Mathematics Test 8 - Matrix And Determinants, Definite And Indefinite Integration | 25 Questions MCQ Test Mock Test Series for JEE Main & Advanced 2022 JEE

QUESTION: 1

A.
1
B.
C.
D.
0

Solution:

QUESTION: 2

A.
4abc
B.
abc
C.
0
D.
None

Solution: Fisrt apply operation of R1 ->R1+R2+R3 you will get all the elements of row 1 equals to zero. And now expanding it along R1 u will get the value of determinant be equal to zero.

QUESTION: 3

A. abc
B. p+q+r
C.
D. 0

Solution:

QUESTION: 4

If

then

=

A. 0
B.
C.
D. none

Solution:

QUESTION: 5

If

then

=

A. -1
B.
C. 0
D.

Solution:

QUESTION: 6

If

&

then

is equal to

A. 1
B. 2
C. -1
D. 1/2

Solution:

QUESTION: 7

The value of the determinant

is

A. 0
B. log(xyz)
C. log(6 xyz)
D. 6 log(xyz)

Solution:

QUESTION: 8

If p + q + r = a + b + c =0, then the value of is

A.
0
B.
aq+bq+cr
C.
1
D.
none of these

Solution:

QUESTION: 9

If A,B,C be the angles of a triangle, then

is

A. -1
B. 0
C. 1
D. 2

Solution:

QUESTION: 10

If a,b,c are respectively the pth,qth and rth terms of an H.P., then

A. abc
B. p+q+r
C. 0
D. none

Solution:

QUESTION: 11

If x,y,z (>0) are the pth, qth rth terms of a G.P. then the determinant

is

A. 0
B. x+y+z
C. pqr
D. xyz

Solution:

QUESTION: 12

If f(x)

=

then g =

A. –200
B. 100
C. 112
D. –108

Solution:

QUESTION: 13

If

then a,b,c are in

A. A.P
B. G.P.
C. H.P
D. None

Solution:

QUESTION: 14

If be the determinant given in last question and =0 then system of lines given by the equation ax by c=0 pass through the point

A.
(0,0)
B.
(1,2)
C.
(1,1)
D.
(1,–2)

Solution:

QUESTION: 15

If the three digit numbers A28,3B9, and62C where A,B and C are integers between 0 and 9 which are divisible by

the D =

is divisible by

A.
B.
C. 2
D. none

Solution:

QUESTION: 16

if

is imaginary cube root of unity then the value of

is equal to

A. 0
B. 2
C. 2
D. -3

Solution:

ω(ω2)=1

1+ω+ω2=0

Then you get a very interesting result:

a3+b3+c3−3abc

QUESTION: 17

If

= k xyz, then k =

A. 1
B. 2
C. 3
D. 4

Solution:

*Multiple options can be correct

QUESTION: 18

The value of lying between =0 and and satisfying then equation
are

A.
B.
C.
D.

Solution:

Correct Answer : a,c

Explanation : A = {(1+sin²θ, cos²θ, 4sin4θ) (sin²θ, 1+cos²θ, 4sin4θ) (sin2θ, cos2θ, 1+4sin4θ)}

C1 ----> C1 + C2

=> {(1+sin²θ, cos²θ, 4sin4θ) (sin²θ, 1+cos²θ, 4sin4θ) (sin²θ, cos²θ, 1+4sin4θ)} = 0

=> {(1+1, cos²θ, 4sin4θ) (1+1, 1+cos²θ, 4sin4θ) (1, cos²θ, 1+4sin4θ)} = 0

=> {(2, cos²θ, 4sin4θ) (2, 1+cos²θ, 4sin4θ) (1, cos²θ, 1+4sin4θ)} = 0

R2 : R2-->R2-R1, R3-->R3-R1

=> {(2, cos²θ, 4sin4θ) (2-2, 1+cos²θ-cos²θ, 4sin4θ-4sin4θ) (1-2, cos²θ-cos²θ, 1+4sin4θ-4sin4θ)} = 0

=> {(2, cos²θ, 4sin4θ) (0, 1, 0) (-1, 0,1)} = 0

Expand

0 + 1[2 - (-1)4sin4θ] = 0

2 + 4sin4θ = 0

Sin4θ = -2/4

sin4θ = -½

4θ = π + π/6, 2θ = 2π-π/6

4θ = 7π/6, 2θ = 11π/6

θ = 7π/24, 2θ = 11π/24

QUESTION: 19

If A is any m×n matrix such that AB and BA are both defined, then B is a matrix of type

A. m×n
B. n×m
C. m×m
D. n×n

Solution:

QUESTION: 20

If a matrix has 13 elements, then the possible dimensions (order) it can have are

A. 1×13, 13×1
B. 1×26, 26×1
C. 2×13, 13×2
D. none of these

Solution: