CBSE Class 10 Maths Question Paper 2019 with Solutions

Question 1)

Find the coordinates of a point A, where AB is diameter of circle whose centre is (2,-3) and B is the point (1,4).

Question 2)

For what values of , the roots of the equation are real?

Question 3)

Find the value of for which the roots of the equation are reciprocal of each other.

View Solutions

Question 4)

Find A if

Question 5)

Find the value of .

Question 6)

How many two digit numbers are divisible by 3?

Question 7)

In fig.1, What is the ratio of to the ?

Question 8)

Find a rational number between .

Question 9)

Find the HCF of 1260 and 7344 using Euclid's algorithm.

Question 10)

Show that every positive odd integer is of the form (4q+1) or (4q+3), where q is some integer.

Question 11)

Which term of the AP 3,15,27,39,...will be 120 more than its 21st term?

Question 12)

If the sum of first terms of an AP is given by find the th term.

Question 13)

Find the ratio in which the segment joining the points (1,-3) and (4,5) is divided by x-axis? also find the coordinates of this point on x-axis.

Question 14)

A game consists of tossing a coin 3 times and noting the outcome each time. If getting the same result in all the tosses is a success, find the probability of losing the game.

Question 15)

A die is thrown once. Find the probability of getting a number which (i) is a prime number (ii) lies between 2 and 6.

Question 16)

Find if the system of equations has infinitely many solutions?

Question 17)

Prove that is an irrational number.

Question 18)

Find the value of k such that polynomial has sum of its zeros equal to half of their product.

Question 19)

A father's age is three times the sum of the ages of his two children. After 5 years his age will be two times the sum of their ages.Find the present age of the father.

Question 20)

A fraction becomes when 2 is subtracted from the numerator and it becomes when 1 is subtracted from the denominator. Find the fraction.

Question 21)

Find the point on y-axis which is equidistant from the points (5,-2) and (-3,2).

Question 22)

The line segment joining the points A(2,1) and B(5,-8) is trisected at the points P and Q such that P is nearer to A. If P also lies on the line given by , find the value of k.

Question 23)

Prove that

Question 24)

Prove that

Question 25)

In fig.2, PQ is a chord of length 8cm of a circle of radius 5cm and centre O.

The tangents at P and Q intersect at point T. Find the length of TP.

Question 26)

In fig3 prove that .

Question 27)

If P and Q are the points on side CA and CB respectively of right angled at C, prove that

Question 28)

Find the area of the shaded region in Fig.4 if ABCD is a rectangle with sides 8cm and 6cm and O is the centre of circle. (Take)

Question 29)

Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes; if 8cm standing water is needed?

Question 30)

Find the mode of the following frequency distribution.

Question 31)

Two water taps together can fill a tank in hours. The tap with longer diameter takes 2 hours less than the tap with smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.

Question 32)

A boat goes 30km upstream and 44km downstream in 10 hours. In 13 hours, it can go 40km upstream and 55 km downstream. Determine the speed of stream and that of the boat in still water.

Question 33)

If the sum of first four terms of an AP is 40 and that of first 14 terms is 280. Find the sum of it's first n terms.

Question 34)

Prove that

Question 35)

A man in a boat rowing away from a light house 100m high takes 2 minutes to change the angle of elevation of the top of the light house from . Find the speed of the boat in metres per minute. [Use ].

Question 36)

Two poles of equal heights are standing opposite each other on either side of the road, which is 80m wide. From a point between them on the road, the angles of elevation of the top of the poles are respectively. Find the height of the poles and the distances of the point from the poles.

Question 37)

Construct a in which CA=6cm and AB=5cm and Then construct a triangle whose sides are of the corresponding sides of .

Question 38)

A bucket open at the top is in the form of a frustum of a cone with a capacity of . The radii of the top and bottom of a circular ends of the bucket are 20cm and 12cm respectively. Find the height of the bucket and also the area of the metal sheet used in making it. (Use ).

Question 39)

Prove that in a right angle triangle, the square of the hypotenuse is equal the sum of squares of the other two sides.

