Discriminant Questions

DETERMINANT
BASIC CPP
Questions Questions
based on Expansion of Determinants based on


a 1 1 1 Q.6 The cofactors of 1, – 2, – 3 and 4 in
Q.1 If 1 1 1 = 4, then the value a is -
1 1 1 1 2
are -
3 4
(A) 1 (B) – 1 (C) –2 (D) 0
(A) 4, 3, 2, 1 (B) – 4, 3, 2, –1
(C) 4, – 3, – 2, 1 (D)– 4, – 3, – 2, – 1
x y 2 3
Q.2 If = 7 and = 4, then - Q.7 The minors of the elements of the first row in the
4 2 y x

2 1 4
5
(A) x = – 3, y = – 4 2 3
2 determinant are-
1 1 2
5
(B) x = – , y = – 3 (A) 2, 7, 11 (B) 7, 11, 2
2
(C) 11, 2, 7 (D) 7, 2, 11
SV
5
(C) x = 3, y =
2
a1 b1 c1
5
(C) x = , y = 3 Q.8 If  = a 2 b2 c2 and A 2, B 2 , C 2 are
2
M

a3 b3 c3

respectively cofactors of a2, b2, c2 then
5  i 3 i a1A2 + b1B2 + c1C2 is equal to -
Q.3 The value of is -
4i 5 i (A) –  (B) 0
(C)  (D) None of these
(A) 12 (B) 17 (C) 14 (D) 24

Q.9 If A = (aij) is a 4 × 4 matrix and cij is the
co-factor of the element aij in Det (A) , then
sec x sin x tan x
0 1 0 the expression a11c11+ a12c12+ a13c13 + a14 c14
Q.4 is equal to - equals-
tan x cot x sec x
(A) 0 (B) – 1
(A) 0 (B) – 1 (C) 1 (D) Det. (A)
(C) 1 (D) None of these
Q.10 If cof actor of 2x in the determinant
1 0 0
1
Q.5 The value of 3 x3 1 is - x 1 2
xy 3
5 y 1 1 2x x  1 is zero, then x equals to -
x 1 x 0
(A) x + y (B) x2 – xy + y2 (A) 0 (B) 2 (C) 1 (D) –1
(C) x2 + xy + y2 (D) x3 – y3

, Questions
based on Some basic properties a ab abc
Q.17 The value of 2a 3 a  2b 4a  3b  2c is
a1 ma1 b1 3a 6a  3b 10a  6b  3 c
Q.11 The value of the determinant a2 ma2 b2
a3 ma3 b3 equal to -
is - (A) a3 (B) b3
(A) 0 (B) ma1a2a3 (C) c3 (D) a3 + b3 + c3
(C) ma1b2a2 (D) mb1b2b3
Q.18 The v alue of the determinant

a 0 0 p 2a 0 0 ka k 2  a2 1
b c a pb c a kb k 2  b 2 1 is -
Q.12 If  = , then is equal
c a b pc a b kc k 2  c 2 1
to -
(A) p  (B) p2  (A) k (a + b) (b + c) (c + a)
(C) p3  (D) 2p  (B) k abc (a2 + b2 + c2)
(C) k (a – b) (b – c) ( c – a)
(D) k (a + b – c) (b + c – a) (c + a – b)
1/ a 1 bc
Q.13 The value of the determinant 1/ b 1 ca is
1/ c 1 ab r x n(n  1) / 2 n
2
equal to Q.19 If Dr = 2r  1 y n , then D r
(A) abc
(C) 0
SV
(B) 1/abc
(D) None of these
3r  2 z n(3n  1) / 2 r 1


is equal to -
Q.14 If each row of a determinant of third order of
value  is multiplied by 3, then the value of 1 1 2
(A) n(n + 1)(2n + 1) (B) n (n + 1)2
6 4
M
new determinant is -
(A)  (B) 27  (C) 21  (D) 54  (C) 0 (D) None of these

Q.15 The sum of infinite series
a x a x a x
1 a x a x a x
1 2 Q.20 If = 0, then value of x
1 2 2 4
+ 2 + 2 + ........ is - a x a x a x
6 4 2 4 4
3 are-
(A) –10 (B) 0 (C) 10 (D)  (A) 0, a (B) 0, – a (C) a, – a (D) 0, 3a


a ma  nx x a b c
2 2
Q.16 The value of b mb  ny y is - a b c2
Q.21 The value of the determinant
c mc  nz z bc ca ab
(A) a + b + c is -
(B) x + y + z (A) abc (a – b) (b – c) (c – a)
(C) m(a + b + c) + n(x + y + z) (B) (a – b) (b – c) (c – a) (a + b + c)
(D) 0
(C) (a – b) (b – c) (c – a) (ab + bc + ca)
(D) None of these