# Mathematics Test 8 - Matrix And Determinants, Definite And Indefinite Integration

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

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Attempt Mathematics Test 8 - Matrix And Determinants, Definite And Indefinite Integration | 25 questions in 60 minutes | Mock test for JEE preparation | Free important questions MCQ to study Mock Test Series for JEE Main & Advanced 2022 for JEE Exam | Download free PDF with solutions
QUESTION: 1
Solution:
QUESTION: 2
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
Solution:
QUESTION: 4
If then =
Solution:
QUESTION: 5
If then =
Solution:
QUESTION: 6
If then is equal to
Solution:
QUESTION: 7
The value of the determinant
is
Solution:
QUESTION: 8

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

Solution:
QUESTION: 9
If A,B,C be the angles of a triangle, then is
Solution:
QUESTION: 10
If a,b,c are respectively the pth,qth and rth terms of an H.P., then
Solution:
QUESTION: 11
If x,y,z (>0) are the pth, qth rth terms of a G.P. then the determinant
is
Solution:
QUESTION: 12
If f(x) = then g =
Solution:
QUESTION: 13
If then a,b,c are in
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

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
Solution:
QUESTION: 16
if is imaginary cube root of unity then the value of  is equal to
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 =
Solution:
*Multiple options can be correct
QUESTION: 18

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

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
Solution:
QUESTION: 20
If a matrix has 13 elements, then the possible dimensions (order) it can have are
Solution:
*Answer can only contain numeric values
QUESTION: 21

then r is equal to

Solution:

*Answer can only contain numeric values
QUESTION: 22

If y = cos θ + sin θ and then numbers of values of θ ∈ [0, 2π] is

Solution:

*Answer can only contain numeric values
QUESTION: 23

If then value of (k + a + b) = ?

Solution:

*Answer can only contain numeric values
QUESTION: 24

Let t(x) = is

Solution:

*Answer can only contain numeric values
QUESTION: 25

The value of  is

Solution:
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