# CBSE Class 10 Maths Question Paper 2019 with Solutions

**CBSE Class 10 Maths Question Paper 2019 with Solutions** - Maths is one of the subjects which require a good amount of practice to score well in the exam. So practising CBSE previous year question papers Class 10 Maths 2019 is very important. Here solutions of CBSE 10 maths question paper 2019 is given in detail. Students can practice all the questions from CBSE Class 10 question papers here. If any doubts arise while solving there is an option to view CBSE class 10 maths question paper 2019 with solutions. Also, set wise and chapter wise analysis of CBSE previous year question papers Class 10 are given here. Read below to get CBSE class 10 maths question paper 2019 with solutions for each question.

Also, check CBSE previous year papers for other subjects.

**CBSE class 12 Mathematics 2019 q****uestion paper **Set Wise

**CBSE class 12 Mathematics 2019 q**Set Wise

**uestion paper**Go through the following CBSE Class 10 maths previous year paper with solutions:

**CBSE 10 Class 2019 Paper: 30-1-1 Maths**

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).

View SolutionsQuestion 3)

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

Question 10)

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

View SolutionsQuestion 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.

View SolutionsQuestion 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.

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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.

View SolutionsQuestion 18)

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

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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.

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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.

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Question 21)

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

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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.

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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.

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Question 27)

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

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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)

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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?

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Question 30)

Find the mode of the following frequency distribution.

Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

Frequency | 8 | 10 | 10 | 16 | 12 | 6 | 7 |

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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.

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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.

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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.

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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 ].

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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.

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Question 37)

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

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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 ).

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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.

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Question 40)

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

Marks | No. Of Students |

0-5 | 2 |

5-10 | 5 |

10-15 | 6 |

15-20 | 8 |

20-25 | 10 |

25-30 | 25 |

30-35 | 20 |

35-40 | 18 |

40-45 | 4 |

45-50 | 2 |

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

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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 |

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### CBSE 10 Class 2019 Paper: 30-1-2 Maths

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).

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Question 2)

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

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Question 3)

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

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
---|---|---|---|---|---|

Frequency | 12 | 15 | 32 | k | 13 |

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Question 4)

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

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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.

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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.

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Question 7)

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

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### CBSE 10 Class 2019 Paper: 30-1-3 Maths

Question 1)

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

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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.

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Question 8)

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

Daily Income (in Rs.) | 200-220 | 220-240 | 240-260 | 260-280 | 280-300 |
---|---|---|---|---|---|

Number of workers | 12 | 14 | 8 | 6 | 10 |

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

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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.

Daily Expenditure (in Rs.) | 100-150 | 150-200 | 200-250 | 250-300 | 300-350 |
---|---|---|---|---|---|

Number of Households | 4 | 5 | 12 | 2 | 2 |

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### CBSE 10 Class 2019 Paper: 30-2-1 Maths

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).

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Question 7)

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

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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.

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Question 10)

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

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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.

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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.

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Question 13)

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

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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?

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Question 15)

Find the mode of the following frequency distribution :

Class Interval | 25-30 | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 |
---|---|---|---|---|---|---|

Frequency: | 25 | 34 | 50 | 42 | 38 | 14 |

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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

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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.

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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

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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.

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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)

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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)

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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.

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Question 26)

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

Marks: | 30-35 | 35-40 | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 |
---|---|---|---|---|---|---|---|

Number of Students: | 14 | 16 | 28 | 23 | 18 | 8 | 3 |

Find the mean marks of the students.

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Question 28)

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

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Question 29)

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

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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.

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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.

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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)

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Question 33)

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

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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.

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Question 35)

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

Class Interval: | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
---|---|---|---|---|---|---|---|

Frequency: | 7 | 5 | 8 | 10 | 6 | 6 | 8 |

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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.

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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.

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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.

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### CBSE 10 Class 2019 Paper: 30-2-2 Maths

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

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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.

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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.

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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.

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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?

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### CBSE 10 Class 2019 Paper: 30-2-3 Maths

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.

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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

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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.

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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.

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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)

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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.