Question 40)

The marks obtained by 100 students of a class in an examination are given below.

Draw 'a less than' type cumulative frequency curves (ogive). Hence find the median.

Question 41)

If the median of the following frequency distribution is 32.5. Find the values of .

Class	0-10	10-20	20-30	30-40	40-50	50-60	60-70	Total
Frequency		5	9	12		3	2	40

Question 1)

Find the coordinates of a point A, where AB is a diameter of the circle with centre (-2,2) and B is the point with coordinates (3,4).

Question 2)

Find the value of k for the following pair of linear equations have infinitely many solutions.

Question 3)

The arithmetic mean of the following frequency distribution is 53. Find the value of k.

Question 4)

Find the area of the segment shown in Fig 2, if the radius of the circle is 21 cm and .

Question 5)

In Fig. 4, a circle is inscribed in a ABC having sides BC = 8 cm, AB = 10cm and AC = 12 cm. Find the lengths BL, CM and AN.

Question 6)

The first term of an AP is 3, the last term is 83 and the sum of all its terms in 903. Find the number of terms and the common difference of the AP.

Question 7)

Construct a triangle ABC with side BC = 6cm, . Then construct another triangle whose side are times the corresponding sides of ABC.

Question 8)

Prove that

Question 1)

Two positive integers a and b can be written as and . x,y, are prime numbers. Find LCM(a,b)s

Question 2)

Find, how many two-digit natural numbers are divisible by 7.

Question 3)

If the sum of first n terms of an AP is n², then find its 10th term.

Question 4)

Find all the zeros of the polynomial if one of is zero is 1.

Question 5)

Prove that is an irrational number, given that is an irrational number.

Question 6)

if find

Question 7)

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.

Question 8)

The following distribution gives the daily income of 50 workers of a factory.

Convert the distribution above to a 'less than type' cumulative frequency distribution and draw its ogive.

Question 9)

The table below shows the daily expenditure on the food of 25 households in a locality. Find the mean daily expenditure on food.

Question 1)

If HCF (336, 54) = 6, find LCM (336, 54).

Question 2)

Find the nature of roots of the quadratic equation .

Question 3)

Find the common difference of the Arithmetic Progression (A.P.)

Question 4)

Evaluate:

Question 5)

If , calculate

Question 6)

Write the coordinates of a point P on x axis which is equidistant from the points A(– 2, 0) and B(6, 0).

Question 7)

In Figure 1, ABC is an isosceles triangle right angled at C with AC = 4 cm. Find the length of AB

Question 8)

In Figure 2, DE BC. Find the length of side AD, given that AE = 1·8 cm, BD = 7·2 cm and CE = 5·4 cm.

Question 9)

Write the smallest number which is divisible by both 306 and 657.

Question 10)

Find the area of a triangle whose vertices are given as (1, – 1) (– 4, 6) and (– 3, – 5).

Question 11)

The probability of selecting a blue marble at random from a jar that contains only blue, black and green marbles is . The probability of selecting a black marble at random from the same jar is . If the jar contains 11 green marbles, find the total number of marbles in the jar.

Question 12)

Find the value(s) of k so that the pair of equations x + 2y = 5 and 3x + ky + 15 = 0 has a unique solution.

Question 13)

The larger of two supplementary angles exceeds the smaller by . Find the angles.

Question 14)

Sumit is 3 times as old as his son. Five years later, he shall be two and a half times as old as his son. How old is Sumit at present?

Question 15)

Find the mode of the following frequency distribution :

Question 16)

Prove that is an irrational number, given that is an irrational number.

Question 17)

Using Euclid’s Algorithm, find the HCF of 2048 and 960

Question 18)

Two right triangles ABC and DBC are drawn on the same hypotenuse BC and on the same side of BC. If AC and BD intersect at P, prove that

Question 19)

Diagonals of a trapezium PQRS intersect each other at the point O, PQ RS and PQ = 3RS. Find the ratio of the areas of triangles POQ and ROS.

