CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 0744 ‐3040000 Page # 1 C A REER POINT DAILY PRACTICE PROBLEM SHEET MATHEMATICS Determinants-1 ANSWER KEY 1. (2) 2. (2) 3. (4) 4. (4) 5. (3) 6. (1) 7. (2) P Live ourse PRE ENGINEERING Expansion of determinant: Q.1 If a, b, c be positive and not all equal, then the value of the determinant b a c a c b c b a is- (1) positive (2) negative (3) zero (4) None of these Q.2 If A r = r 1 r 1 r r − − where r is natural number, then the value of ∑ = 2008 1 r r A must be (1) 0 (2) 2008 (3) 2 2008 (4) None Properties of Determinants: Q.3 If m is a positive integer ∆ r = ) 1 m ( sin ) m ( sin ) m ( sin 1 m 2 1 m 1 C 1 r 2 2 2 2 2 m 2 r m + + − − then find the value of ∑ = ∆ m 0 r r (1) 2 (2) 1 (3) 3 (4) None Q.4 If a, b, c, d, e and f are in G.P. then the value of z f c y e b x d a 2 2 2 2 2 2 depends on (1) x and y (2) x and z (3) y and z (4) Independent of x, y & z Q.5 a b 2 a b a b a a b 2 a b 2 a b a a + + + + + + = mb n (a + b), then (1) m = 9, n =1 (2) m = 1, n = 2 (3) m = 9, n = 2 (4) None of these Q.6 Let ∆ r = ) 1 n ( n 1 )!– 1 n ( 1 2 c b a r 2 r 1 1 )! 1 r ( 2 n 1 r + + − + + − , then value of ∑ = ∆ n 1 r r is (1) 0 (2) (n + 3)! (3) a (n)! + b (4) None of these Q.7 The value of 8 m 7 m 6 m 3 m 4 m 5 m 2 m 1 m m i i i i i i i i i + + + + + + + + where i = 1 − is (1) 1 if m is multiple of 4 (2) 0 for all real m (3) –i if m is multiple of 3 (4) None of these

DPPS-01 Determinant

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CAREER POINT, CP Tower, IPIA, Road No.1, Kota (Raj.), Ph: 07443040000 Page # 1

CAREER POINT

DAILY PRACTICE PROBLEM SHEET

MATHEMATICS

Determinants-1

ANSWER KEY

1. (2) 2. (2) 3. (4) 4. (4) 5. (3) 6. (1) 7. (2)

CP Live CoursePRE ENGINEERING

Expansion of determinant: Q.1 If a, b, c be positive and not all equal, then the

value of the determinant bacacbcba

is-

(1) positive (2) negative (3) zero (4) None of these

Q.2 If Ar = r1r1rr

where r is natural number,

then the value of

=

2008

1rrA must be

(1) 0 (2) 2008 (3) 22008 (4) None

Properties of Determinants:

Q.3 If m is a positive integer

r = )1m(sin)m(sin)m(sin

1m21m1C1r2

2222

m2r

m

++

then find the value of =

m

0rr

(1) 2 (2) 1 (3) 3 (4) None

Q.4 If a, b, c, d, e and f are in G.P. then the value of

zfcyebxda

22

22

22

depends on

(1) x and y (2) x and z (3) y and z (4) Independent of x, y & z

Q.5 ab2aba

baab2ab2abaa

++++++

= mbn (a + b), then

(1) m = 9, n =1 (2) m = 1, n = 2 (3) m = 9, n = 2 (4) None of these

Q.6 Let r = )1n(n1)!1n(12

cba

r2

r11

)!1r(2

n

1r

++

++

, then value

of =

n

1rr is

(1) 0 (2) (n + 3)! (3) a (n)! + b (4) None of these

Q.7 The value of 8m7m6m

3m4m5m

2m1mm

iiiiiiiii

++++++++

where i = 1

is (1) 1 if m is multiple of 4 (2) 0 for all real m (3) i if m is multiple of 3 (4) None of these