understand the basic concepts in a better way as these cover all the topics mentioned in syllabus comprehensive also include step by step explanation of each problem. When we equate the quadratic polynomial to zero, then we get a quadratic equation. NCERT Solutions for Class 10 Maths will help students to get indept understanding of the concepts and thus help students to strategise their preparation. They must complete the NCERT Class 10 Maths syllabus to the earliest so that they can revise in a strategic way. Each exercises of Quadratic Equation Class 10 are solved here in detailled manner.

Understanding quadratic equations chapter 4 maths class 10 is crucial as they appear in various real-life scenarios. Students must focus on mastering this chapter in the 2023-24 CBSE Syllabus to excel in Class 10 Math exams. NCERT solutions are valuable tools for comprehension and self-assessment. Regular practice with these solutions aids in addressing weaknesses. In mathematics, answers are either right or wrong, making concentration essential for achieving full marks.

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NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations PDF Free Download

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NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations - Important Formulae

Quadratic Equation:

f(x) = ax2 + bx + c, Where a, b, c ∈ R and a ≠ 0.

Quadratic Formula - Roots:

  • (α, β) = [-b ± (b2 - 4ac)]/2a

Roots of Quadratic Equation:

  • x = [-b ± D]/2a

  • D = b2 - 4ac

Nature of Roots of Quadratic Equation:

  • D > 0: Roots are real and distinct.

  • D = 0: Roots are real and equal.

  • D < 0: Roots are imaginary.

The sum of Roots:

  • S = α + β = -b/a

Product of Roots:

  • P = αβ = c/a

Quadratic Equation in terms of Roots:

  • x2 - (α + β)x + αβ = 0

Common Roots of Quadratic Equations:

  • One common root: (b1c2 - b2c1) / (c1a2 - c2a1) = (c1a2 - c2a1) / (a1b2 - a2b1)

  • Both roots common: a1/a2 = b1/b2 = c1/c2

Quadratic Equation Simplified Form:

  • ax2 + bx + c = 0 or [(x + b/2a)2 -D/(4a2)]

Extreme Values of Quadratic Equation:

  • If a > 0, minimum value = (4ac - b2)/4a at x = -b/(2a)

  • If a < 0, maximum value = (4ac - b2)/4a at x = -b/(2a)

The sum of Roots of Cubic Equation:

  • If α, β, γ are roots of the cubic equation: ax3 + bx2 + cx + d = 0

α + β + γ = -b/a.

αβ + βγ + γα = c/a.

αβγ = -d/a.

Free download NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations PDF for CBSE Exam.

NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations (Intext Questions and Exercise)

Quadratic Equation Class 10 Excercise: 4.1

Q1 (i) Check whether the following are quadratic equations : (x+1)^2 = 2(x-3)

Answer:

We have L.H.S. (x+1)^2 = x^2+2x+1

Therefore, (x+1)^2 = 2(x-3) can be written as:

\Rightarrow x^2+2x+1 = 2x-6

i.e., x^2+7 = 0

Or x^2+0x+7 = 0

This equation is of type: ax^2+bx+c = 0 .

Hence, the given equation is a quadratic equation.

Q1 (ii) Check whether the following are quadratic equations : x^2 - 2x = (-2)(3-x)

Answer:

Given equation x^2 - 2x = (-2)(3-x) can be written as:

\Rightarrow x^2 -2x = -6+2x

i.e., x^2-4x+6 = 0

This equation is of type: ax^2+bx+c = 0 .

Hence, the given equation is a quadratic equation.

Q1 (iii) Check whether the following are quadratic equations : (x-2)(x+1) = (x-1)(x+3)

Answer:

L.H.S. (x-2)(x+1) can be written as:

= x^2+x-2x-2 = x^2-x-2

and R.H.S (x-1)(x+3) can be written as:

= x^2+3x-x-3 = x^2+2x-3

\Rightarrow x^2-x-2 = x^2+2x-3

i.e., 3x-1 = 0

The equation is of the type: ax^2+bx+c = 0,a\neq0 .

Hence, the given equation is not a quadratic equation since a=0.

Q1 (iv) Check whether the following are quadratic equations : (x-3)(2x+1) = x(x+5)

Answer:

L.H.S. (x-3)(2x+1) can be written as:

= 2x^2+x-6x-3 = 2x^2-5x-3

and R.H.S (x)(x+5) can be written as:

= x^2+5x

\Rightarrow 2x^2-5x-3 = x^2+5x

i.e., x^2-10x-3 = 0

This equation is of type: ax^2+bx+c = 0,a\neq0 .

Hence, the given equation is a quadratic equation.

Q1 (v) Check whether the following are quadratic equations : (2x -1)(x-3) = (x+5)(x-1)

Answer:

L.H.S. (2x-1)(x-3) can be written as:

= 2x^2-6x-x+3 = 2x^2-7x+3

and R.H.S (x+5)(x-1) can be written as:

=x^2-x+5x-5 = x^2+4x-5

\Rightarrow 2x^2-7x+3 = x^2+4x-5

i.e., x^2-11x+8 = 0

This equation is of type: ax^2+bx+c = 0,a \neq 0 .

Hence, the given equation is a quadratic equation.

Q1 (vi) Check whether the following are quadratic equations : x^2 +3x +1 = (x-2)^2

Answer:

L.H.S. x^2+3x+1

and R.H.S (x-2)^2 can be written as:

= x^2-4x+4

\Rightarrow x^2+3x+1 = x^2- 4x+4

i.e., 7x-3 = 0

This equation is NOT of type: ax^2+bx+c = 0 , a\neq0 .

Here a=0, hence, the given equation is not a quadratic equation.

