JEE Mains 2002

is (a) 21 (b) 25 (c) 26 (d) None of these

The coefficient of

x^{5}

(1 + 2 x + 3 x^{2} + \dots)^{- 3/2}

Topic:

Binomial Theorem

Exam:

JEE Mains 2002

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Question 2

, then the coefficient of

∣ x ∣ < 1

x^{n}

in the expansion of

(1 + x + x^{2} + x^{3} + \dots)^{2}

is (a)

n

n - 1

n + 2

n + 1

Topic:

Binomial Theorem

Exam:

JEE Mains 2002

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Question 3

1, lo g_{3} (3^{1 - x} + 2), lo g_{3} (4 \cdot 3^{x} - 1)

are in AP. Then,

x

lo g_{3} 4

1 - lo g_{3} 4

1 - lo g_{4} 3

lo g_{4} 3

Topic:

Sequences and Series

Exam:

JEE Mains 2002

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Question 4

The value of

2^{1/4} \cdot 4^{1/8} \cdot 8^{1/16} \dots \infty

is (a) 1 (b) 2 (c)

\frac{3}{2}

(d) 4

Topic:

Sequences and Series

Exam:

JEE Mains 2002

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Question 5

5th term of a GP is 2 , then the product of its 9 terms is (a) 256 (b) 512 (c) 1024 (d) None of these

Topic:

Sequences and Series

Exam:

JEE Mains 2002

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Question 6

\sum_{n = 0}^{\infty} \frac{( l o g _{e} x ) ^{n}}{n !}

lo g_{e} x

x

lo g_{x} e

(d) None of these

Topic:

Sequences and Series

Exam:

JEE Mains 2002

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Question 7

e^{(x - 1) - \frac{1}{2} (x - 1)^{2} + \frac{( x - 1 ) ^{3}}{3} - \frac{( x - 1 ) ^{4}}{4}} + \dots

lo g (x - 1)

lo g x

x

(d) None of these

Topic:

Sequences and Series

Exam:

JEE Mains 2002

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Question 8

y = (x + 1 + x^{2})^{n}

(1 + x^{2}) \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x}

n^{2} y

- n^{2} y

- y

2 x^{2} y

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2002

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Question 9

lim_{x \to 0} \frac{1 - c o s 2 x}{2 x}

λ

- 1

Topic:

Limits and Derivatives

Exam:

JEE Mains 2002

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Question 10

lim_{x \to \infty} (\frac{x ^{2} + 5 x + 3}{x ^{2} + x + 2})^{x}

e^{4}

e^{2}

e^{3}

e

Topic:

Limits and Derivatives

Exam:

JEE Mains 2002

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Question 11

sin y = x sin (a + y)

\frac{d y}{d x}

\frac{s i n a}{s i n ^{2} ( a + y )}

\frac{s i n ^{2} ( a + y )}{s i n a}

sin a sin^{2} (a + y)

\frac{s i n ^{2} ( a - y )}{s i n a}

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2002

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Question 12

x^{y} = e^{x - y}

\frac{d y}{d x}

\frac{1 + x}{1 + l o g x}

\frac{1 - l o g x}{1 + l o g x}

\frac{l o g x}{( 1 + l o g x ) ^{2}}

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2002

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Question 13

(a) cut at right angle (b) touch each other (c) cut at an angle

The two curves

x^{3} - 3 x y^{2} + 2 = 0

and

3 x^{2} y - y^{3} - 2 = 0

\frac{π}{3}

(d) cut at angle

\frac{π}{4}

Topic:

Application of Derivatives

Exam:

JEE Mains 2002

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Question 14

increases in the interval (a)

The function

f (x) = cot^{- 1} x + x

(1, \infty)

(- 1, \infty)

(- \infty, \infty)

(0, \infty)

Topic:

Application of Derivatives

Exam:

JEE Mains 2002

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Question 15

The greatest value of

f (x) = (x + 1)^{1/3} - (x - 1)^{1/3}

[0, 1]

is (a) 1 (b) 2 (c) 3 (d)

1/3

Topic:

Application of Derivatives

Exam:

JEE Mains 2002

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Question 16

For

x \in R, lim_{x \to \infty} (\frac{x - 3}{x + 2})^{x}

e

e^{- 5}

e^{- 1}

e^{5}

Topic:

Limits and Derivatives

Exam:

JEE Mains 2002

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Question 17

Let

f (2) = 4

and

f^{'} (2) = 4

. Then,

lim_{x \to 2} \frac{x f ( 2 ) - 2 f ( x )}{x - 2}

is given by (a) 2 (b)

- 2

- 4

(d) 3

Topic:

Continuity and Differentiability

Exam:

JEE Mains 2002

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Question 18

is equal to (a) 20 (b) 8 (c) 10 (d) 18

\int_{0}^{10 x} ∣ sin x ∣ d x

Topic:

Integrals

Exam:

JEE Mains 2002

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Question 19

I_{n} = \int_{0}^{π /4} tan^{n} x d x

lim_{n \to \infty} n [I_{n} + I_{n + 2}]

\frac{1}{2}

(b) 1 (c)

\infty

(d) 0

Topic:

Integrals

Exam:

JEE Mains 2002

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Question 20

\int_{0}^{2} [x^{2}] d x

2 - 2

2 + 2

2 - 1