Question 20)

In Figure 3, PQ and RS are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersecting PQ at A and RS at B. Prove that

Question 21)

Find the ratio in which the line x – 3y = 0 divides the line segment joining the points (– 2, – 5) and (6, 3). Find the coordinates of the point of intersection.

Question 22)

Evaluate:

Question 23)

In Figure 4, a square OABC is inscribed in a quadrant OPBQ. If OA = 15 cm, find the area of the shaded region. (Use = 3·14)

Question 24)

In Figure 5, ABCD is a square with side cm and inscribed in a circle. Find the area of the shaded region. (Use = 3·14)

Question 25)

A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 20 cm and the diameter of the cylinder is 7 cm. Find the total volume of the solid.

Question 26)

The marks obtained by 110 students in an examination are given below :

Find the mean marks of the students.

Question 27)

For what value of k, is the polynomial

completely divisible by ?

Question 28)

Find the zeros of the quadratic polynomial and verify the relationship between the zeroes and the coefficients.

Question 29)

Write all the values of p for which the quadratic equation has equal roots. Find the roots of the equation so obtained.

Question 30)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, then prove that the other two sides are divided in the same ratio.

Question 31)

Amit, standing on a horizontal plane, finds a bird flying at a distance of 200 m from him at an elevation of 30^o. Deepak standing on the roof of a 50 m high building, finds the angle of elevation of the same bird to be 45^o. Amit and Deepak are on opposite sides of the bird. Find the distance of the bird from Deepak.

Question 32)

A solid iron pole consists of a cylinder of height 220 cm and base diameter 24 cm, which is surmounted by another cylinder of height 60 cm and radius 8 cm. Find the mass of the pole, given that 1 cm 3 of iron has approximately 8 gm mass. (Use = 3.14)

Question 33)

Construct an equilateral ABC with each side 5 cm. Then construct another triangle whose sides are times the corresponding sides of .

Question 34)

Draw two concentric circles of radii 2 cm and 5 cm. Take a point P on the outer circle and construct a pair of tangents PA and PB to the smaller circle. Measure PA.

Question 35)

Change the following data into ‘less than type’ distribution and draw its ogive :

Question 36)

Prove that :

Question 37)

Prove that :

Question 38)

Which term of the Arithmetic Progression –7, –12, –17, –22, ... will be –82? Is –100 any term of the A.P. ? Give reason for your answer.

Question 39)

How many terms of the Arithmetic Progression 45, 39, 33, ... must be taken so that their sum is 180 ? Explain the double answer.

Question 40)

In a class test, the sum of Arun’s marks in Hindi and English is 30. Had he got 2 marks more in Hindi and 3 marks less in English, the product of the marks would have been 210. Find his marks in the two subjects.

Question 1)

Find the 21^st term of the A.P.

Question 2)

For what value of k, will the following pair of equations have infinitely many solutions :
2x + 3y = 7 and (k + 2) x – 3 (1 – k) y = 5k + 1

Question 3)

Point A lies on the line segment XY joining X(6, – 6) and Y(– 4, – 1) in such a way that . If point A also lies on the line 3x + k (y + 1) = 0, find the value of k.

Question 4)

Solve for x :

Question 5)

Find A and B if and , where A and B are acute angels.

Question 6)

Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares on their corresponding sides.

Question 7)

Two poles of equal heights are standing opposite to each other on either side of the road which is 80 m wide. From a point P between them on the road, the angle of elevation of the top of a pole is 60^o and the angle of depression from the top of the other pole of point P is 30^o. Find the heights of the poles and the distance of the point P from the poles.

Question 8)

The total cost of a certain length of a piece of cloth is Rs. 200. If the piece was 5 m longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the piece and what is its original rate per metre?

Question 1)

Find the nature of the roots of the quadratic equation .

Question 2)

A die is thrown twice. Find the probability that

(i) 5 will come up at least once.

(ii) 5 will not come up either time.

Question 3)

Find the ratio in which the y-axis divides the line segment joining the points (–1, – 4) and (5, – 6). Also, find the coordinates of the point of intersection

Question 4)

Find the value of :

Question 5)

Two spheres of same metal weigh 1 kg and 7 kg. The radius of the smaller sphere is 3 cm. The two spheres are melted to form a single big sphere. Find the diameter of the new sphere.

