ANSWERS & HINTS

WBJEE - 2010 (Answers & Hints)

Mathematics

ANSWERS & HINTS for

WBJEE - 2010

MULTIPLE CHOICE QUESTIONS

SUB : MATHEMATICS

cot x tan x 1. The value of cot 2x is

(A) 1

(B) 2

(C) ?1

Ans : (B)

Hints :

cos2 x sin2 x u sin 2x sin x cos x cos 2x

2 cos 2x u sin 2x sin 2x cos 2x

2

2. The number of points of intersection of 2y = 1 and y = sin x, in 2S d x d 2S is

(A) 1 Ans : (D)

(B) 2

(8) (C) 3 4 1|cos x||cos2 |.................f

3

(D) 4 (D) 4

1 Hints : y = = sin x

2

2S d x d 2S

x S , 5S , 7S , 11S 66 6 6

No. of soln 4

3. Let R be the set of real numbers and the mapping f : R o R and g : R o R be defined by f(x) = 5 ? x2 and g(x) = 3x ? 4 , then the value of (fog)(?1) is

(A) ?44

(B) ?54

(C) ?32

(D) ?64

Ans : (A)

Hints : f(g(?1)) = f(?3?4) = f(?7) = 5 ? 49 = ? 44

4. A = {1, 2, 3, 4}, B = {1, 2, 3, 4, 5, 6} are two sets, and function f : A o B is defined by f(x) = x + 2 x A, then the function f is

(A) bijective

(B) onto

(C) one?one

(D) many?one

Ans : (C) Hints : f(x) = f(y) x + 2 = y + 2 x = y ?one?one

?1 1 ?

5.

If the matrices A

?2 1 3? ??4 1 0?? and B

??0 ??5

2?? , then AB will be 0 ??

?17 0? (A) ??4 2?? Ans : (A)

?4 0? (B) ??0 4??

?17 4 ? (C) ??0 2??

?0 0? (D) ??0 0??

WBJEE - 2010 (Answers & Hints)

Mathematics

?1 1 ?

Hints : AB

?2 ??4

1 1

3? 0??

??0 ??5

2?? 0 ??

?17 ??4

0? 2??

x Z2 Z 1

6. Z is an imaginary cube root of unity and Z 1

Z2 1 x = 0 then one of the values of x is x Z Z2

(A) 1 Ans : (B)

(B) 0

(C) ?1

(D) 2

x

Hints : C1c oC1 C2 C3 o x x

Z1

1Z 1

Z2 1 x x 1 Z2 1 x

x Z Z2

1 x Z Z2

1Z 1

x 0 Z2 Z x

x{(Z2 Z)(Z2 1) x2} 0 x = 0 One value of x = 0

0

x Z2 1

? 1 2?

7.

If A

? ?

4

1?? then A?1 is

1 ?1 2?

(A) 7 ?? 4

1??

Ans : Both (A) & (C)

Hints : |A| = ? 1 + 8 = 7

?(1) adj (A) ??(4)

1 ? 1 2? (B) 7 ?? 4 1??

(2) ? ?1 2?

(1)??

? ?

4

1??

1 ? 1 2? (C) 7 ?? 4 1??

A1

1 ?1 7 ?? 4

2? 1??

Both (A and C)

8.

The

value of

2 3!

4 5!

6 ........ 7!

is

1

(A) e2 Ans : (B)

(B) e?1

(C) e

Hints : tn

2n (2n 1)!

2n 1 1 (2n 1)! (2n 1)!

1 1 (2n)! (2n 1)!

?f tn

n1

1 1 1 1 ........f e1 2! 3! 4! 5!

(D) Does not exist

(D)

1

e3

4

3

9.

If sum of an infinite geometric series is

5

and its 1st term is

, then its common ratio is 4

7 (A) 16 Ans : (A)

9 (B) 16

1 (C) 9

7 (D) 9

WBJEE - 2010 (Answers & Hints)

Mathematics

a4 Hints : 1 r 3

3

Then

4 1

r

4 3

r 1 9 7 16 16

10. The number of permutations by taking all letters and keeping the vowels of the word COMBINE in the odd places is

(A) 96

(B) 144

(C) 512

(D) 576

Ans : (D)

Hints : Vowels : O, I, E

No. of Odd place : 4

No of ways = 4P3 ? 4! = 576

11.

If

C n?1 3

+

C n?1 4

>

nC3

,

then

n

is

just

greater

than

integer

(A) 5

(B) 6

(C) 4

(D) 7

Ans : (D)

Hints

:

C n?1 3

+

C n?1 4

>

nC3

n

C4

!n

C3

n! ! 4!(n 4)!

n! 3!(n 3)!

1 4

!

