Question.1
If y = sinpx and yn is the nth
derivative of y, then D = is
equal to
(A) zero
(B) independent of x
(C) constant other than zero
(D) none of these
Solution
D =
Taking –p6 common from R3 , R1
and R3 becomes identical . .
Question.2
If a, b, c are
sides of a triangle ABC and A, B, C are angles opposite to a, b, c then D gives
(A) D = area of triangle
(B) D = Perimeter of Triangle
(C) D = åa2
(D) None of these
Solution
Using , modify the given
determinant and then by taking a common from C1 and R1
both D =0 by applying
C2 →C2 –C1
sinB and C3→
C3 – C1sinC
Question.3
If =
0 then x is equal to
(A) 9
(B) -9
(C) 0
(D) None of these
Solution
By circulant determinant property
a + b + c = 0
&⇒ x + 3 + 6 = x + 2+ 7 = x +
4 + 5 = 0
&⇒ x = -9
Question.4
D = is
always
(A) real
(B) imaginary
(C) zero
(D) none of these
Solution
Since D = \ D is
real only
Question.5
Let m be a positive integer and
. Then the value of
is given by
(A) 0
(B) m2 –1
(C) 2m
(D) 2m sin2 (2m)
Solution
Using concept of summation of determinant.
We get R1, R2 identical so is zero.
Question.6
If , then p is given by
(A) xn
(B) (n+ 1)
(C) either A or B
(D) both A and B
Solution
C1 and C3 become equal for p = xn
and R1 and R3 become equal for p = n + 1. .
Question.7
is equal to
(A) D
= 0
(B) D
> 0
(C) D
= f(x,y,z)
(D) None of these
Solution
D
=
Question.8
If the equations x = ay + z, y = az + x and z = ax + y
are the consistent having non-trivial solution, then
(A) a3 = 1
(B) a3 + 1= 0
(C) a + 1 = 0
(D) None of these
Solution
D
=
&⇒
a3 + 3a = 0
Question.9
The value of the determinant is
(A) 0
(B) 2 sinq
(C) sin2q
(D) none of these
Solution
Operating R1 → R1 + R2
+ R3 and using trigonometric identities, the given determinant
=
= 0
Question.10
If
then
(A) D1 = D2
(B) D1 > D2
(C) D1 = (a3 +
b3 + c3 - 3abc)2
(D) None of these
Solution
D2 = =