Question 6)

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite the first side is a right angle.

Question 7)

From a point P on the ground, the angle of elevation of the top of a tower is 30^o and that of the top of the flag-staff fixed on the top of the tower is 45^o. If the length of the flag-staff is 5 m, find the height of the tower. (Use =1.732)

Question 8)

A right cylindrical container of radius 6 cm and height 15 cm is full of ice-cream, which has to be distributed to 10 children in equal cones having hemispherical shape on the top. If the height of the conical portion is four times its base radius, find the radius of the ice-cream cone.

Question 1)

Write the discriminant of the quadratic equation .

Question 2)

Find after how many places of decimal the decimal form of the number will terminate.

Question 3)

Express 429 as a product of its prime factors.

Question 4)

Find the sum of first 10 multiples of 6.

Question 5)

Find the value(s) of x, if the distance between the points A(0, 0) and B(x, – 4) is 5 units.

Question 6)

Two concentric circles of radii a and b (a > b) are given. Find the length of the chord of the larger circle which touches the smaller circle.

Question 7)

In Figure 1, PS = 3 cm, QS = 4 cm, and . Evaluate .

Question 8)

If , find the value of .

Question 9)

Points A(3, 1), B(5, 1), C(a, b) and D(4, 3) are vertices of a parallelogram ABCD. Find the values of a and b.

Question 10)

Points P and Q trisect the line segment joining the points A(– 2, 0) and B(0, 8) such that P is near to A. Find the coordinates of points P and Q.

Question 11)

Solve the following pair of linear equations :

3x – 5y = 4

2y + 7 = 9x

Question 12)

If HCF of 65 and 117 is expressible in the form 65n – 117, then find the value of n.

Question 13)

On a morning walk, three persons step out together and their steps measure 30 cm, 36 cm, and 40 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?

Question 14)

A die is thrown once. Find the probability of getting (i) a composite number, (ii) a prime number.

Question 15)

Using completing the square method, show that the equation has no solution.

Question 16)

Cards numbered 7 to 40 were put in a box. Poonam selects a card at random. What is the probability that Poonam selects a card which is a multiple of 7?

Question 17)

The perpendicular from A on side BC of a ABC meets BC at D such that DB = 3CD. Prove that .

Question 18)

AD and PM are medians of triangles ABC and PQR respectively where . Prove that

Question 19)

Check whether g(x) is a factor of p(x) by dividing polynomial p(x) by polynomial g(x),

where

Question 20)

Find the area of the triangle formed by joining the mid-points of the sides of the triangle ABC, whose vertices are A(0, – 1), B(2, 1) and C(0, 3).

Question 21)

Draw the graph of the equations x – y + 1 = 0 and 3x + 2y – 12 = 0. Using this graph, find the values of x and y which satisfy both the equations.

Question 22)

Prove that is an irrational number.

Question 23)

Find the largest number which on dividing 1251, 9377 and 15628 leave remainders 1, 2 and 3 respectively.

Question 24)

A, B and C are interior angles of a triangle ABC. Show that

(i)

(ii) If , then find the value of .

Question 25)

If and then find the values of A and B.

Question 26)

In Figure 2, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T. Find the length TP.

Question 27)

Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.

Question 28)

Water in a canal, 6 m wide and 1·5 m deep, is flowing with a speed of 10 km/h. How much area will it irrigate in 30 minutes if 8 cm of standing water is needed?

Question 29)

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.

Question 30)

A car has two wipers that do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle . Find the total area cleaned at each sweep of the blades. .

Question 31)

A pole has to be erected at a point on the boundary of a circular park of diameter 13 m in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 m. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

Question 32)

If m times m^th term of an Arithmetic progression is equal to n times its n^th term and m n, show that the is zero.

Question 33)

The sum of the first three numbers in an Arithmetic Progression is 18. If the product of the first and the third term is 5 times the common difference, find the three numbers.

