Maths paper class X sa 2
MODEL QUESTION PAPER
MATHEMATICS
CLASS X
MAX. MARKS90
TIME:3 HOURS
GENERAL INSTRUCTIONS: 1) All questions are compulsory.
2) The questions paper consists of 30 questions divided into four sections A, B, C and D. Section A contains 8 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 10 questions of 4 marks each.
3) There is no overall choice. However an internal choice has been provided in 1 question of 2 marks, three questions of 3 marks, and 2 questions of 4 marks each.
4) In questions on construction, the drawing should be neat and exactly as per given measurements.
5) Use of calculators is not allowed.
_______________________________________________________________________ SECTION A
1. The angle of elevation of the sun when the shadow of a pole ‘h’ meters high is 3 h m. long is…
A) 30°
B) 45°
C) 60°
D) 90°
2. The perimeter of a triangle with vertices (0,4), (0,0) and (3,0) is … A) 5
B) 7
C) 11
D) 12
2
3. The roots of a quadratic equation 2 x kx+k=0 are equal. The value of ‘k’ is … A) 0 only
B) 4
C) 8 only
D) 0 and 8
4. Volumes of two spheres are in the ratio 64:27. The ratio of their surface areas is …
A) 3:4
B) 4:3
C) 9:16
D) 16:9
5. If the common difference of an A.P is 5 then the value of A) 5
B) 75
C) 15
D) 27
a
21

a
6
is …
6. Twelve solid spheres of the same size are made by melting a solid metallic Page 1
cylinder of base diameter 2cm. and height 16cm. The diameter of each sphere is …
A) 4cm.
B) 3cm.
C) 2cm.
D) 6cm.
7. If the points A (1,2) , O (0,0) and C (a ,b) are collinear, then A) 2a=b
B) a=b
C) a=2b
D) a= b
8. If two tangents drawn to a circle of radius 3cm. are inclined at an angle 60°, then the length of each tangent is equal to ..
3 3
A) 6cm.
B) 3 3 cm. C) 3cm.
D)
cm.
2
SECTION B
9. The sum of the first ‘n’ terms of an A.P is given by Sn =
2n
2
. Find its 7th term.
10. Are the points A (1,0 ) , B (3, 1 ) , C (2,2 ) and D (2,1 ), the vertices of a parellologram? Verify.
11. A charity trust decided to build an anti disaster hall having a carpet area of 210 sq.m. If the length is 1 more than twice its breadth, construct the quadratic Equation to solve for the length and breadth ?
What value do you imbibe from this act?
12. In the given figure PQ, is a chord of a circle and PT is a tangent at ‘p’, such that angle QPT = 60° . Find the measure of angle PRQ.
Q
O
R
P
T
13. A die is thrown once. The probability of getting a prime number is
2
. Is it
3
True? Justify your answer.
OR
Page 2
An integer is chosen between 0 and 100. What is the probability that it is, a) Divisible by 7
b) Not divisible by 7
14. A cone of radius 4 cm. is divided into 2 parts by drawing a plane through the mid point of its axis and parallel to its base. Compare the volumes of the two parts
4 cm
A
O
D
C
B
SECTION C
15. A bag contains 24 balls of which ‘x’ are red, 2x are white and 3x are blue. A ball is selected at random. What is the probability that it is
a) not red
b) white
16. Solve for ‘x’.
2
2
2
6a x  7abx 3b = 0 , (a≠0) using quadratic formula .
OR
The sum of the reciprocals of a child’s age (in years ), 3 years ago and 5 years from 1
now is . Find his present age.
3
17. Find the ratio in which the line x+3y14=0 divided the line segment joining the Points A (2, 4) and B (3, 7).
18. An urn contains white, black and red balls only. A ball is drawn at random from Page 3
the bag. The probability of getting a white ball is
3
and that of a black ball is
10
2
. Find the probability of getting a red ball.
5
If the bag contains 20 black balls, then find the total number of balls in the bag..
19. As New Year’s resolution Ritika planned to save from her pocket money everyday. Starting from 5th January, she decided...
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