Q1 (vii) Check whether the following are quadratic equations : (x+2)^3 = 2x(x^2 -1)

Answer:

L.H.S. (x+2)^3 can be written as:

= x^3+8+6x(x+2) =x^3+6x^2+12x+8

and R.H.S 2x(x^2-1) can be written as:

= 2x^3-2x

\Rightarrow x^3+6x^2+12x+8 = 2x^3-2x

i.e., x^3-6x^2-14x-8 = 0

This equation is NOT of type: ax^2+bx+c = 0 .

Hence, the given equation is not a quadratic equation.

Q1 (viii) Check whether the following are quadratic equations : x^3 -4x^2 -x +1 = (x -2)^3

Answer:

L.H.S. x^3 -4x^2 -x +1 ,

and R.H.S (x-2)^3 can be written as:

= x^3-6x^2+12x-8

\Rightarrow x^3-4x^2-x+1 = x^3-6x^2+12x-8

i.e., 2x^2-13x+9=0

This equation is of type: ax^2+bx+c = 0 .

Hence, the given equation is a quadratic equation.

Q2 (i) Represent the following situations in the form of quadratic equations : The area of a rectangular plot is 528m^2 . The length of the plot (in meters) is one more than twice its breadth. We need to find the length and breadth of the plot.

Answer:

Given the area of a rectangular plot is 528m^2 .

Let the breadth of the plot be 'b' .

Then, the length of the plot will be: = 2b +1 .

Therefore the area will be:

=b(2b+1)\ m^2 which is equal to the given plot area 528m^2 .

\Rightarrow 2b^2+b = 528

\Rightarrow 2b^2+b - 528 = 0

Hence, the length and breadth of the plot will satisfy the equation 2b^2+b - 528 = 0

Q2 (ii) Represent the following situations in the form of quadratic equations : The product of two consecutive positive integers is 306. We need to find the integers.

Answer:

Given the product of two consecutive integers is 306.

Let two consecutive integers be 'x' and 'x+1' .

Then, their product will be:

x(x+1) = 306

Or x^2+x- 306 = 0 .

Hence, the two consecutive integers will satisfy this quadratic equation x^2+x- 306 = 0 .

Q2 (iii) Represent the following situations in the form of quadratic equations: Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Answer:

Let the age of Rohan be 'x' years.

Then his mother age will be: 'x+26' years.

After three years,

Rohan's age will be 'x+3' years and his mother age will be 'x+29' years.

Then according to question,

The product of their ages 3 years from now will be:

\Rightarrow (x+3)(x+29) = 360

\Rightarrow x^2+3x+29x+87 = 360 Or

\Rightarrow x^2+32x-273 = 0

Hence, the age of Rohan satisfies the quadratic equation x^2+32x-273 = 0 .

Q2 (iv) Represent the following situations in the form of quadratic equations : A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.

Answer:

Let the speed of the train be 's' km/h.

The distance to be covered by the train is 480\ km .

\therefore The time taken will be

=\frac{480}{s}\ hours

If the speed had been 8\ km/h less, the time taken would be: \frac{480}{s-8}\ hours .

Now, according to question

\frac{480}{s-8} - \frac{480}{s} = 3

\Rightarrow \frac{480x - 480(x-8)}{(x-8)x} = 3

\Rightarrow 480x - 480x+3840 = 3(x-8)x

\Rightarrow 3840 = 3x^2-24x

\Rightarrow 3x^2 -24x-3840 = 0

Dividing by 3 on both the side

x^2 -8x-1280 = 0

Hence, the speed of the train satisfies the quadratic equation x^2 -8x-1280 = 0


Quadratic Equation Class 10 Excercise: 4.2

Q1 (i) Find the roots of the following quadratic equations by factorization: x^2 - 3x - 10 =0

Answer:

Given the quadratic equation: x^2 - 3x - 10 =0

Factorization gives, x^2 - 5x+2x - 10 =0

\Rightarrow x^2 - 5x+2x - 10 =0

\Rightarrow x(x-5) +2(x-5) =0

\Rightarrow (x-5)(x+2) =0

\Rightarrow x= 5\ or\ -2

Hence, the roots of the given quadratic equation are 5\ and\ -2 .

Q1 (ii) Find the roots of the following quadratic equations by factorization: 2x^2 + x - 6 = 0

Answer:

Given the quadratic equation: 2x^2 + x - 6 = 0

Factorisation gives, 2x^2 +4x-3x - 6 = 0

\Rightarrow 2x(x+2) -3(x+2) =0

\Rightarrow (x+2)(2x-3) = 0

\Rightarrow x= -2\ or\ \frac{3}{2}

Hence, the roots of the given quadratic equation are

-2\ and\ \frac{3}{2}

Q1 (iii) Find the roots of the following quadratic equations by factorization: \sqrt2x^2 + 7x + 5\sqrt2 = 0

Answer:

Given the quadratic equation: \sqrt2x^2 + 7x + 5\sqrt2 = 0

Factorization gives, \sqrt2x^2 + 5x+2x + 5\sqrt2 = 0

\Rightarrow x(\sqrt2 x +5) +\sqrt2 (\sqrt 2 x +5)= 0

\Rightarrow (\sqrt2 x +5)(x+\sqrt{2}) = 0

\Rightarrow x=\frac{-5}{\sqrt 2 }\ or\ -\sqrt 2

Hence, the roots of the given quadratic equation are

\frac{-5}{\sqrt 2 }\ and\ -\sqrt 2

Q1 (iv) Find the roots of the following quadratic equations by factorization: 2x^2 -x + \frac{1}{8} = 0

Answer:

Given the quadratic equation: 2x^2 -x + \frac{1}{8} = 0

Solving the quadratic equations, we get

16x^2-8x+1 = 0

Factorization gives, \Rightarrow 16x^2-4x-4x+1 = 0

\Rightarrow 4x(4x-1)-1(4x-1) = 0

\Rightarrow (4x-1)(4x-1) = 0

\Rightarrow x=\frac{1}{4}\ or\ \frac{1}{4}

Hence, the roots of the given quadratic equation are

\frac{1}{4}\ and\ \frac{1}{4}

Q1 (v) Find the roots of the following quadratic equations by factorization: 100x^2 -20x +1 = 0

Answer:

Given the quadratic equation: 100x^2 -20x +1 = 0

Factorization gives, 100x^2 -10x-10x +1 = 0

\Rightarrow 10x(10x-1)-10(10x-1) = 0

\Rightarrow (10x-1)(10x-1) = 0

\Rightarrow x=\frac{1}{10}\ or\ \frac{1}{10}

Hence, the roots of the given quadratic equation are

\frac{1}{10}\ and\ \frac{1}{10} .