Question 34)

Construct a triangle ABC with side BC = 6 cm, AB = 5 cm and . Then construct another triangle whose sides are of the corresponding side of triangle ABC.

Question 35)

In Figure 3, a decorative block is shown which is made of two solids, a cube, and a hemisphere. The base of the block is a cube with an edge 6 cm and the hemisphere fixed on the top has a diameter of 4·2 cm. Find

1. the total surface area of the block.
2. the volume of the block formed.

Question 36)

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308·8 cm³. The radii of the top and bottom circular ends are 20 cm and 12 cm respectively. Find the height of the bucket and the area of metal sheet used in making the bucket. (Use = 3·14)

Question 37)

Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question 38)

If , then prove that or

Question 39)

Change the following distribution to a ‘more than type’ distribution. Hence draw the ‘more than type’ ogive for this distribution.

Question 40)

The shadow of a tower standing on level ground is found to be 40 m longer when the Sun’s altitude is 30^o than when it was 60^o. Find the height of the tower. (Given)

Question 41)

If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, prove that the other two sides are divided in the same ratio.

Question 1)

Find the sum of the first 10 multiples of 3.

Question 2)

Solve the following pair of linear equations :
3x + 4y = 10
2x – 2y = 2

Question 3)

A chord of a circle of radius 14 cm subtends an angle of 60^o at the center. Find the area of the corresponding minor segment of the circle.

Question 4)

Find the value of k so that the area of triangle ABC with A(k + 1, 1), B(4, – 3) and C(7, – k) is 6 square units.

Question 5)

If and -3 are the zeroes of the polynomial , then find the values of a and b.

Question 6)

Construct a triangle, the lengths of whose sides are 5 cm, 6 cm and 7 cm. Now construct another triangle whose sides are times the corresponding sides of the first triangle.

Question 7)

Prove that :

Question 8)

A motorboat whose speed in still water is 9 km/h, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream.

Question 1)

For what values of k does the quadratic equation have no real roots ?

Question 2)

Find the distance between the points (a, b) and (– a, – b).

Question 3)

Find a rational number between and .

Question 4)

Write the number of zeroes in the end of a number whose prime factorization is .

Question 5)

Let and their areas be respectively, 64 and 121 If EF = 15.4 cm, find BC.

Question 6)

Evaluate :

Question 7)

Express in terms of trigonometric ratios of the angle between and .

Question 8)

Find the number of terms in the A.P.

Question 9)

A bag contains 15 balls, out of which some are white and the others are black. If the probability of drawing a black ball at random from the bag is , then find how many white balls are there in the bag.

Question 10)

A card is drawn at random from a pack of 52 playing cards. Find the probability of drawing a card which is neither a spade nor a king.

Question 11)

Find the solution of the pair of equations :

Question 12)

Find the value(s) of k for which the pair of equations has a unique solution.

Question 13)

How many multiples of 4 lie between 10 and 205?

Question 14)

Determine the A.P. whose third term is 16 and 7^th term exceeds the 5^th term by 12.

Question 15)

Use Euclid’s division algorithm to find the HCF of 255 and 867.

Question 16)

The point R divides the line segment AB, where A(– 4, 0) and B(0, 6) such that Find the coordinates of R.

Question 17)

Prove that :

Question 18)

Prove that :

Question 19)

In what ratio does the point P(– 4, y) divides the line segment joining the points A(– 6, 10) and B(3, – 8)? Hence find the value of y.

Question 20)

Find the value of p for which the points (– 5, 1), (1, p) and (4, – 2) are collinear.

Question 21)

ABC is a right triangle in which . If AB = 8 cm and BC = 6 cm, find the diameter of the circle inscribed in the triangle.

Question 22)

In Figure 1, BL and CM are medians of a right-angled at A. Prove that

Question 23)

Prove that the sum of the squares of the sides of a rhombus is equal to the sum of the squares of its diagonals.

Question 24)

In Figure 2, two concentric circles with centre O, have radii 21 cm and 42 cm. If , find the area of the shaded region.