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### CBSE 10 Class 2019 Paper: 30-3-1 Maths

Question 2)

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

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Question 5)

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

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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.

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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.

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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.

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Question 12)

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

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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?

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Question 14)

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

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Question 15)

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

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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?

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Question 17)

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

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Question 18)

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

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Question 19)

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

where

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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).

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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.

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Question 23)

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

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Question 24)

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

(i)

(ii) If , then find the value of .

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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.

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Question 27)

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

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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?

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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.

Number of days: | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 | 30-36 | 36-40 |
---|---|---|---|---|---|---|---|

Number of students: | 10 | 11 | 7 | 4 | 4 | 3 | 1 |

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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. .

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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?

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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.

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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.

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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.

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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

- the total surface area of the block.
- the volume of the block formed.

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Question 36)

A bucket open at the top is in the form of a frustum of a cone with a capacity of 12308·8 cm^{3}. 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)

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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.

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Question 39)

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

Class Interval: | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
---|---|---|---|---|---|---|---|

Frequency: | 10 | 8 | 12 | 24 | 6 | 25 | 15 |

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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)

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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.

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### CBSE 10 Class 2019 Paper: 30-3-3 Maths

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.

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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.

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Question 5)

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

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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.

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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.

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### CBSE 10 Class 2019 Paper: 30-4-2 Maths

Question 4)

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

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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.

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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.

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Question 12)

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

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Question 14)

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

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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.

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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.

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Question 20)

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

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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.

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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.

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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.

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Question 25)

Calculate the mode of the following distribution :

Class : | 10-15 | 15-20 | 20-25 | 25-30 | 30-35 |

Frequency | 4 | 7 | 20 | 8 | 1 |

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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.

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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?

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Question 28)

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

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Question 29)

Sum of the areas of two squares is 157 m^{2}. If the sum of their perimeters is 68 m, find the sides of the two squares.

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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.

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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.

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Question 32)

Find the dimensions of a rectangular park whose perimeter is 60 m and area 200 m^{2}.

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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.

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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.

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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.

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Question 39)

Calculate the mean of the following frequency distribution :

Class : | 10-30 | 30-50 | 50-70 | 70-90 | 90-110 | 110-130 |

Frequency : | 5 | 8 | 12 | 20 | 3 | 2 |

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Question 40)

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

Production yield(kg/hectare): | 40-45 | 45-50 | 50-55 | 55-60 | 60-65 | 65-70 |

Number of farms: | 4 | 6 | 16 | 20 | 30 | 24 |

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

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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 cm^{2}. (Take = 3·14)

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### CBSE 10 Class 2019 Paper: 30-4-3 Maths

Question 3)

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

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Question 4)

A die is thrown once. Find the probability of getting

(a) a prime number

(b) an odd number.

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Question 6)

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

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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.

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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.

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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.

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Question 12)

The sum of the areas of two squares is 640 m^{2}. If the difference of their perimeters is 64 m, find the sides of the square.

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### CBSE 10 Class 2019 Paper: 30-5-1 Maths

Question 1)

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

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Question 3)

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

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Question 7)

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

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Question 9)

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

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Question 11)

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

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Question 12)

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

A |

B |

C |

A |

A |

B |

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

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Question 14)

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

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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.

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Question 16)

For what value of , does the system of linear equations

have an infinite number of solutions?

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Question 19)

Point P divides the line segment joining the points and

such that If lies on the line , find the value of

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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.

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Question 25)

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

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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.

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Question 28)

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

Age(in years): | 20- 30 | 30-40 | 40-50 | 50-60 | 60-70 |

No. of Participants: | 8 | 40 | 58 | 90 | 83 |

Find the modal age of the participants.

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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.

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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.

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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.

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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 .

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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.

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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.

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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

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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 )

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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.

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Question 39)

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

Marks: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | Total |

No. of Students: | 10 | x | 25 | 30 | y | 10 | 100 |

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Question 40)

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

Class: | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 |

Frequency: | 5 | 15 | 20 | 23 | 17 | 11 | 9 |

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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 )

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### CBSE 10 Class 2019 Paper: 30-5-2 Maths

Question 2)

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

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Question 3)

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

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Question 5)

Find the mean of the following frequency distribution :

Class: | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |

Frequency: | 17 | 28 | 32 | 24 | 19 |

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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.

