MATHS PRACTICE PAPER -1 CLASS-XII
SECTION A
Q1 Let f:R-R
be defined as f(x)= x4:
(A) one-one onto (B)
one-one into (C) many-one onto (D) many-one into
Q2 If 4
sin¹x +3 cos³x = 2
, then x=
(A)0
(B) 1
C)-1/2
D)3/2
Q3 If A=
- . then A²-54-71 is
(A)O
(B)1
C)diagonal matrices
D) A2
Q4 If A =
then A¹ exists f
(8) a=2
(C) a=0
D)None of these
Q5 sin-(sin(-600°)
then is
A)
2
B)
C)
-2
D)
Q.6 if tan
¹2x+tan- 3x then is equal to
(A) 1
(B)0
C)1/6
D)none
(C) diagonal matrix
(
Q.7if Set A has 3 elements and set B has 4 elements
then the number of injective mappings that can be defined from A to B
(A) 12
(B) 144
(c) 24
Q.8 sin -x+sin-¹y+sin-z
and f(1)=2
(A)D
(B) 1
C)2
D)3
Q:9 Write
the principal value of cos- (cos7
)
(A) 
(B)
(C) 2
(D) 3
Q10 If A and
B are square matrices of the same order and AB = 3I, then A-¹ is
equal to
(A)
3B
(B)
3B
(C)
1/3B
(D)
B
Q. 11 If 
is an identity matrix,
find a and B.
(A) 0,
(B) 0, ,
(C) ,
D)0,0
Q.12 F(x) = 
(A) F(x)
(B) F(xy)
C)F(x+y)
D)F(x-y)
Q 13 The
matrix A satisfies the equation 
A=
(A) 
(C) 
(D) 
(D) 
Q.14 Given
set A=(1, 2, 3) and a relation R = {(1, 2), (2, 1)), the relation R will be
(A) reflexive if (1, 1) is added (C) transitive if (1, 1) is
added
(8) symmetric if (2, 3) is added
(D) symmetric if (3, 2) is added
Q. 15 If A
is a square matrix such that A² =I then A-¹ is
A)2A
(B) 0
C)A
D)A+I
Q. 16 f: RàR, f(x) = 2x+ |cos x| then f
is.............function.
(A) One one and onto
B)One one but not onto
(C) Neither one one nor onto
(D) Not one one but
onto
Q17 Let R be
the relation on the set (1, 2, 3, 4) given by R=((1, 2), (2, 2), (1, 1), (4;
4), (1, 3), (3,3), (3,2)). then
(A) R is reflexive and symmetric but not transitive.
(B) R is symmetric and transitive but not reflexive.
(C) R is an equivalence relation.
(D) R is reflexive and transitive but not symmetric
Q18 If A is a orthogonal matrix, then
(A) det(A) = 0,
(B) det(A) = ±1.
(C) det(A) = 2,
(D) None of these
Q.19 if a relation R on set (1,2,3) be …defined by R={(1,2)}
A)Reflexive
B)Symmetric
C)Transtive
D)None of these
Q.20) If tan-x=/10 for some x belongs to R
then the value of cot-x is
A)2/5
B) 
C) 3
D)10/
Q.21 the value of tan(cos-3/5+tan-1/4)
A)19/8
B)8/19
C)19/12
D)3/4
Q.22 If A=
then find k if |2A|=K
IAI.
(A) 12
(B)-6
(C)-12
(D) 4
Q. 23 Let R
be the relation in the set N given by R = [(a,b): a-b-3, b>6} then correct
option is
(A) (1,4)€ R
(B) (3, 7)e R
(C) (6,9)€ R
(D) (8, 7)€ R
Q. 24 If A
and B are invertible matrices, then which of the following is not correct.
(A)adjA= |A|A-¹
B)det(A-1)=(det(A))-1
(C)(AB)¹ = B-¹A-¹
D)(A+B)-1=A-+B-
Q.25 tan
¹(1) + tan-¹(2) + tan¹(3):
(A)
(B) 
C)
D)None of these
Q. 26 The
domain of sin-¹(3x) is
(A) [-1,1]
(B) [0,1]
(C) [-1/3,1/3]
D)[-3,-3]
Q.27 If A=
then |adjA|
A)a2
B)a9
C)a27
D)a6
Q.28 det A=2 3 4
4x 6x 8x
5 7 8
=
A)18x
B)1
C)0
D)18x2
Q. 29 detA= sin 35°
- cos 35⁰ =……………….
sin 55°
cos 55°
A)0
(B) 1
C)-1
D)2
Q.30 The
function f given by f(x) = tan2x is not defined on the set
(A) {(2n + 1):n € Z}
(C) {nn: n € Z}
(B) {(2n + 1) :n € Z}
(D) {(2n + 1):n € R}
Q. 31 If a
matrix has 6 elements, then number of possible orders of the matrix can be
(A) 2
(B) 1
(C) 3
(D) 6
(B) 1
(D) 2
Q.30 The
function f given by f(x) = tan2x is not defined on the set
(A) {(2n+1):n € Z}
(C) {nn: n € Z}
(8) {(2n+1): nez)
(D) {(2n + 1) :n € R}
Q. 31 If a
matrix has 6 elements, then number of possible orders of the matrix can be (A)
2 (B) 4
(C) 3
(D) 6
Q. 32 If A =
[ay] is a 2 x 3 matrix, such that aij = (-1+2j)²
-, then a23
(A) 1/5
(B) 2/5
(C) 9/5
(D) 16/5
Q. 33 If A = [cosa sina], then for what value of a. A is an
identity matrix? cosa
(B) 0°
(C) 45°
(A) 90°
(D) 180°
Q. 35 If 1-x
x 3 = 0, then its roots are 0 0 xl
0 x 0
0
0 x
(A) 1 only
(B) 0,1
(C) O
(D) -1,0,1
SECTION-B
Two schools
P and Q want to award their selected students on the values of Tolerance,
Kindness, and Leadership. The school P wants to award Rs x each, Rs y each and
Rs z each for the three respective values to 3, 2 and 1 students respectively
with total award money of
Rs. 2200.
School Q
wants to spend Rs 3100 to award its 4, 1 and 3 students on the respective
values (by giving the School Q wants to spend Rs 3100 to award its 4, 1 and 3
students on the respective values (by giving the same award money to the three
values as school P). If the total amount of award for one prize on each value
is Rs1200.
(D) ±6
(D) -1,0,1
School Q wants to spend Rs 3100 to award its 4, 1 and 3
students on the respective values (by giving the same award money to the three
values as school P). If the total amount of award for one prize on each value
is Rs1200.
Using matrices, find the following:
Q.36 What is
award money for Tolerance?
(A) Rs. 350
(B) Rs. 300
C)Rs.500
D)Rs.400
Q.37 What is
the award money for Leadership?
(A) Rs. 300
(B) Rs. 280
C)Rs.450
D)Rs.500
Q.38 What is
the award money for Kindness?
(A) Rs. 500
(B) Rs. 400
(C) Rs. 300
(D) Rs. 450
Q.39 If a
matrix A is both symmetric and skew-symmetric, then
(A) A is a diagonal matrix
(C) A is a zero matrix
(8) A is a scalar matrix
(D) A is a square matrix
Q.40 If A
and B are two matrices such that AB = B and BA = A, then B² is equal to
(A) B
(B) A
(C) 1
D)0
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