This document contains a 30 question objective test on various mathematics topics. The questions cover topics like trigonometry, algebra, relations, functions, polynomials, and integers. Test takers have 60 minutes to complete the 30 questions online. The questions require calculating values, identifying true statements, finding remainders, and factoring polynomials.

1. OBJECTIVE TEST ‐01 (ON LINE)
Total questions:30 Time:60 minutes
1.In a triangle ABC , If 90B∠ = and
a
SinA
b
= ,then the value of 2S in A
equals
(a)
2
1
a a
b b
⎛ ⎞
− ⎜ ⎟
⎝ ⎠
(b) 2
2
1
a a
b b
⎛ ⎞
− ⎜ ⎟
⎝ ⎠
(c)
2
1
a
b
⎛ ⎞
− ⎜ ⎟
⎝ ⎠
(d) 2
2
1
a a
b b
⎛ ⎞
+ ⎜ ⎟
⎝ ⎠
2.The value of sin15
(1)
3 1
2 2
+
(2)
3 1
2
+
(3)
3 1
2 2
−
(4)
3 1
2 2
− +
3. os2C A equals
(a) 2
2 os 1C A − (b) 2
1 2Sin A− (c) 2 2
Cos A Sin A− (d) all the above
4.If
2 5
2 3
A
⎛ ⎞
= ⎜ ⎟
⎝ ⎠
and
1 0
0 1
I
⎛ ⎞
= ⎜ ⎟
⎝ ⎠
,then AI equals
(a)
3 5
2 1
⎛ ⎞
⎜ ⎟
⎝ ⎠
(b)
3 5
1 1
⎛ ⎞
⎜ ⎟
⎝ ⎠
(c)
2 5
2 3
⎛ ⎞
⎜ ⎟
⎝ ⎠
(d)
2 0
0 3
⎛ ⎞
⎜ ⎟
⎝ ⎠
5, If { } { } { }1,3,5,6 , 2,4,5,6 1,2,3,4.....6A B and= = =∪ Which Of the following is
true
(a) ( ) ( ) ( )n A B n A n B∪ = + (b) ( ) ( ) ( )n A B n A n B∪ = −
(c) ( ) ( ) ( ) ( )n A B n A n B n A B∪ = + + ∩
(d) ( ) ( ) ( ) ( )n A B n A n B n A B∪ = + − ∩
6.Which of the following is the dmagan;s law

2. (a) φ ∪ =∪ ∪ (b) ( )
cc
A A=
(c) ( )
c c c
A B A B∩ = ∩ (d) ( )
c c c
A B A B∩ = ∪
7. How many minimum number of ordered pair should be included to the
given relation as an equivalence relation
( ) ( ) ( ) ( ){ }1,1 , 2,2 , 3,3 , 1,3R =
Where { }if 1,2,3R A A A⊆ × = and hence find domain and range of inverse
relation of the equivalence relation.
(a)1 (b) 2 (c)3 (d) none of these
8. The domain of the real function
2
1
( )
25
f x
x
=
−
is
(a) [ )25,∞ (b) [ ]5,5− (c) ( )5,5− (d) ( )25,25−
9.The range of the real function ( ) 3f x x= − is
(a) R (b) R+
(c) R−
(d) [ )0,∞
10.Which of the following graph will be a function
(a) (b) (c) (d)
11.If 2
4b ac− is a square number ,then the roots of the equation 2
0ax bx c+ + =
are
(a) equal real numbers (b) different real numbers
(c) different rational numbers (d) roots are not real

3. 12.If ,α β are the roots of the equation 2
3 4 7 0x x− + = ,then the value of
1 1
α β
+
(a)
4
7
(b)
7
3
(c)
3
4
(d)
4
3
13.If one root of a quadratic equation 2 3− ,then the equation will be
(a) 2
4 7 0x x− + = (b) 2
4 7 0x x+ + = (c) 2
4 7 0x x+ − = (d) none of these
14.If ( )( )3 6 0x x− − ≤ , then x∈
(a) ( ],3−∞ (b) [ )6,∞ (c) ( )3,6 (d) [ ]3,6
15.If 2 2 2
x a b c ab bc ac= + + − − − ,then
(a) 0x ≥ (b) 0x > (c) 0x < (4) 0x ≤
16. The number 90 90
107 76− is divisible by
(a) 61 (b) 62 (c) 64 (d) none of these
17.Number of three digit number from the digits 3,5,6 ,7(without
repetition)
(a) 6 (b) 12 (c) 24 (d) none of these
18.Number of words can be formed from the letters of the word
TERMINAL
(a) 64 (b) 120 (c) 8! (d) none of these
19.The value of 10
2P is
(a) 20 (b) 100 (c) 90 (d) 50
20. Given 2 2
2 3 35,x y+ = then the number of ordered pairs (x,y) where (x,y)
are integers satisfying the above equation is

4. (a) 2 (b) 4 (c) 8 (d) 16
21. For how many integers n is ( )
2
9 2n− + a real number?
(a) 3 (b) 5 (c) 7 (d) infinitely many
Linked comprehensive type
Paragraph for Question Nos.22 to 24
If a and b are two integers and n is a positive integer, then a is said to be
congruent to b modulo m if m / a – b in notation form we express it as a b≡
(mod m) or 0a b− ≡ (mod m)
22.The remainder in the division of
20
2
by 7
(a) 4 (b) 2 (c) 0 (d) 3
23. The remainder in the division of
40
3
by 23
(a) 4 (b) 2 (c) 0 (d) 3
24.The remainder when
57
2
is divided by 8
(a) 4 (b) 2 (c) 0 (d) 3
Paragraph for Questions Nos. 53 to 55
If x is any real number, then the largest integer, which does not exceed x is
called the integers part of x, the integer [ ]x is often called the bracket
function / step function.
25. For a real number x, [ ]x denotes the integral part of x the value of
1
2
1 1 1 1 2 1 99
......
2 2 100 2 100 2 100
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤
+ + + + + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦
is

5. (a)50 (b) 47 (c) 45 (d) 52
26. The number of zeros at the end of 400!
(a) 67 (b) 99 (c) 78 (d) 85
27. If ‘n’ is any positive integer then
1 2 4
........
2 4 8
n n n
is
+ + +⎡ ⎤ ⎡ ⎤ ⎡ ⎤
+ + +⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦ ⎣ ⎦
(a)n (b)
2
n
(c)
4
n
(d)
8
n
28. The factors of the polynomial expressions 2
15 16x x− − are
(a) (3x +5) and (2x +3) (b) ( 5 – 3x) and ( 2x + 3)
(c) (3 – 2x) and ( 3x + 5) (d) none of these
29. The value of P for which x – 4 may be a factor of ( )3 2
5 ( 4) 4x P x Px P− + − − +
is
(a) 2 (b) 12 (c) 8 (d) none of these
30. If the polynomials 3 2
4 3 4ax x x+ + − and 3
4x x a− + leave the same
remainder when divided by x – 3 then the value of a is
(a) 2 (b) 1 (c) -1 (d) 3