Time : 90 Minutes
Maximum Marks : 40 MATHEMATICS (STANDARD)
CBSE
Sample Question Papers
Self Assessment Paper
General Instructions :
1. The question paper contains three parts A, B and C.
2. Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
3. Section B consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
4. Section C consists of 10 questions based on two Case Studies. Attempt any 8 questions.
5. There is no negative marking.
SECTION - A
Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
1. If two positive integers p and q can be expressed as p = ab2
and q = a3
b; a, b being prime numbers, then
LCM (p, q) is
(A) ab. (B) a2
b2
.
(C) a3
b2
. (D) a3
b3
.
2. The solution of a system of equations x + y = 6 and x – y = 2 is:
(A) x = 2, y = 4 (B) x = 4, y = 2
(C) x = y = 6 (D) x = 3, y = 1
3. If the system of equations are x + 2y = 5 and 2x + y = 4, then the value of y is:
(A) 1 (B) 2
(C) 3 (D) – 3
4. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is
(A) 10. (B) 100.
(C) 504. (D) 2,520.
5. ABC and BDE are two equilateral triangles such that D is the mid-point of BC. Ratio of the areas of
triangles ABC and BDE is:
(A) 2 : 1 (B) 1 : 2
(C) 4 : 1 (D) 1 : 4
6. The product of a non-zero rational and an irrational number is :
(A) always irrational. (B) always rational.
(C) rational or irrational. (D) one.
5
7. Sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio :
(A) 2 : 3 (B) 4 : 9
(C) 81 : 16 (D) 16 : 81
8. Graphically, the pair of equations
6x – 3y + 10 = 0
2x – y + 9 = 0
represents two lines which are
(A) intersecting at exactly one point (B) intersecting at exactly two points
(C) coincident (D) parallel
9. In the figure given below, ∠BAC = 90° and AD ⊥ BC. Then :
(A) BD × CD = BC2 (B) AB × AC = BC2
(C) BD × CD = AD2 (D) AB × AC = AD2
10. If 4 tan θ = 3, then
4
4
sin cos
sin cos
θ θ
θ θ
-
+
is equal to:
(A) 2
3 (B) 1
2
(C) 1
3 (D) 3
4
11. If ΔABC ~ ΔEDF and ΔABC is not similar to ΔDEF, then which of the following is not true?
(A) BC × EF = AC × FD (B) AB × EF = AC × DE
(C) BC × DE = AB × EF (D) BC × DE = AB × FD
12. If the circumference of a circle and the perimeter of a square are equal, then:
(A) Area of the circle = Area of the square
(B) Area of the circle > Area of the square
(C) Area of the circle < Area of the square
(D) Nothing definite can be said about the relation between the areas of the circle and square.
13. Given that sin α = 1
2
and cos β = 1
2 , then the value of (α + β) is:
(A) 0˚ (B) 30˚
(C) 60˚ (D) 90˚
Sample Question Papers 99
16. If an event that cannot occur, then its probability is:
(A) 1 (B) 3
4
(C) 1
2 (D) 0
17. Which of the following cannot be the probability of an event ?
(A) 1
3 (B) 0.1
(C) 3% (D) 17
16
18. If in two triangles ABC and PQR,
AB
QR
BC
PR
CA
PQ = = then:
(A) ΔPQR ~ ΔCAB (B) ΔPQR ~ ΔABC
(C) ΔCBA ~ ΔPQR (D) ΔBCA ~ ΔPQR
19. If ΔABC is right angled at C, then the value of cos (A+B) is:
(A) 0 (B) 1
(C) 1
2 (D) 3
2
20. An event is very unlikely to happen. Its probability is closest to:
(A) 0.0001 (B) 0.001
(C) 0.01 (D) 0.1
SECTION - B
Section A consists of 20 questions of 1 mark each. Any 16 questions are to be attempted
21. The values of x and y which satisfy the equation 2x – 5y = 9, will be:
(A) x = 5, y = 2 (B) x = – 5, y = – 2
(C) x = 2, y = – 1 (D) x = – 2, y = 1
22. LCM of two numbers is 1449 and their HCF is 23. If one of the numbers is 207, then other number is :
(A) 160 (B) 159
(C) 161 (D) 162
23. If the ratio of the corresponding altitudes of two similar triangles is 3
5
, then the ratio of their areas is :
(A) 9
25 (B) 9
24
(C) 4
9 (D) 25
9
24. If HCF of 108 and 396 is expressed in the form 17m + 2, then the value of m is :
(A) 1 (B) 3
(C) 2 (D) 4
25. The smallest number which is divisible by both 270 and 405, is :
(A) 800 (B) 820
(C) 840 (D) 810
26. The HCF and LCM of two numbers are 27 and 162. If one number is 81, then the other number is :
(A) 51 (B) 52
(C) 54 (D) 56
27. Prime factorisation of 4620 is :
(A) 23
× 3 × 5 × 7 × 11 (B) 23
× 3 × 5 × 7 × 11
(C) 22
× 32
× 5 × 7 × 11 (D) 22
× 33
× 5 × 7 × 11
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