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Question 8)

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

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### CBSE 10 Class 2019 Paper: 30-5-3 Maths

Question 1)

Find the values of x for which the distance between the points and is units.

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Question 2)

Find the probability that a number selected at random from the numbers will be their mean.

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Question 3)

Find the mode of the following frequency distribution :

Class : | 10-14 | 14-18 | 18-22 | 22-26 | 26-30 | 30-34 | 34-38 |

Frequency : | 8 | 6 | 11 | 20 | 25 | 22 | 10 |

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Question 4)

In two concentric circles, prove that all chords of the outer circle which touch the inner circle, are of equal length.

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Question 6)

In an A.P., the n^{th} term is and the m^{th} term is Find (i) term, (ii) sum of first terms.

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Question 7)

Construct a pair of tangents to a circle of radius 4 cm which are inclined to each other at an angle of .

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### CBSE 10 Class Compartment 2019 Paper: 30-1-1 Maths

Question 1)

The radii of the circular ends of the frustum of a cone of height 45 cm, are 28 cm and 7 cm. Find its volume and curved surface area.

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Question 2)

If the mean of the following frequency distribution is 62·8, then find the missing frequency x :

Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 100-120 |

Frequency | 5 | 8 | x | 12 | 7 | 8 |

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Question 5)

Draw a circle of radius 3 cm. Take a point A on its extended diameter at a distance of 7 cm from its centre. Draw two tangents to the circle from A.

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Question 6)

As observed from the top of a lighthouse, 75 m high from the sea level, the angles of depression of two ships are and . If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships

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Question 7)

The angles of depression of the top and bottom of a 8 m tall building from the top of a tower are and respectively. Find the height of the tower and the distance between the tower and the building.

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Question 11)

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

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Question 12)

In figure 2, ABC is a right-angled triangle at A. Semi-circles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

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Question 13)

Two cones with same base diameter 16 cm and height 15 cm are joined together along their bases. Find the surface area of the shape so formed.

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Question 14)

A hemispherical tank full of water is emptied by a pipe at the rate of litres per second. How much time will it take to empty the tank, if it is 3 m in diameter ?

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Question 15)

The weights of tea in 70 packets is given in the following table :

Weight (in g.) | No. of packets |

200-201 | 12 |

201-202 | 26 |

202-203 | 20 |

203-204 | 9 |

204-205 | 2 |

205-206 | 1 |

Find the modal weight.

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Question 20)

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

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Question 23)

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

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Question 24)

The perpendicular from A on the side BC of a intersects BC at D, such that . Prove that .

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Question 25)

ABCD is a trapezium with . E and F are points on non-parallel sides AD and BC respectively, such that . Show that .

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Question 26)

A bag contains some balls of which x are white, 2x are black and 3x are red. A ball is selected at random. What is the probability that it is (i) not red (ii) white ?

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Question 27)

A pair of dice is thrown once. Find the probability of getting (i) even number on each dice (ii) a total of 9.

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Question 28)

Find the relation between p and q if and is the solution of the pair of equations and .

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Question 36)

In what ratio is the line segment joining the points P(3, - 6) and Q(5, 3) divided by x-axis ?

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Question 37)

The LCM of two numbers is 9 times their HCF. The sum of LCM and HCF is 500. Find the HCF of the two numbers.

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Question 39)

Find the relation between x and y such that the points (x, y), (1, 2) and (7, 0) are collinear.

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Question 41)

If the term of an A.P. is zero, then show that its term is double of its term.

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### CBSE 10 Class Compartment 2019 Paper: 30-1-2 Maths

Question 2)

A pair of dice is thrown once. Find the probability of getting (i) even number on each dice (ii) a total of 9.

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Question 3)

If A(– 2, 2), B(5, 2) and C(k, 8) are the vertices of a right-angled triangle ABC with , then find the value of k.

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Question 4)

PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at an external point T. Find the length of PT.