1 (n 3)

n3! 4

n

!7

a 12. If in the expansion of (a ? 2b)n , the sum of the 5th and 6th term is zero, then the value of b is

n4

2(n 4)

5

(A) 5

(B)

5

(C) n 4

(D)

Ans : (B)

Hints : (a 2b)n t5 + t6 = 0

n

? n Cr (a)nr (2b)r

r0

n C4 (a)n4 (2b)4 n C5 (a)n5 (2b)5

0

n! 4!(n

an4 (2b)4 4)!

n! (a)n5 (2b)5 5!(n 5)!

5 2(n 4)

1 u a 1 (2b) a 2(n 4)

(n 4)

5

b5

 13. 23n 1 will be divisible by (n N)

(A) 25 Ans : (C)

(B) 8

(C) 7

(D) 3

Hints : 23n = (8)n = (1 + 7)n = n C0 n C17 n C2 72 ....... n Cn 7n

23n 1 7 ?? n C1 n C2 7 ............ n Cn 7n1 ??

?divisible by 7

14. Sum of the last 30 coeffivients in the expansion of (1 + x)59 , when expanded in ascending powers of x is

(A) 259

(B) 258

(C) 230

(D) 229

Ans : (B)

Hints : Total terms = 60

Sum of all the terms 259

Sum of first 30 terms =

=

258

2

2

15. If (1 ? x + x2)n = a + a x +.....+ a x2n then the value of a + a + a + ....... + a is

0 1

2n ,

0 2 4

2n

(A) 3n 1 2

(B) 3n 1 2

3n 1 (C)

2

Ans : (D)

3n 1 (D)

2

WBJEE - 2010 (Answers & Hints)

Mathematics

Hints : x = 1 1 a0 a1 a2 a3 ............ a2n

x 1, 3n a0 a1 a2 a3 ............ a2n ???????????????????????????????????

1 3n 2[a0 a 2 a4 ............ a 2n ]

a0 a2 a4 .............. a2n

1 3n 2

16. If DE be the roots of the quadratic equation x2 + x + 1 = 0 then the equation whose roots are D19 , E7 is

(A) x2 ? x + 1 = 0

(B) x2 ? x ? 1 = 0

(C) x2 + x ? 1 = 0

(D) x2 + x + 1 = 0

Ans : (D)

Hints : Roots are ZZ2

Let D ZE Z

D ZE Z

? Equation remains same i.e. x2 + x+ 1 = 0

17. The roots of the quadratic equation x2 2 3x 22 0 are :

(A) imaginry

(B) real, rational and equal

(C) real, irrational and unequal

(D) real, rational and unequal

Ans : (C)

Hints : x2 2 3 22 0 D 12 (4u 22) ! 0

' coeffs are irrational,

x 2 3 r 12 88 2

?Roots are irrational, real, unequl. 18. The qudratic equation x2 + 15 |x| + 14 = 0 has

(A) only positive solutions (C) no solution Ans : (C)

Hints : x2 + 15 |x| + 14 > 0 x Hence no solution

(B) only negative solutions (D) both positive and negative solution

19.

If z

4 1 i , then z is (where z is complex conjugate of z )

(A) 2 (1 + i) Ans : (D)

(B) (1 + i)

2 (C) 1 i

4 (D) 1 i

Hints : z 4 1i

z4 1 i

WBJEE - 2010 (Answers & Hints)

20. If S arg(z) S then arg z arg(z) is 2

(A) S Ans : (A) Hints : (Z)(-x,y)

(B) S

S (C)

2

Mathematics S (D) ? 2

Z (-x,-y)

Z

if arg(z) S T arg(z) S T arg(z) T arg(z) arg(z) S T (T) S T T S 21. Two dice are tossed once. The probability of getting an even number at the first die or a total of 8 is

1 (A) 36

3 (B) 36

Ans : () Hints : A = getting even no on 1st dice

B = getting sum 8

So |A| = 18 |B| = 5 | A B | 3

11 (C) 36

23 (D) 36

So P(A * B)

18 5 3 36

20 36 (No option matches)

22. The probability that at least one of A and B occurs is 0.6 . If A and B occur simultaneously with probability 0.3, then P(Ac) P(Bc)

is

(A) 0.9

(B) 0.15

(C) 1.1

(D) 1.2

Ans : (C)

Hints : P(A * B) 0.6

P(A) P(B) P(A * B) P(A B) 0.9

P(A B) 0.3

P(Ac) P(Bc) 2 0.9 1.1

log3 5u log25 27 u log49 7

23. The value of

log81 3

is

(A) 1 Ans : (D)

(B) 6

2 (C) 3

(D) 3

Hints

:

? ? ?

log 5 log 3

u

3 2

log 3 u log 5

log 7 2 log 7

? ? ?

3

? log 3 ?

? ?

4

log

3

? ?

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download