Q2 Solve the problems given in Example 1. (i) x^2-45x+324 = 0 (ii) x^2-55x+750 = 0

Answer:

From Example 1 we get:

Equations:

(i) x^2-45x+324 = 0

Solving by factorization method:

Given the quadratic equation: x^2-45x+324 = 0

Factorization gives, x^2-36x-9x+324 = 0

\Rightarrow x(x-36) - 9(x-36) = 0

\Rightarrow (x-9)(x-36) = 0

\Rightarrow x=9\ or\ 36

Hence, the roots of the given quadratic equation are x=9\ and \ 36 .

Therefore, John and Jivanti have 36 and 9 marbles respectively in the beginning.

(ii) x^2-55x+750 = 0

Solving by factorization method:

Given the quadratic equation: x^2-55x+750 = 0

Factorization gives, x^2-30x-25x+750 = 0

\Rightarrow x(x-30) -25(x-30) = 0

\Rightarrow (x-25)(x-30) = 0

\Rightarrow x=25\ or\ 30

Hence, the roots of the given quadratic equation are x=25\ and \ 30 .

Therefore, the number of toys on that day was 30\ or\ 25.

Q3 Find two numbers whose sum is 27 and the product is 182.

Answer:

Let two numbers be x and y .

Then, their sum will be equal to 27 and the product equals 182.

x+y = 27 ...............................(1)

xy =182 .................................(2)

From equation (2) we have:

y = \frac{182}{x}

Then putting the value of y in equation (1), we get

x+\frac{182}{x} = 27

Solving this equation:

\Rightarrow x^2-27x+182 = 0

\Rightarrow x^2-13x-14x+182 = 0

\Rightarrow x(x-13)-14(x-13) = 0

\Rightarrow (x-14)(x-13) = 0

\Rightarrow x = 13\ or\ 14

Hence, the two required numbers are 13\ and \ 14 .

Q4 Find two consecutive positive integers, the sum of whose squares is 365.

Answer:

Let the two consecutive integers be 'x'\ and\ 'x+1'.

Then the sum of the squares is 365.

. x^2+ (x+1)^2 = 365

\Rightarrow x^2+x^2+1+2x = 365

\Rightarrow x^2+x-182 = 0

\Rightarrow x^2 - 13x+14x+182 = 0

\Rightarrow x(x-13)+14(x-13) = 0

\Rightarrow (x-13)(x-14) = 0

\Rightarrow x =13\ or\ 14

Hence, the two consecutive integers are 13\ and\ 14 .

Q5 The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.

Answer:

Let the length of the base of the triangle be b\ cm .

Then, the altitude length will be: b-7\ cm .

Given if hypotenuse is 13\ cm .

Applying the Pythagoras theorem; we get

Hypotenuse^2 = Perpendicular^2 + Base^2

So, (13)^2 = (b-7)^2 +b^2

\Rightarrow 169 = 2b^2+49-14b

\Rightarrow 2b^2-14b-120 = 0 Or b^2-7b-60 = 0

\Rightarrow b^2-12b+5b-60 = 0

\Rightarrow b(b-12) + 5(b-12) = 0

\Rightarrow (b-12)(b+5) = 0

\Rightarrow b= 12\ or\ -5

But, the length of the base cannot be negative.

Hence the base length will be 12\ cm .

Therefore, we have

Altitude length = 12cm -7cm = 5cm and Base length = 12\ cm

Q6 A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

Answer:

Let the number of articles produced in a day = x

The cost of production of each article will be =2x+3

Given the total production on that day was Rs.90 .

Hence we have the equation;

x(2x+3) = 90

2x^2+3x-90 = 0

\Rightarrow 2x^2+15x-12x-90 = 0

\Rightarrow x(2x+15) - 6(2x+15) = 0

\Rightarrow (2x+15)(x-6) = 0

\Rightarrow x =-\frac{15}{2}\ or\ 6

But, x cannot be negative as it is the number of articles.

Therefore, x=6 and the cost of each article = 2x+3 = 2(6)+3 = 15

Hence, the number of articles is 6 and the cost of each article is Rs.15.


Class 10 Maths Chapter 4 Quadratic Equations Excercise: 4.3

Q1 (i) Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 - 7x +3 = 0

Answer:

Given equation: 2x^2 - 7x +3 = 0

On dividing both sides of the equation by 2, we obtain

\Rightarrow x^2-\frac{7}{2}x+\frac{3}{2} = 0

\Rightarrow (x-\frac{7}{4})^2 + \frac{3}{2} - \frac{49}{16} = 0

\Rightarrow (x-\frac{7}{4})^2 = \frac{49}{16} - \frac{3}{2}

\Rightarrow (x-\frac{7}{4})^2 =\frac{25}{16}

\Rightarrow (x-\frac{7}{4}) =\pm \frac{5}{4}

\Rightarrow x =\frac{7}{4}\pm \frac{5}{4}

\Rightarrow x = \frac{7}{4}+\frac{5}{4}\ or\ x = \frac{7}{4} - \frac{5}{4}

\Rightarrow x = 3\ or\ \frac{1}{2}

Q1 (ii) Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 + x -4 = 0

Answer:

