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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

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

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+sin ^{2}θ, cos^{2}θ, 4sin4θ) (sin^{2}θ, 1+cos^{2}θ, 4sin4θ) (sin2θ, cos2θ, 1+4sin4θ)}**

**C1 ----> C1 + C2**

**=> {(1+sin ^{2}θ, cos^{2}θ, 4sin4θ) (sin^{2}θ, 1+cos^{2}θ, 4sin4θ) (sin^{2}θ, cos^{2}θ, 1+4sin4θ)} = 0**

**=> {(1+1, cos ^{2}θ, 4sin4θ) (1+1, 1+cos^{2}θ, 4sin4θ) (1, cos^{2}θ, 1+4sin4θ)} = 0**

**=> {(2, cos ^{2}θ, 4sin4θ) (2, 1+cos^{2}θ, 4sin4θ) (1, cos^{2}θ, 1+4sin4θ)} = 0**

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

**=> {(2, cos ^{2}θ, 4sin4θ) (2-2, 1+cos^{2}θ-cos^{2}θ, 4sin4θ-4sin4θ) (1-2, cos^{2}θ-cos^{2}θ, 1+4sin4θ-4sin4θ)} = 0**

**=> {(2, cos ^{2}θ, 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:

QUESTION: 21

If A = then is equal to

Solution:

QUESTION: 22

If each element of a 3×3 matrix is multiplied by 3, then the determinant of the newly formed matrix is

Solution:

QUESTION: 23

If A= is a 4×4 matrix and is the co-factor of the element in |A|, then the expression is equal to

Solution:

QUESTION: 24

If A is a square matrix such that = A, then |A| equals

Solution:

QUESTION: 25

If then k is

Solution:

QUESTION: 26

=

Solution:

QUESTION: 27

If f(x) = then f(x) =

Solution:

QUESTION: 28

Solution:

QUESTION: 29

Solution:

QUESTION: 30

Solution:

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