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Question 6)

In figure 2, find the area of the shaded region, where ABCD is a square of side 14 cm in which four semi-circles of same radii are drawn as shown. (Take )

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Question 7)

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

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Question 8)

A container, open at the top, made up of metal sheet is in the form of the frustum of a cone of height 16 cm with radii of lower and upper circular ends as 8 cm and 20 cm respectively. Find the cost of milk which can completely fill the container at the rate of Rs 40 per litre and also find the cost of metal sheet used if it costs Rs 10 per . (Use )

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Question 9)

Construct tangents to a circle of radius 4 cm from a point on the concentric circle of radius 7 cm.

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### CBSE 10 Class Compartment 2019 Paper: 30-1-3 Maths

Question 2)

Find the relation between x and y such that the point P(x, y) is equidistant for points A(7, 1) and B(3, 5) .

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Question 3)

Find all the zeroes of the polynomial , given that two of its zeroes are 3 and - 5.

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Question 5)

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

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Question 6)

A motorboat whose speed is 18 km/h in still water takes 1 hr 30 minutes more to go 36 km upstream than to return downstream to the same spot. Find the speed of the stream.

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Question 7)

A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

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**Also read - **

- CBSE Class 10 Maths Question Paper 2016 with Solutions
- CBSE Class 10 Maths Question Paper 2017 with Solutions
- CBSE Class 10 Maths Question Paper 2018 with Solutions
- CBSE Class 10 Maths Preparation Tips

## CBSE Class 10 Maths Question Paper 2019 with Solutions - All Sets

There are a total of 13 sets of 2019 class 10 board exam paper. From these sets, an analysis of 5 sets is given here. Rest of the sets are similar to one among the 5 sets and only around 30% questions are different. For example, if the sets 30/1/1, 30/1/2, 30/1/3 are considered 70% of questions from each set are similar and the mark distributions of all these 3 sets are exactly similar. So only one set is considered for the analysis. The total analysis of papers gives an idea about which chapters are given high weightage and what is the pattern of the CBSE class 10 maths previous year question papers.

## CBSE 10 Maths Question Paper 2019** **Pattern

Total number of questions in 2019 class 10 maths CBSE board paper: 30

The total duration of class 10 2019 maths paper: 3 hours

#### Section-wise Division of CBSE Class 10 Maths Question Paper 2019

Sl. No | Sections | Marks | Number of questions | Total marks |

1 | A | 1 | 6 | 6 |

2 | B | 2 | 6 | 12 |

3 | C | 3 | 10 | 30 |

4 | D | 4 | 8 | 32 |

There is no overall choice but an internal choice has been provided in two questions of 1 mark each, two questions of 2 marks each, four questions of 3 marks each and three questions of 4 marks each. Students have to attempt only one of the alternatives in all such questions.

**CBSE class 10 Mathematics 2019 q****uestion paper analysis**

**uestion paper analysis**

The overall analysis of the class 10 maths paper shows that all the chapters are important with a minimum of 3 mark weightage. Marks from some chapters can be easily secured. For example, 4 marks from the chapter construction are sure if all the constructions in the chapters are practised. Similarly, questions from the chapter statistics can be scored easily if all the questions of the books are practised with care in calculations.

Sl.No | Chapter Name | Set 30/1/1 | Set 30/2/1 | Set 30/3/1 | Set 30/4/2 | Set 30/5/1 |