Given equation: 2x^2 + x -4 = 0

On dividing both sides of the equation by 2, we obtain

\Rightarrow x^2+\frac{1}{2}x-2 = 0

Adding and subtracting \frac{1}{16} in the equation, we get

\Rightarrow (x+\frac{1}{4})^2 -2 - \frac{1}{16} = 0

\Rightarrow (x+\frac{1}{4})^2 =2+\frac{1}{16}

\Rightarrow (x+\frac{1}{4})^2 = \frac{33}{16}

\Rightarrow (x+\frac{1}{4}) =\pm \frac{\sqrt{33}}{4}

\Rightarrow x =\pm \frac{\sqrt{33}}{4} -\frac{1}{4}

\Rightarrow x = \frac{\pm \sqrt{33} - 1}{4}

\Rightarrow x = \frac{ \sqrt{33} - 1}{4}\ or\ x = \frac{ -\sqrt{33} - 1}{4}

Q1 (iii) Find the roots of the following quadratic equations, if they exist, by the method of completing the square 4x^2 + 4\sqrt3 + 3 = 0

Answer:

Given equation: 4x^2 + 4\sqrt3 + 3 = 0

On dividing both sides of the equation by 4, we obtain

\Rightarrow x^2+\sqrt3x+\frac{3}{4} = 0

Adding and subtracting (\frac{\sqrt3}{2})^2 in the equation, we get

\Rightarrow (x+\frac{\sqrt3}{2})^2 +\frac{3}{4} - (\frac{\sqrt3}{2})^2 = 0

\Rightarrow (x+\frac{\sqrt3}{2})^2 = \frac{3}{4} - \frac{3}{4} = 0

\Rightarrow (x+\frac{\sqrt3}{2}) = 0\ or\ (x+\frac{\sqrt3}{2}) = 0

Hence there are the same roots and equal:

\Rightarrow x = \frac{-\sqrt3}{2}\ or\ \frac{-\sqrt3}{2}

Q2 (iv) Find the roots of the following quadratic equations, if they exist, by the method of completing the square 2x^2 + x + 4 = 0

Answer:

Given equation: 2x^2 + x + 4 = 0

On dividing both sides of the equation by 2, we obtain

\Rightarrow x^2+\frac{x}{2}+2 = 0

Adding and subtracting (\frac{1}{4})^2 in the equation, we get

\Rightarrow (x+\frac{1}{4})^2 +2- (\frac{1}{4})^2 = 0

\Rightarrow (x+\frac{1}{4})^2 = \frac{1}{16} -2 = \frac{-31}{16}

\Rightarrow (x+\frac{1}{4}) = \pm \frac{\sqrt{-31}}{4}

\Rightarrow x = \pm \frac{\sqrt{-31}}{4} - \frac{1}{4}

\Rightarrow x = \frac{\sqrt{-31}-1}{4} \ or\ x = \frac{-\sqrt{-31}-1}{4}

Here the real roots do not exist (in the higher studies we will study how to find the root of such equations).

Q2 Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Answer:

(i) 2x^2-7x+3 = 0

The general form of a quadratic equation is : ax^2+bx+c = 0 , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get

a = 2,\ b = -7\ c = 3

And the quadratic formula for finding the roots is:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

Substituting the values in the quadratic formula, we obtain

\Rightarrow x= \frac{7 \pm \sqrt{49-24}}{4}

\Rightarrow x= \frac{7 \pm 5}{4}

\Rightarrow x= \frac{7 + 5}{4} = 3\ or\ x= \frac{7 - 5}{4} = \frac{1}{2}

Therefore, the real roots are: x =3,\ \frac{1}{2}


(ii) 2x^2+x-4 = 0

The general form of a quadratic equation is : ax^2+bx+c = 0 , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get

a = 2,\ b = 1\ c =-4

And the quadratic formula for finding the roots is:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

Substituting the values in the quadratic formula, we obtain

\Rightarrow x= \frac{-1 \pm \sqrt{1+32}}{4}

\Rightarrow x= \frac{-1 \pm \sqrt{33}}{4}

\Rightarrow x= \frac{-1 + \sqrt{33}}{4} \ or\ x= \frac{-1 - \sqrt{33}}{4}

Therefore, the real roots are: x = \frac{-1+\sqrt{33}}{4}\ or\ \frac{-1-\sqrt{33}}{4}

(iii) 4x^2+4\sqrt3x+3 = 0

The general form of a quadratic equation is : ax^2+bx+c = 0 , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get

a = 4,\ b = 4\sqrt{3}\ c =3

And the quadratic formula for finding the roots is:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

Substituting the values in the quadratic formula, we obtain

\Rightarrow x= \frac{-4\sqrt{3} \pm \sqrt{48-48}}{8}

\Rightarrow x= \frac{-4\sqrt{3} \pm 0}{8}

Therefore, the real roots are: x = \frac{-\sqrt{3}}{2}\ or\ \frac{-\sqrt{3}}{2}

(iv) 2x^2+x+4 = 0

The general form of a quadratic equation is : ax^2+bx+c = 0 , where a, b, and c are arbitrary constants.

Hence on comparing the given equation with the general form, we get

a = 2,\ b = 1,\ c =4

And the quadratic formula for finding the roots is:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

Substituting the values in the quadratic formula, we obtain

\Rightarrow x= \frac{-1 \pm \sqrt{1-32}}{4}

\Rightarrow x= \frac{-1 \pm \sqrt{-31}}{4}

Here the term inside the root is negative

Therefore there are no real roots for the given equation.

