CBSE Previous Year Question Papers Class 10 Maths

CBSE Previous Year Question Papers Class 10 Maths

 

CBSE Previous Year Question Papers
Class 10 Maths

2019

ime Allowed: 3 hours Maximum

Marks: 80

General Instructions:

● All questions are compulsory.
● This question paper consists of 30 questions divided into four sections- A, B, C and D.
● Section A contains 6 questions of 1 mark each, Section B contains 6 questions of 2 marks each,
Section C contains 10 questions of 3 marks each and Section D contains 8 questions of 4 marks
each.
● There is no overall choice. However, 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. You have to attempt only one of the alternative in all such questions.
● Use of calculators is not permitted.

Section – A

Question 1.

Find the coordinates of a point A, where AB is diameter of a circle whose centre is (2, -3) and B is the point (1,
4). [1]
Question 2.
For what values of k, the roots of the equation x2 + 4x + k = 0 are real? [1]
OR

2

Find the value of k for which the roots of the equation 3×2 – 10x + k = 0 are reciprocal of each other.
Question 3.
Find A if tan 2A = cot (A – 24°) [1]

OR

Find the value of (sin2 33° + sin 2 57°)

Question 4.
Flow many two digits numbers are divisible by 3? [1]
Question 5.
In Fig., DE || BC, AD = 1 cm and BD = 2 cm. what is the ratio of the ar (ΔABC) to the ar (ΔADE) ? [1]

Question 6.

Find a rational number between √2 and √3. [1]
Section – B

Question 7.

Find the HCF of 1260 and 7344 using Euclid’s algorithm. [2]

3

 

OR

Show that every positive odd integer is of the form (4q + 1) or (4q + 3), where q is some integer.
Question 8.
Which term of the A.P. 3, 15, 27, 39, …… will be 120 more than its 21st term? [2]

OR

If Sn, the sum of first tt terms of an A.P. is given by Sn = 3n2 – 4n, find the nth term.
Question 9.

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 the x-axis. [2]
Question 10.
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. [2]
Question 11.
A die is thrown once. Find the probability of getting a number which
(i) is a prime number
(ii) lies between 2 and 6. [2]
Question 12.
Find c if the system of equations cx + 3y + (3 – c) = 0, 12x + cy – c = 0 has infinitely many solutions?
[2]

4

 

Section – C

Question 13.
Prove that √2 is an irrational number. [3]

Question 14.
Find the value of k such that the polynomial x2 – (k + 6)x + 2(2k – 1) has sum of its zeros equal to half to
their product. [3]
Question 15.

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. [3]
OR

1
A fraction becomes 3

1
when 2 is subtracted from the numerator and it becomes 2

when 1 is subtracted from the denominator. Find the fraction.

Question 16.
Find the point on y-axis which is equidistant from the points (5, -2) and (-3, 2). [3] OR
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 2x – y + k = 0, find the value of k.
Question 17.

Prove that (sin θ + cosec θ )2 + (cos θ + sec θ) 2 = 7 + tan 2 θ + cot 2 θ. [3]

5

 

OR

Prove that (1 + cot A – cosec A) (1 + tan A + sec A) = 2.

Question 18.
In Fig. PQ is a chord of length 8 cm of a circle of radius 5 cm and centre O. The tangents at P and Q intersect
at point T. Find the length of TP. [3]

Question 19.

In Fig. ∠ACB = 90° and CD ⊥ AB, prove that CD2 = BD × AD. [3]

OR

If P and Q are the points on side CA and CB respectively of ΔABC, right-angled at C, prove that (AQ2
+ BP2) = (AB2 + PQ 2).
Question 20.
Find the area of the shaded region in Fig. if ABCD is a rectangle with sides 8 cm and 6 cm and D is the centre
of the circle. [3]

6

 

[Take π = 3.14]

Question 21.

Water in a canal, 6 m wide and 1.5 m deep, is flowing with a speed of 10 km/hour. How much area will it
irrigate in 30 minutes, if 8 cm standing water is needed? [3]
Question 22.
Find the mode of the following frequency distribution. [3]

Section – D

Question 23.

Two water taps together can fill a tank in 1 hours. The tap with longer diameter takes 2 hours less than the
tap with a smaller one to fill the tank separately. Find the time in which each tap can fill the tank separately.
[4]

7

 

OR

A boat goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours, it can go 40 km upstream and
55 km downstream. Determine the speed of the stream and that of the boat in still water.
Question 24.

If the sum of first four terms of an A.P. is 40 and that of first 14 terms is 280. Find the sum of its first n terms.
[4]

Question 25.

Question 26.

A man in a boat rowing away from a lighthouse 100 m high takes 2 minutes to change the angle of elevation
of the top of the lighthouse from 60° to 30°. Find the speed of the boat in metres per minute. [Use √3 =
1.732] [4]
Question 27.

Construct a ΔABC in which CA = 6 cm, AB = 5 cm and ∠BAC = 45°. Then construct a triangle whose sides are
of the corresponding sides of ΔABC. [4]
Question 28.

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 of circular ends of the bucket are 20 cm and 12 cm respectively. Find the height of the
bucket and also the area of the metal sheet used in making it. (Use π = 3.14) [4]
Question 29.

8

Prove that in a right-angle triangle, the square of the hypotenuse is equal the sum of squares of the other
two sides. [4]
Question 30.

If the median of the following frequency distribution is 32.5. Find the values of f1 and f 2. [4]

OR

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.

9

CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi
Set II
Note: Except for the following questions, all the remaining questions have been asked in previous sets.
Section – A

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). [1]
Section – B

Question 7.

Find the value of k for which the following pair of linear equations have infinitely many solutions. [2]
2x + 3y = 7, (k + 1)x + (2k – 1)y = 4k + 1
Section – C

Question 13.

The arithmetic mean of the following frequency distribution is 53. Find the value of k. [3]

Question 14.

Find the area of the segment shown in Fig. if radius of the circle is 21 cm and ∠AOB = 120° (π =

10

 

22

7
) [3]
Question 16.
In Fig. a circle is inscribed in a ΔABC having sides BC = 8 cm, AB = 10 cm and AC = 12 cm. Find the lengths BL,
CM and AN. [3]
Section – D

Question 23.

Question 24.

The first term of an A.P. is 3, the last term is 83 and the sum of all its terms is 903. Find the number of terms
and the common difference of the A.P. [4]

.

Question 25.

Construct a triangle ABC with side BC = 6 cm, ∠B = 45°, ∠A = 105°. Then construct another triangle whose
sides are 3/4 times the corresponding sides of the ΔABC. [4]
CBSE Previous Year Question Papers Class 10 Maths 2019 Delhi
Set III
Note: Except for the following questions, all the remaining questions have been asked in previous sets.

11

 

Section – A

Question 1.
Two positive integers a and b can be written as a = x3y 2 and b = xy 3. x, y are prime numbers. Find
LCM (a, b). [1]
Section – B

Question 7.

Find, how many two-digit natural numbers are divisible by 7. [2]
OR

If the sum of first n terms of an A.P. is n2, then find its 10th term.
Section – C

Question 13.

Find all zeroes of the polynomial 3×3 + 10x 2 – 9x – 4 if one of its zero is 1. [3]

Question 15. Prove that

Section – D

Question 23.

If sec θ = x +
Question 24.

Prove that the ratio of the areas of two similar triangles is equal to the square of the ratio of their
corresponding sides. [4]
Question 25.

12

 

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. [4]
OR

The table below shows the daily expenditure on the food

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