CLASS TEST
CLASS TEST # 41 MATHEMATICS
TIME : 60 Min. M.M. : 54
SECTION–I(i)
Straight Objective Type ( 3 Marks each, –1 for wrong answer)
b c a2
1. In ABC if 1 , then angle A is-
c b bc
(A) 15º (B) 30º (C) 45º (D) 60º
C
2. If in ABC using standard notation, A , then tan is equal to
2 2
a c ab a c c
(A) (B) (C) (D)
2b 2c b ab
a 2 b 2 c2
3. If in ABC with usual notations A: B : C = 1 : 2 : 3, then the value of is -
ab bc ca
2 8 8 2
(A) (B) (C) (D)
3 1 3 32 3 3 1 3 1
4. Consider a ABC in which b = 4, A = 30º and a is given such that two triangle are possible, then
number of possible integral value(s) of a is/are -
(A) 0 (B) 1 (C) 2 (D) 3
5. In ABC, if a,b and c represent the length of sides opposite to the vertices A, B, C such that
2 2 2
a + b + c = ab + bc + ca, then the distance between circumcentre and orthocentre is -
abc 2 a b b c c a
(A) a 2 b2 c 2 (B) (C) (2a –(b + c)) (D)
4 5
1 3 5 7
6. The sum of infinite series .... is equal to
3 3.7 3.7.11 3.7.11.15
1 1 4 8
(A) (B) (C) (D)
2 6 3 3
7. Number of integral values of 'a' for which every solution of the inequality x 2 1 0 is also the solution
of the inequality a 1 x 2 a | a 1 | 2 x 1 0, is
(A) 0 (B) 1 (C) 2 (D) 3
8 . If A and B are any two non empty sets and A is proper subset of B. If n(A) = 4, then minimum possible
value of n(A B) is (where denotes symmetric difference of set A and set B) -
(A) 2 (B) 1 (C) 0 (D) 4
9 . If the roots of the equation x2 + 2ax + b = 0 are real and distinct and differ by at most '2', then b lies in the
interval (a, b R0) -
(A) (a2, a2 +1] (B) [a2 – 1, a2) (C) [a2 – 4, a2 –1] (D) [a2 – 2, a2 – 1]
10. The number of ordered pairs (x,y) satisfying 4(log2x)2 + 1 = 2log2y and log2x2 > log2y is equal to -
(A) 1 (B) 2 (C) 3 (D) infinite
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CLASS TEST
Linked Comprehension Type (Single Correct Answer Type) (3 Marks each, –1 for wrong answer)
Paragraph for Question 11 & 12
Consider system of equation in variables ,
[sin() + cos( + 2)sin]2 = 4cossinsin() and tan = 3tan
a
11. If sum of all possible values of sin2 is (where a and b are coprime numbers), then value of 2a + b is-
b
(A) 17 (B) 25 (C) 13 (D) 22
12. Number of possible value(s) of in [–, 4], is -
(A) 10 (B) 12 (C) 14 (D) 16
Paragraph for Question 13 & 14
(x + 1.5) (x + 0.5) x x
Let ƒ(x) = 4 +9 – 10 × 6 & g(x) = log10(2 + 1) – log106 – xlog105.
On the basis of above information, answer the following questions :
13. Sum of values of x satisfying the equation ƒ(x) = 0, is -
3 5
(A) log25 (B) log711 (C) log 2 / 3 (D) log3 / 4
8
9
14. Value of x satisfying g(x) = –x is -
(A) 0 (B) 1 (C) 2 (D) 3
SECTION–III(i)
Numerical Grid Type (Single digit Ranging from 0 to 9) (4 Marks each, –1 for wrong answer)
1. If equation e2x + (k – 1)ex+1 + k = 0 has roots of opposite sign, then [k] is equal to
(where [.] denotes greatest integer function)
2. If the angles of a triangle are in A.P. with common difference equal to the least angle, so that the sides are
in ratio a : b : c , (where a, b, c are coprime pairwise), then the value of a + b + c is
b 2 sin 2C c 2 sin 2B
3. In a triangle ABC using standard notation, is always equal to -
4. In ABC, AC > AB, the internal angle bisector of angle A meets BC at D and E (E is inside the triangle)
is the foot of the perpendicular from B on AD. Suppose AB = 5 and BE = 4, the value of the expression
AC AB
(ED) is
AC AB
Q. 1 2 3 4 5 6 7 8 9 10
SECTION-I
A. A A A C B D B C A,D A,C,D
Q. 1 2 3 4 5 6 7 8
SECTION-II
A. 6.00 4.00 6.00 6.00 0.60 3.00 3.00 3.00
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