1 | Real Numbers | 6 | 6 | 6 | 6 | 6 |

2 | Polynomials | 3 | 3 | 3 | 3 | 3 |

3 | Pair of Linear Equations in Two Variables | 5 | 4 | 5 | 6 | 5 |

4 | Quadratic Equations | 5 | 8 | 7 | 4 | 5 |

5 | Arithmetic Progressions | 7 | 5 | 5 | 7 | 7 |

6 | Triangles | 8 | 8 | 7 | 8 | 8 |

7 | Coordinate Geometry | 6 | 6 | 6 | 6 | 6 |

8 | Introduction to Trigonometry | 8 | 8 | 8 | 8 | 8 |

9 | Some Applications of Trigonometry | 4 | 4 | 4 | 4 | 4 |

10 | Circles | 3 | 3 | 4 | 3 | 3 |

11 | Constructions | 4 | 4 | 4 | 4 | 4 |

12 | Areas Related to Circles | 3 | 3 | 3 | 3 | 3 |

13 | Surface Areas and Volumes | 7 | 7 | 7 | 7 | 7 |

14 | Statistics | 7 | 9 | 7 | 7 | 7 |

15 | Probability | 4 | 2 | 4 | 4 | 4 |

CBSE Class 10 Maths chapter wise average marks distribution 2019

Sl.No | Chapter Name | Set 30/1/1 |

1 | Real Numbers | 6 |

2 | Polynomials | 3 |

3 | Pair of Linear Equations in Two Variables | 5 |

4 | Quadratic Equations | 5.8 |

5 | Arithmetic Progressions | 6.2 |

6 | Triangles | 7.8 |

7 | Coordinate Geometry | 6 |

8 | Introduction to Trigonometry | 8 |

9 | Some Applications of Trigonometry | 4 |

10 | Circles | 3 |

11 | Constructions | 4 |

12 | Areas Related to Circles | 3.2 |

13 | Surface Areas and Volumes | 7 |

14 | Statistics | 7.4 |

15 | Probability | 3.6 |

The chapter-wise average mark distribution of CBSE Maths class 10 board papers shows that the chapters introductions to trigonometry, triangles, statistics and surface area and volumes are important. Mathematics papers are always a concern for students. For getting good marks in maths paper students go for extra classes. The main thing to score well in mathematics paper is self-practice. While practising there will be mistakes and through these mistakes, students can rectify their area of weakness. Solving previous year question papers of class 10 mathematics helps in completing the exam on time.

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## Questions related to CBSE Class 10th

### Age criteria to appear in class 10 CBSE exam

Hello Bishal

According to guidelines of CBSE, minimum age to appear for class x must be 14 years. There is no upper limit to appear for class x cbse board.

A candidate can appear for maximum three attempts.

Some candidates give private exams or sometimes students fail in standard ix then they privately appear for class x then their age must be more than 14 years. Sometimes students appear for x class after one year gap of passing class ix then also their age would be 15 or 16 as there is no upper limit age.

### My child is supposed to make another attempt at compartment exam of 10th cbse Missed last date for applying. since the boards are postponed to May 4th can I pay her fees and apply now.

Hello sir I'm sorry to inform you but now you're not eligible to fill the registration form as last date to fill the registration Form was 9th December 2020. Yes examination gets postponed to May but portal to fill the registration form is not open , in case if the registration form portal will open again you can fill the registration form and make the payment.

Feel free to comment if you've any doubt

Good luck

### i want to know the sample paper and marking scheme of 10 th science

Hello there,

To get the sample papers for
**
CBSE Class
**
10th, you should visit the official CBSE website. There you can get all the papers. Solving the previous year papers, will be very beneficial for you. So, solve as much papers as you can.

As per the latest CBSE Class 10 exam pattern 2020-21, the theory paper will be of 80 marks, while 20 marks will be for internal assessment. To know more about exam pattern, please visit the link given below.

https://www.google.com/amp/s/school.careers360.com/articles/cbse-10th-exam-pattern/amp

Check out the papers here:

https://www.google.com/amp/s/school.careers360.com/articles/cbse-class-10-sample-papers/amp

### will the 2021 board exams for grade 10 conducted online or offline

Hello,

The 10th CBSE board exam will be conducted in offline mode only, These board exams will not be conducted in online mode. Central Board of Secondary Education conducts class 10th board examination for regular and private students. The exams of CBSE 10th 2021 will be conducted in February and March 2021. Candidates can fill CBSE 10th application form 2021 online on cbse.nic.in from October 24 to November 11, 2020.

### is unit exam marks taken into consideration for cbse internal marks grade 10.

Hey,

Your concern completely depends upon school. School management plans the division of marks. For few schools they must consider even class test on the other hand some just focus on mid and end . So the division of marks vary from school to school. What the school do is continuous access the student and then give marks accorrdingly. In my opinion focus on each and every test. Apart from internals it work for you in finals as well.

All the best