Q3 (i) Find the roots of the following equations: x - \frac{1}{x} = 3, x\neq 0

Answer:

Given equation: x - \frac{1}{x} = 3, x\neq 0

So, simplifying it,

\Rightarrow \frac{x^2-1}{x} = 3

\Rightarrow x^2-3x-1 = 0

Comparing with the general form of the quadratic equation: ax^2+bx+c = 0 , we get

a=1,\ b=-3,\ c=-1

Now, applying the quadratic formula to find the roots:

x= \frac{-b \pm \sqrt{b^2-4ac}}{2a}

\Rightarrow x= \frac{3 \pm \sqrt{9+4}}{2}

\Rightarrow x= \frac{3 \pm \sqrt{13}}{2}

Therefore, the roots are

\Rightarrow x = \frac{3+\sqrt{13}}{2}\ or\ \frac{3 - \sqrt{13}}{2}

Q3 (ii) Find the roots of the following equations: \frac{1}{x+4} - \frac{1}{x- 7} = \frac{11}{30},\ x\neq -4,7

Answer:

Given equation: \frac{1}{x+4} - \frac{1}{x- 7} = \frac{11}{30},\ x\neq -4,7

So, simplifying it,

\Rightarrow \frac{x-7-x-4}{(x+4)(x-7)} = \frac{11}{30}

\Rightarrow \frac{-11}{(x+4)(x-7)} = \frac{11}{30}

\Rightarrow (x+4)(x-7) = -30

\Rightarrow x^2-3x-28 = -30 or \Rightarrow x^2-3x+2 = 0

Can be written as:

\Rightarrow x^2-x-2x+2 = 0

\Rightarrow x(x-1) -2(x-1) = 0

\Rightarrow (x-2)(x-1) = 0

Hence the roots of the given equation are:

\Rightarrow x = 1\ or\ 2

Q4 The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is \frac{1}{3} . Find the present age.

Answer:

Let the present age of Rehman be 'x' years.

Then, 3 years ago, his age was (x-3) years.

and 5 years later, his age will be (x+5) years.

Then according to the question we have,

\frac{1}{(x-3)}+\frac{1}{(x+5)} = \frac{1}{3}

Simplifying it to get the quadratic equation:

\Rightarrow \frac{x+5+x-3}{(x-3)(x+5)} = \frac{1}{3}

\Rightarrow \frac{2x+2}{(x-3)(x+5)} = \frac{1}{3}

\Rightarrow 3(2x+2)= (x-3)(x+5)

\Rightarrow 6x+6 = x^2+2x-15

\Rightarrow x^2-4x-21 = 0

\Rightarrow x^2-7x+3x-21 = 0

\Rightarrow x(x-7)+3(x-7) = 0

\Rightarrow (x-7)(x+3) = 0

Hence the roots are: \Rightarrow x = 7,\ -3

However, age cannot be negative

Therefore, Rehman is 7 years old in the present.

Q5 In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects.

Answer:

Let the marks obtained in Mathematics be 'm' then, the marks obtain in English will be '30-m'.

Then according to the question:

(m+2)(30-m-3) = 210

Simplifying to get the quadratic equation:

\Rightarrow m^2-25m+156 = 0

Solving by the factorizing method:

\Rightarrow m^2-12m-13m+156 = 0

\Rightarrow m(m-12)-13(m-12) = 0

\Rightarrow (m-12)(m-13) = 0

\Rightarrow m = 12,\ 13

We have two situations when,

The marks obtained in Mathematics is 12, then marks in English will be 30-12 = 18.

Or,

The marks obtained in Mathematics is 13, then marks in English will be 30-13 = 17.

Q6 The diagonal of a rectangular field is 60 meters more than the shorter side. If the longer side is 30 meters more than the shorter side, find the sides of the field.

Answer:

Let the shorter side of the rectangle be x m.

Then, the larger side of the rectangle wil be = (x+30)\ m .

Diagonal of the rectangle:

= \sqrt{x^2+(x+30)^2}\ m

It is given that the diagonal of the rectangle is 60m more than the shorter side.

Therefore,

\sqrt{x^2+(x+30)^2} = x+60

\Rightarrow x^2+(x+30)^2 = (x+60)^2

\Rightarrow x^2+x^2+900+60x = x^2+3600+120x

\Rightarrow x^2-60x-2700 = 0

Solving by the factorizing method:

\Rightarrow x^2-90x+30x-2700 = 0

\Rightarrow x(x-90)+30(x-90)= 0

\Rightarrow (x+30)(x-90) = 0

Hence, the roots are: x = 90,\ -30

But the side cannot be negative.

Hence the length of the shorter side will be: 90 m

and the length of the larger side will be (90+30)\ m =120\ m

Q7 The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find the two numbers.

Answer:

Given the difference of squares of two numbers is 180.

Let the larger number be 'x' and the smaller number be 'y'.

Then, according to the question:

x^2-y^2 = 180 and y^2 = 8x

On solving these two equations:

\Rightarrow x^2-8x =180

\Rightarrow x^2-8x -180 = 0

Solving by the factorizing method:

\Rightarrow x^2-18x+10x -180 = 0

\Rightarrow x(x-18)+10(x-18) = 0

\Rightarrow (x-18)(x+10) = 0

\Rightarrow x=18,\ -10

As the negative value of x is not satisfied in the equation: y^2 = 8x

Hence, the larger number will be 18 and a smaller number can be found by,

y^2 = 8x putting x = 18, we obtain

y^2 = 144\ or\ y = \pm 12 .

Therefore, the numbers are 18\ and\ 12 or 18\ and\ -12 .

Q8 A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.

Answer:

Let the speed of the train be x\ km/hr.

Then, time taken to cover 360km will be:

=\frac{360}{x}\ hr

According to the question,

\Rightarrow (x+5)\left ( \frac{360}{x}-1 \right ) = 360

\Rightarrow 360-x+\frac{1800}{x} - 5 = 360

Making it a quadratic equation.

\Rightarrow x^2+5x-1800 = 0

Now, solving by the factorizing method:

\Rightarrow x^2+45x-40x-1800 = 0

\Rightarrow x(x+45)-40(x+45) = 0

\Rightarrow (x-40)(x+45) = 0

\Rightarrow x = 40,\ -45

However, the speed cannot be negative hence,

The speed of the train is 40\ km/hr .

Answer:

Let the time taken by the smaller pipe to fill the tank be x\ hr.

Then, the time taken by the larger pipe will be: (x-10)\ hr .