Question 25)

Calculate the mode of the following distribution :

Question 26)

A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere and hence find the surface area of this sphere.

Question 27)

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/hr, in how much time will the tank be filled?

Question 28)

Prove that is an irrational number when it is given that is an irrational number.

Question 29)

Sum of the areas of two squares is 157 m². If the sum of their perimeters is 68 m, find the sides of the two squares.

Question 30)

Find the quadratic polynomial, sum and product of whose zeroes are –1 and – 20 respectively. Also, find the zeroes of the polynomial so obtained.

Question 31)

A plane left 30 minutes later than the scheduled time and in order to reach its destination 1500 km away on time, it has to increase its speed by 250 km/hr from its usual speed. Find the usual speed of the plane.

Question 32)

Find the dimensions of a rectangular park whose perimeter is 60 m and area 200 m².

Question 33)

Find the value of x, when in the A.P. given below

Question 34)

if , show that .

Question 35)

In (Figure 3), , Prove that

Question 36)

A moving boat is observed from the top of a 150 m high cliff moving away from the cliff. The angle of depression of the boat changes from to in 2 minutes. Find the speed of the boat in m/min.

Question 37)

There are two poles, one each on either bank of a river just opposite to each other. One pole is 60 m high. From the top of this pole, the angle of depression of the top and foot of the other pole are and respectively. Find the width of the river and height of the other pole.

Question 38)

Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are of the corresponding sides of the first triangle.

Question 39)

Calculate the mean of the following frequency distribution :

Question 40)

The following table gives production yield in kg per hectare of wheat of 100 farms of a village :

Change the distribution to a ‘more than type’ distribution, and draw its ogive.

Question 41)

A container opened at the top and made up of a metal sheet, is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container, at the rate of Rs 50 per litre. Also find the cost of metal sheet used to make the container, if it costs Rs10 per100 cm². (Take = 3·14)

Question 1)

Which terms of the A.P. -4,-1,2,---- is 101?

Question 2)

Find the value of k for which the quadratic equation has two equal roots.

Question 3)

Three different coins are tossed simultaneously. Find the probability of getting exactly one head.

Question 4)

A die is thrown once. Find the probability of getting
(a) a prime number
(b) an odd number.

Question 5)

Show that is not a rational number, given that is an irrational number.

Question 6)

Obtain all the zeroes of the polynomial when 2 and – 2 are two zeroes of the above polynomial.

Question 7)

A motorboat whose speed is 18 km/hr in still water takes one hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.

Question 8)

In an A.P., the first term is – 4, the last term is 29 and the sum of all its terms is 150. Find its common difference.

Question 9)

Draw a circle of radius 4 cm. From a point 6 cm away from its centre, construct a pair of tangents to the circle and measure their lengths.

Question 10)

Prove that :

Question 11)

Solve for x:

Question 12)

The sum of the areas of two squares is 640 m². If the difference of their perimeters is 64 m, find the sides of the square.

Question 1)

The HCF of two numbers a and b is 5 and their LCM is 200. Find the product ab.

Question 2)

Find the value of k for which is a solution of the equation .

Question 3)

Find the value/s of for which the quadratic equation has real and equal roots.

Question 4)

If in an A.P., ,, and , then find the value of .

Question 5)

If ; and is an acute angle, find the value of .

Question 6)

Find the value of .

Question 7)

The area of two similar triangles are 25 sq. cm and 121 sq. cm. Find the ratio of their corresponding sides.

Question 8)

Find the value of ‘a’ so that the point lies on the line represented by .

Question 9)

If , the sum of the first n terms of an A.P. is given by , then find its term.

Question 10)

If the term of an A.P. exceeds its term by , find the common difference.

Question 11)

The mid-point of the line segment joining and is . Find the values of and .

Question 12)

A child has a die whose faces show the letters given below :

The die is thrown once. What is the probability of getting (i) A (ii) B ?

Question 13)

Find the of and using prime factorisation.

Question 14)

Show that any positive odd integer is of the form or or , where is some integer.

