FLCD 1

4 Answers

1133
Sourish Ghosh ·

1) C
2) A
3) B
4) C
5) A

591
Akshay Ginodia ·

1.c
3.b
4.b
5.a

in q.2 my answer for b is coming out to be 4

1357
Manish Shankar ·

Answers:
1. C
2. A
3. A
4. C
5. A

2305
Shaswata Roy ·

1)(C)

2)(A)

Given expression:

limx→0 x-3[3x-(3x)33!+.....]+ax2+b

= limx→0 1x2(3+a) +(-276+b) +....

The rest of the terms are equal to 0.

Therefore,

3x2 +ax2=0

-276+b = 0

3)(A)f(g(x))=x

Differentiating both sides,

f'(g(x))*g'(x)=1
→g'(x)=1f'(g(x))=1+[g(x)]5

4)(C)

f'(x)= mxm-1sin(1x)-xm-2cos(1x) for x≠0
and
f'(x)= 0 for x = 0

sin and cos of any number lies between 0 and 1.

Hence for limx→0f'(x) to be 0 limx→0xm-2 should be 0.
The smallest natural number m satisfying this condition is 3.

5)(A)

arctan(2)+arctan(20k)=arctan(k)

arctan(2+20k1-40k)=arctan(k)

→ 40k2+19k+2=0

Sum of roots = -1940

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