The fraction of the tank filled by a smaller pipe in 1 hour:

= \frac{1}{x}

The fraction of the tank filled by the larger pipe in 1 hour.

= \frac{1}{x-10}
Given that two water taps together can fill a tank in 9\frac{3}{8} = \frac{75}{8} hours.

Therefore,

\Rightarrow \frac{1}{x}+\frac{1}{x-10} = \frac{8}{75}

\Rightarrow \frac{x-10+x}{x(x-10)} = \frac{8}{75}

\Rightarrow \frac{2x-10}{x(x-10)} = \frac{8}{75}

Making it a quadratic equation:

\Rightarrow 150x-750 = 8x^2-80x

\Rightarrow 8x^2-230x+750 = 0

\Rightarrow 8x^2-200x-30x+750 = 0

\Rightarrow 8x(x-25) - 30(x-25) = 0

\Rightarrow (x-25)(8x+30) = 0

Hence the roots are \Rightarrow x = 25,\ \frac{-30}{8}

As time is taken cannot be negative:

Therefore, time is taken individually by the smaller pipe and the larger pipe will be 25 and 25-10 =15 hours respectively.

Q10 An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore (without taking into consideration the time they stop at intermediate stations). If the average speed of the express train is 11 km/h more than that of the passenger train, find the average speed of the two trains.

Answer:

Let the average speed of the passenger train be x\ km/hr .

Given the average speed of the express train = (x+11)\ km/hr

also given that the time taken by the express train to cover 132 km is 1 hour less than the passenger train to cover the same distance.

Therefore,

\Rightarrow \frac{132}{x} - \frac{132}{x+11} = 1

\Rightarrow 132\left [ \frac{x+11-x}{x(x+11)} \right ] = 1

\Rightarrow \frac{132\times11}{x(x+11)} = 1

Can be written as quadratic form:

\Rightarrow x^2+11x-1452 = 0

\Rightarrow x^2+44x-33x-1452 = 0

\Rightarrow x(x+44)-33(x+44)= 0

\Rightarrow (x+44)(x-33) = 0

Roots are: \Rightarrow x = -44,\ 33

As the speed cannot be negative.

Therefore, the speed of the passenger train will be 33\ km/hr and

The speed of the express train will be 33+11 = 44\ km/hr .

Q11 Sum of the areas of two squares is 468 m 2 . If the difference of their perimeters is 24 m, find the sides of the two squares.

Answer:

Let the sides of the squares be 'x'\ and\ 'y' . (NOTE: length are in meters)

And the perimeters will be: 4x\ and\ 4y respectively.

Areas x^2\ and\ y^2 respectively.

It is given that,

x^2 + y^2 = 468\ m^2 .................................(1)

4x-4y = 24\ m .................................(2)

Solving both equations:

x-y = 6 or x= y+6 putting in equation (1), we obtain

(y+6)^2 +y^2 = 468

\Rightarrow 2y^2+36+12y = 468

\Rightarrow y^2+6y - 216 = 0

Solving by the factorizing method:

\Rightarrow y^2+18y -12y-216 = 0

\Rightarrow y(y+18) -12(y+18) = 0

\Rightarrow (y+18)(y-12)= 0

Here the roots are: \Rightarrow y = -18,\ 12

As the sides of a square cannot be negative.

Therefore, the sides of the squares are 12m and (12\ m+6\ m) = 18\ m .


Quadratic Equation Class 10 Excercise: 4.4

Q1 (i) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

2x^2 - 3x +5 = 0

Answer:

For a quadratic equation, ax^2+bx+c = 0 the value of discriminant determines the nature of roots and is equal to:

D = b^2-4ac

If D>0 then roots are distinct and real.

If D<0 then no real roots.

If D= 0 then there exists two equal real roots.

Given the quadratic equation, 2x^2 - 3x +5 = 0 .

Comparing with general to get the values of a,b,c.

a = 2, b =-3,\ c= 5

Finding the discriminant:

D= (-3)^2 - 4(2)(5) = 9-40 = -31

\because D<0

Here D is negative hence there are no real roots possible for the given equation.

Q1 (ii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them: 3x^2 - 4\sqrt3x + 4 = 0

Answer:

b^2-4ac=(-4\sqrt{3})^2-(4\times4\times3)=48-48=0

Here the value of discriminant =0, which implies that roots exist and the roots are equal.

The roots are given by the formula

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{4\sqrt{3}\pm\sqrt{0}}{2\times3}=\frac{2}{\sqrt{3}}

So the roots are

\frac{2}{\sqrt{3}},\ \frac{2}{\sqrt{3}}

Q1 (iii) Find the nature of the roots of the following quadratic equations. If the real roots exist, find them:

2x^2 - 6x + 3 = 0

Answer:

The value of the discriminant

b^2-4ac=(-6)^2-4\times2\times3=12

The discriminant > 0. Therefore the given quadratic equation has two distinct real root

roots are

x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}=\frac{-6\pm\sqrt{12}}{2\times2}=\frac{3}{2}\pm\frac{\sqrt{3}}{2}

So the roots are

\frac{3}{2}+\frac{\sqrt{3}}{2}, \frac{3}{2}-\frac{\sqrt{3}}{2}

Q2 (i) Find the values of k for each of the following quadratic equations so that they have two equal roots.

2x^2 + kx + 3 = 0

Answer:

For two equal roots for the quadratic equation: ax^2+bx+c =0

The value of the discriminant D= 0 .

Given equation: 2x^2 + kx + 3 = 0

Comparing and getting the values of a,b, and, c.

a = 2, \ b = k,\ c = 3

The value of D = b^2-4ac = (k)^2 - 4(2)(3)

\Rightarrow (k)^2 = 24

Or, \Rightarrow k=\pm \sqrt{24} = \pm 2\sqrt{6}

Q2 (ii) Find the values of k for each of the following quadratic equations so that they have two equal roots

kx(x-2) + 6 = 0

Answer:

For two equal roots for the quadratic equation: ax^2+bx+c =0

The value of the discriminant D= 0 .

