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2002 13 questions

Q22002 · 27 Apr 2002 · Shift 1
Which one is not periodic?
1. A. $∣ sin 3 x ∣ + sin^{2} x$
2. B. $cos x + cos^{2} x$
3. C. $cos 4 x + tan^{2} x$
4. D. $cos 2 x + sin x$
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Answer: B
Q62002 · 27 Apr 2002 · Shift 1
If $α \neq = β$ but $α^{2} = 5 α - 3$ and $β^{2} = 5 β - 3$ then the equation having $α / β$ and $β / α$ as its roots is
1. A. $3 x^{2} - 19 x + 3 = 0$
2. B. $3 x^{2} + 19 x - 3 = 0$
3. C. $3 x^{2} - 19 x - 3 = 0$
4. D. $x^{2} - 5 x + 3 = 0$
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Answer: A
Q102002 · 27 Apr 2002 · Shift 1
If $a, b, c$ are distinct $+ v e$ real numbers and $a^{2} + b^{2} + c^{2} = 1$ then $ab + b c + c a$ is
1. A.less than 1
2. B.equal to 1
3. C.greater than 1
4. D.any real no.
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Answer: A
Q122002 · 27 Apr 2002 · Shift 1
The positive integer just greater than $(1 + 0.0001)^{10000}$ is
1. A.4
2. B.5
3. C.2
4. D.3
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Answer: D
Q162002 · 27 Apr 2002 · Shift 1
The sum of integers from 1 to 100 that are divisible by 2 or 5 is :
1. A.3000
2. B.3050
3. C.3600
4. D.3250
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Answer: B
Q232002 · 27 Apr 2002 · Shift 1
If $y = (x + 1 + x^{2})^{n}$ , then $(1 + x^{2}) \frac{d ^{2} y}{d x ^{2}} + x \frac{d y}{d x}$ is
1. A. $n^{2} y$
2. B. $- n^{2} y$
3. C. $- y$
4. D. $2 x^{2} y$
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Answer: A
Q292002 · 27 Apr 2002 · Shift 1
$\int_{0}^{2} [x^{2}] d x$ is
1. A. $2 - 2$
2. B. $2 + 2$
3. C. $2 - 1$
4. D. $- 2 - 3 + 5$
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Answer: D
Q422002 · 27 Apr 2002 · Shift 1
In a class of 100 students there are 70 boys whose average marks in a subject are 75. If the average marks of the complete class is 72, then what is the average marks of the girls?
1. A.73
2. B.65
3. C.68
4. D.74
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Answer: B
Q492002 · 27 Apr 2002 · Shift 1
$f$ is defined in $[- 5, 5]$ as $f (x) = x$ if $x$ is rational $= - x$ if $x$ is irrational. Then
1. A. $f (x)$ is continuous at every x, except $x = 0$
2. B. $f (x)$ is discontinuous at every $x$ , except $x = 0$
3. C. $f (x)$ is continuous everywhere
4. D. $f (x)$ is discontinuous everywhere
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Answer: B
Q582002 · 27 Apr 2002 · Shift 1
The value of $2^{1/4} . 4^{1/8} . 8^{1/16} \dots \infty$ is
1. A.1
2. B.2
3. C.3/2
4. D.4
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Answer: B
Q592002 · 27 Apr 2002 · Shift 1
$1^{3} - 2^{3} + 3^{3} - 4^{3} + \dots + 9^{3} =$
1. A.425
2. B.- 425
3. C.475
4. D.- 475
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Answer: A
Q632002 · 27 Apr 2002 · Shift 1
The sides of a triangle are $3 x + 4 y, 4 x + 3 y$ and $5 x + 5 y$ where $x, y > 0$ then the triangle is :
1. A.right angled
2. B.obtuse angled
3. C.equilateral
4. D.none of these
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Answer: B
Q702002 · 27 Apr 2002 · Shift 1
$lim_{n \to \infty} \frac{1 ^{p} + 2 ^{p} + 3 ^{p} + \dots\dots + n ^{p}}{n ^{p + 1}}$ is
1. A. $\frac{1}{p + 1}$
2. B. $\frac{1}{1 - p}$
3. C. $\frac{1}{p} - \frac{1}{p - 1}$
4. D. $\frac{1}{p + 2}$
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Answer: A