Question 15)

Cards marked with numbers to (one number on one card) are placed in a box and mixed thoroughly. One card is drawn at random from the box. Find the probability that the number on the card taken out is (i) a prime number less than , (ii) a number which is a perfect square.

Question 16)

For what value of , does the system of linear equations


have an infinite number of solutions?

Question 17)

Prove that is an irrational number.

Question 18)

Find all the zeroes of the polynomial, if two of its zeroes are and .

Question 19)

Point P divides the line segment joining the points and
such that If lies on the line , find the value of

Question 20)

For what value of , are the points and collinear?

Question 21)

Prove that :

Question 22)

If , show that

Question 23)

A part of monthly hostel charges in a college hostel are fixed and the remaining depends on the number of days one has taken food in the mess. When a student A takes food for 25 days, he has to pay , whereas a student B who takes food for 30 days, has to pay . Find the fixed charges per month and the cost of food per day.

Question 24)

In , and is the mid-point of . Prove that

Question 25)

In Figure 1, is a point on produced of an isosceles , with side. If and prove that .

Question 26)

Prove that the parallelogram circumscribing a circle is a rhombus.

Question 27)

In Figure 2, three sectors of a circle of radius , making angles of and at the centre are shaded. Find the area of the shaded region.

Question 28)

The following table gives the number of participants in a yoga camp :

Find the modal age of the participants.

Question 29)

A juice seller was serving his customers using glasses as shown in Figure 3. The inner diameter of the cylindrical glass was but bottom of the glass had a hemispherical raised portion which reduced the capacity of the glass. If the height of a glass was , find the apparent and actual capacity of the glass.

Question 30)

A girl empties a cylindrical bucket full of sand, of base radius 18 cm and
height 32 cm on the floor to form a conical heap of sand. If the height of
this conical heap is 24 cm, then find its slant height correct to one place
of decimal.

Question 31)

A train travels at a uniform speed. If the speed had been more, it would have taken 1 hr less for the same journey. Find the speed of the train.

Question 32)

Solve for :

Question 33)

If the sum of the first p terms of an A.P. is v and the sum of the first v terms is ; then show that the sum of the first terms is .

Question 34)

In a triangle, if the square of one side is equal to the sum of the squares of the other two sides, then prove that the angle opposite to the first side is a right angle.

Question 35)

Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Question 36)

Construct an isosceles triangle whose base is and altitude and then another triangle whose sides are times the corresponding sides of the isosceles triangle

Question 37)

A boy standing on a horizontal plane finds a bird flying at a distance of from him at an elevation of A girl standing on the roof of a high building, finds the elevation of the same bird to be . The boy and the girl are on the opposite sides of the bird. Find the distance of the bird from the girl. (Given )

Question 38)

The angle of elevation of an aeroplane from a point A on the ground is . After a flight of seconds, the angle of elevation changes to . If the plane is flying at a constant height of metres, find the speed of the aeroplane.

Question 39)

Find the values of frequencies and in the following frequency distribution table, if and median is .

Question 40)

For the following frequency distribution, draw a cumulative frequency curve (ogive) of ‘more than type’ and hence obtain the median value.

Question 41)

Prove that :

Question 42)

An open metallic bucket is in the shape of a frustum of a cone. If the diameters of the two circular ends of the bucket are and and the vertical height of the bucket is , find the area of the metallic sheet used to make the bucket. Also, find the volume of the water it can hold. (Use )

Question 1)

Write the common difference of the A.P.

Question 2)

Find the coordinates of a point A, where AB is a diameter of the circle with centre and the point B is .

Question 3)

Prove that tangents drawn at the ends of a diameter of a circle are parallel.

Question 4)

Apply division algorithm to check if is a factor of the polynomial .

Question 5)

Find the mean of the following frequency distribution :

Question 6)

Evaluate :

Question 7)

Construct a right triangle in which sides (other than the hypotenuse) are 8 cm and 6 cm. Then construct another triangle whose sides are times the corresponding sides of the right triangle.

Question 8)

Find the sum of all the two digit numbers which leave the remainder 2 when divided by 5.

Question 1)