Given equation: kx(x-2) + 6 = 0

Can be written as: kx^2-2kx+6 = 0

Comparing and getting the values of a,b, and, c.

a = k, \ b = -2k,\ c = 6

The value of D = b^2-4ac = (-2k)^2 - 4(k)(6) = 0

\Rightarrow 4k^2 - 24k = 0

\Rightarrow 4k(k-6) = 0

\Rightarrow k= 0\ or\ 6

But k= 0 is NOT possible because it will not satisfy the given equation.

Hence the only value of k is 6 to get two equal roots.

Q3 Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m 2 ? If so, find its length and breadth.

Answer:

Let the breadth of mango grove be 'b' .

Then the length of mango grove will be '2b' .

And the area will be:

Area = (2b)(b) = 2b^2

Which will be equal to 800m^2 according to question.

\Rightarrow 2b^2 = 800m^2

\Rightarrow b^2 - 400 = 0

Comparing to get the values of a,b,c .

a=1, \ b= 0 , \ c = -400

Finding the discriminant value:

D = b^2-4ac

\Rightarrow 0^2-4(1)(-400) = 1600

Here, D>0

Therefore, the equation will have real roots.

And hence finding the dimensions:

\Rightarrow b^2 - 400 = 0

\Rightarrow b = \pm 20

As negative value is not possible, hence the value of breadth of mango grove will be 20m.

And the length of mango grove will be: = 2\times10 = 40m

Q4 Is the following situation possible? If so, determine their present ages. The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48.

Answer:

Let the age of one friend be x\ years.

and the age of another friend will be: (20-x)\ years.

4 years ago, their ages were, x-4\ years and 20-x-4 \ years .

According to the question, the product of their ages in years was 48.

\therefore (x-4)(20-x-4) = 48

\Rightarrow 16x-64-x^2+4x= 48

\Rightarrow -x^2+20x-112 = 0 or \Rightarrow x^2-20x+112 = 0

Now, comparing to get the values of a,\ b,\ c .

a = 1,\ b= -20,\ c =112

Discriminant value D = b^2-4ac = (-20)^2 -4(1)(112) = 400-448 = -48

As D<0 .

Therefore, there are no real roots possible for this given equation and hence,

This situation is NOT possible.

Q5 Is it possible to design a rectangular park of perimeter 80 m and area 400 m 2 ? If so, find its length and breadth.

Answer:

Let us assume the length and breadth of the park be 'l'\ and\ 'b' respectively.

Then, the perimeter will be P = 2(l+b) = 80

\Rightarrow l+b = 40\ or\ b = 40 - l

The area of the park is:

Area = l\times b = l(40-l) = 40l - l^2

Given : 40l - l^2 = 400

l^2 - 40l +400 = 0

Comparing to get the values of a, b and c.

The value of the discriminant D = b^2-4ac

\Rightarrow = b^2-4ac = (-40)^2 - 4(1)(400) = 1600 -1600 = 0

As D = 0 .

Therefore, this equation will have two equal roots.

And hence the roots will be:

l =\frac{-b}{2a}

l =\frac{-40}{2(1)} = \frac{40}{2} =20

Therefore, the length of the park, l =20\ m

and breadth of the park b = 40-l = 40 -20 = 20\ m .

Topics of Class 10 Maths Chapter 4 Quadratic Equations

  • Representation of situation in a quadratic equation.

  • Checking if an equation is quadratic or not.

  • Solving a quadratic equation using factorization/ roots of quadratic solutions.

  • The solution of the quadratic equation using completing the square method.

  • Solving a quadratic equation using the Sridharacharya formula.

  • Product of roots in a quadratic equation.

  • Sum of roots in a quadratic equation.

There are 4 exercise in Class 10 Maths chapter 4. Get the exercise wise solutions from the following links.

NCERT Books and NCERT Syllabus

Key Features For Chapter 4 Maths Class 10

Expertly Crafted: Skilled teachers at Careers360 create these NCERT Solutions with great care.

Accuracy Guaranteed: Class 10 maths chapter 4 solutions are entirely correct, making them perfect for students getting ready for their CBSE board exams.

Thorough Explanation: Even the smallest details are explained to help students feel more confident when facing other competitive exams.

Step-by-Step Answers: Class 10 maths ncert chapter 4 solutions to the textbook exercises are provided step by step. This helps students not only get the right final answers but also understand each part of the process, which can lead to better scores.

NCERT solutions for class 10 Maths - Chapter Wise

Chapter No.

Chapter Name

Chapter 1

Real Numbers

Chapter 2

Polynomials

Chapter 3

Pair of Linear Equations in Two Variables

Chapter 4

Quadratic Equations

Chapter 5

Arithmetic Progressions

Chapter 6

Triangles

Chapter 7

Coordinate Geometry

Chapter 8

Introduction to Trigonometry

Chapter 9

Some Applications of Trigonometry

Chapter 10

Circles

Chapter 11

Constructions

Chapter 12

Areas Related to Circles

Chapter 13

Surface Areas and Volumes

Chapter 14

Statistics

Chapter 15

Probability

How To use Solutions Of Quadratic Equation Class 10 ?

  • First of all list down all the questions in which you need assistance and go through the NCERT Solutions For Class 10 Maths Chapter 4 Quadratic Equations of that particular question.

  • When you complete the first step then your next target should be previous papers. You can pick past year papers and practice them thoroughly.

  • Once you complete NCERTs and previous year papers, try to solve the questions of that particular chapter from different state board books.

NCERT Solutions of Class 10 - Subject Wise

NCERT Exemplar solutions - Subject Wise

Frequently Asked Question (FAQs)

1. What are the important concepts learned in the NCERT Solutions for chapter 4 maths class 10 Quadratic Equations?

Class 10 maths chapter 4 solutions required multiple concepts including what is an equation, how to get the solution of an equation, methods of quadratic equation solution, the factoring method for solving a quadratic equation, the quadratic formula for solving a quadratic equation, the nature of roots of a quadratic equation, graphs of quadratic equations, and many.

