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Crash 2023- Unit test 1 - Entrance oriented questions related on the chapter wise
Mathematics class 11 (041)
University of Kerala
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Crash - 2023
Unit test - 1
Matrices and Determinants
If a square matrix A satisfies A 2 = A, then (a) (I + A) 2 = I + 3A (b) (I + A) 3 = I + 4A
(c) (I + A)n = I + (2n - 1)A , nN
(d) (I + A)n = I + nA, nA
For what value of x, the matrix
2 4 1 x
2 4 x 1
3 x 2 2 is
singular? (a) x = 1 (b) x = 2 (c) x = 0 (d) x = 3 If A and B are square matrices of the same order and AB = 3I, then A-1 is equal to
(a) 3B (b)
3
1
B (c) 3B-1 (d)
3
1
B-
If A =
1 1
1 1
, then AA 100 is equal to
(a) 2 100 A (b) 2 99 A (c) 100A (d) 299A An orthogonal matrix is
(a)
2 sin cos
cos 2 sin (b)
sin cos
cos sin
(c)
sin cos
cos sin (d)
1 1
1 1
Let A =
1 1 1
2 1 3
1 1 1 and 10B =
1 2 3
5 0
4 2 2 . If B is the
inverse of matrix A, then is
(a) -2 (b) 1 (c) 2 (d) 5
If A is a 3 3 non-singular matrix such that AAT = AATA and
B = A-1AT , then BBT is equal to (a) I + B (b) I (c) B-1 (d) (B-1)T
Let A =
3 2 1
2 1 0
1 0 0 , if u 1 and u 2 are column matrices such
that Au 1 =
0
0
1 and Au 2 =
0
1
0 , then u 1 + u 2 is equal to
(a)
0
1
1 (b)
1
1
1 (c)
0
1
1 (d)
1
1
1
The number of 3 3 non-singular matrices, with four entries
as 1 and all other entries as 0, is (a) less than 4 (b) 5 (c) 6 (d) atleast 7
Let A =
3 4
1 2 and B =
0 b
a 0
; a,bN. Then,
(a) there exists more than one but finite number of B’s such that AB = BA (b) there exists exactly one B such that AB = BA (c) there exist infinitely many B’s such that AB = BA (d) there caannot exist any B such that AB = BA
The set of all values of for which the system of linear equa-
tions 2x 1 - 2x 2 + x 3 = x 1 , 2x 1 - 3x 2 + 2x 3 = x 2 and -x 1 + 2x 2 = x 3
has a non-trivial solution, (a) is an empty set (b) is a singleton set (c) contains two elements (d) contains more than two elements
If P =
2 4 4
1 3 3
1 3
is the adjoint of a 3 3 matrix A and | A | = 4,
then is equal to
(a) 4 (b) 11 (c) 5 (d) 0 The number of values of k for which the linear equations 4x
- ky + 2z = 0 , kx + 4y + z = 0 and 2x + 2y + z = 0 posses a non-zero solution, is (a) 2 (b) 1 (c) 0 (d) 3 If the trivial solution is the only solution of the system of equations x - ky + z = 0, kx + 3y - kz = 0 and 3x + y - z = 0. Then, the set of all values of k is (a) {2,-3} (b) -{2,-3} (c) R - {2} (d) R - {-3}
Let A be 2 2 matrix.
Statement I adj(adj A) = A , Statement II |adj A| = A (a) Statement I is false,Statement II is true (b) Statement I is true, Statement II is true; Statement II is a correct explanation for Statement I (c) Statement I is true, Statement II is true; Statement II is not a correct expanation for Statement I (d) Statement I is true, Statement II is false
2
2 n n
n 2 n
n 2 n
2
(a) 0 (b) 1 (c) (d )
is equal to 1
1
1
If 1 , , are the cube roots of unity,then
Let A =
0 0 5
0 5
5 5
. If | AA 2 | = 25, then | | equals
(a) 5 2 (b) 1 (c) 1/5 (d) 5
The inverse of the matrix A =
0 0 4
0 3 0
2 0 0 is
(a)
0 0 4
0 3 0
2 0 0
24
1 (b)
0 0 4
0 3 0
2 0 0
(c)
0 0 1
0 1 0
1 0 0
24
1 (d)
4 0 0 1
0 3 0 1
21 0 0
The value of sin cos sin( )
sin cos sin( )
sin cos sin( )
is
(a) sin sin sin (b) cos cos cos (c) 1 (d) 0
1.
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Time : 45 minutes
XII Max Marks : 120
If a,b and c are in AP, then the value of x 6 x 7 x c
x 4 x 5 x b
x 2 x 3 x a
is
(a) 0 (b) x - (a + b + c) (c) a + b + c (d) 9x 2 + a + b + c
Let A =
1 3
1 2
. If AA 6 = kA - 205 I, then the numerical quantity of k - 40 should be .................
If A =
0 2
1 1
= B 3 + C 3 , where B and C are 2 2 matrices with integer elements, then - tr (B) - tr (C) must be equal to ..................
If
c 1 a
a b is an idempotent matrix and f(x) = x - x 2 and bc = 1/4, then the value of 1/f(a) is .................
If A =
3 0
0 1
and (A 8 + AA 6 + A 4 + A 2 + I) V =
11
0
, where I is the 2 2 identity matrix, then the product of all elements of matrix VV
is .................
If k(b c)(c a)(a b) c a c b 2 c
b a 2 b b c
2 a a b a c
, then the value of k is ...................
Maximum value of sin x cos x 1 4 sin 2 x
sin x 1 cos x 4 sin 2 x
1 sin x cos x 4 sin 2 x
2 2
2 2
2 2
is ................
If A is a square matrix of order n such that | adj (adj A) | = | A | 9 ,then the value of n can be ................
3 z
2 y
5 x
2 , 2 z
2 y
4 x
1 , 3 z
1 y
2 x
1 , then the value of y is ....................
The system 2ax - 23y + 29z = 0, 7x + ay + 4z = 7, 5x + 2y + az = 5 has no solution, if the value of a is ...................
The value of for which the system (sin 3 )x - y + z = 0, (cos 2 ) x + 4y + 3z = 0, 2x + 7y + 7z = 0 has non-trivial solution is
5
,
where is a positive integer, then must be equal to ...................
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Crash 2023- Unit test 1 - Entrance oriented questions related on the chapter wise
Course: Mathematics class 11 (041)
University: University of Kerala