2. What are the important topics covered in the NCERT Solutions for Class 10 Maths Chapter 4?

Chapter 4 quadratic equation class 10 ncert solutions contain multiple topics like Quadratic equations, Solutions of a quadratic equation, Discriminant of a quadratic equation, Factoring method for solving a quadratic equation, Quadratic formula for solving a quadratic equation, Nature of roots of a quadratic equation, and Graphs of quadratic equations.

3. How do you download the Class 10 Maths Quadratic Equations NCERT Textbooks PDF?

Students can visit the NCERT official website. There they can find options to select class, subject, and book title. Using these inputs students can download NCERT chapter 4 maths class 10 which is quadratic equations class 10 pdf. Students can also find solutions to these NCERTs from Careers360's official website

4. How do you solve a quadratic equation in Class 10?

There are multiple methods to solve a quadratic equation including the factoring method, quadratic formula method, graphical method, and many others. These methods depend on the type of quadratic equation so first to know what is quadratic polynomial type and then apply the above methods to find a quadratic polynomial solution.

5. Which of the following is a quadratic equation?

To determine whether an equation is a quadratic equation, you can look for two conditions: firstly, the highest power of the variable is 2 and secondly, the coefficient of the x^2 term (that is, the "a" in the equation) is not equal to zero. These two are some examples of quadratic equations 2x^2+3x+5 and x^2+5x+6.

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Option 1)

0.34\; J

Option 2)

0.16\; J

Option 3)

1.00\; J

Option 4)

0.67\; J

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Option 1)

2.45×10−3 kg

Option 2)

 6.45×10−3 kg

Option 3)

 9.89×10−3 kg

Option 4)

12.89×10−3 kg

 

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Option 1)

2,000 \; J - 5,000\; J

Option 2)

200 \, \, J - 500 \, \, J

Option 3)

2\times 10^{5}J-3\times 10^{5}J

Option 4)

20,000 \, \, J - 50,000 \, \, J

A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

Option 1)

K/2\,

Option 2)

\; K\;

Option 3)

zero\;

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In the reaction,

2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

Option 1)

11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

Option 2)

6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

Option 3)

33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

Option 4)

67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

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Option 1)

0.02

Option 2)

3.125 × 10-2

Option 3)

1.25 × 10-2

Option 4)

2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1)

decrease twice

Option 2)

increase two fold

Option 3)

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Option 4)

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Option 1)

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Option 2)

Weight fraction of solute

Option 3)

Fraction of solute present in water

Option 4)

Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

Option 1)

twice that in 60 g carbon

Option 2)

6.023 × 1022

Option 3)

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Option 4)

558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

Option 1)

less than 3

Option 2)

more than 3 but less than 6

Option 3)

more than 6 but less than 9

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more than 9

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5 Jobs Available
Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
Construction Manager

Individuals who opt for a career as construction managers have a senior-level management role offered in construction firms. Responsibilities in the construction management career path are assigning tasks to workers, inspecting their work, and coordinating with other professionals including architects, subcontractors, and building services engineers.

2 Jobs Available
Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems. 

2 Jobs Available
Naval Architect

A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

2 Jobs Available
Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials. 

2 Jobs Available
Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
Conservation Architect

A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

2 Jobs Available
Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
Veterinary Doctor

A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

5 Jobs Available
Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
Speech Therapist
4 Jobs Available
Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

4 Jobs Available
Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
Healthcare Social Worker

Healthcare social workers help patients to access services and information about health-related issues. He or she assists people with everything from locating medical treatment to assisting with the cost of care to recover from an illness or injury. A career as Healthcare Social Worker requires working with groups of people, individuals, and families in various healthcare settings such as hospitals, mental health clinics, child welfare, schools, human service agencies, nursing homes, private practices, and other healthcare settings.  

2 Jobs Available
Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

4 Jobs Available
Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available
Radio Jockey

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications. 

2 Jobs Available
Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
Fashion Blogger

Fashion bloggers use multiple social media platforms to recommend or share ideas related to fashion. A fashion blogger is a person who writes about fashion, publishes pictures of outfits, jewellery, accessories. Fashion blogger works as a model, journalist, and a stylist in the fashion industry. In current fashion times, these bloggers have crossed into becoming a star in fashion magazines, commercials, or campaigns. 

2 Jobs Available
Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

5 Jobs Available
Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

3 Jobs Available
Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
Advertising Manager

Advertising managers consult with the financial department to plan a marketing strategy schedule and cost estimates. We often see advertisements that attract us a lot, not every advertisement is just to promote a business but some of them provide a social message as well. There was an advertisement for a washing machine brand that implies a story that even a man can do household activities. And of course, how could we even forget those jingles which we often sing while working?

2 Jobs Available
Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

5 Jobs Available
QA Manager
4 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
Production Manager
3 Jobs Available
Procurement Manager

The procurement Manager is also known as  Purchasing Manager. The role of the Procurement Manager is to source products and services for a company. A Procurement Manager is involved in developing a purchasing strategy, including the company's budget and the supplies as well as the vendors who can provide goods and services to the company. His or her ultimate goal is to bring the right products or services at the right time with cost-effectiveness. 

2 Jobs Available
Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
Merchandiser
2 Jobs Available
AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

4 Jobs Available
QA Manager
4 Jobs Available
Azure Administrator

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

4 Jobs Available
Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

3 Jobs Available
Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

3 Jobs Available
ITSM Manager
3 Jobs Available
.NET Developer

.NET Developer Job Description: A .NET Developer is a professional responsible for producing code using .NET languages. He or she is a software developer who uses the .NET technologies platform to create various applications. Dot NET Developer job comes with the responsibility of  creating, designing and developing applications using .NET languages such as VB and C#. 

2 Jobs Available
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