Integral Calculus & Area · NDA previous year questions

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2012 16 questions

Q762012 · 19 Aug 2012
What is $\int a^{x} e^{x} d x$ equal to? where c is the constant of integration
1. A. $\frac{a ^{x} e ^{x}}{l n a} + c$
2. B. $a^{x} e^{x} + c$
3. C. $\frac{a ^{x} e ^{x}}{l n ( a e )} + c$
4. D.None of the above
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Answer: C
Q772012 · 19 Aug 2012
What is $\int_{- 1}^{1} x ∣ x ∣ d x$ equal to?
1. A.2
2. B.1
3. C.0
4. D. $- 1$
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Answer: C
Q782012 · 19 Aug 2012
What is $\int_{0}^{1} \frac{t a n ^{- 1} x}{1 + x ^{2}} d x$ equal to?
1. A. $\frac{π ^{2}}{8}$
2. B. $\frac{π ^{2}}{32}$
3. C. $\frac{π}{4}$
4. D. $\frac{π}{8}$
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Answer: B
Q792012 · 19 Aug 2012
What is $\int_{0}^{π /2} sin 2 x ln (cot x) d x$ equal to?
1. A.0
2. B. $π ln 2$
3. C. $- π ln 2$
4. D. $\frac{π l n 2}{2}$
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Answer: A
Q802012 · 19 Aug 2012
What is the area of the portion of the curve $y = sin x$ , lying between $x = 0, y = 0$ and $x = 2 π$ ?
1. A.1 square unit
2. B.2 square units
3. C.4 square units
4. D.8 square units
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Answer: C
Q812012 · 19 Aug 2012
What is $\int \frac{l n x}{x} d x$ equal to? where c is the constant of integration
1. A. $\frac{( l n x ) ^{2}}{2} + c$
2. B. $\frac{( l n x )}{2} + c$
3. C. $(ln x)^{2} + c$
4. D.None of the above
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Answer: A
Q822012 · 19 Aug 2012
What is the area of the region bounded by the lines $y = x, y = 0$ and $x = 4$ ?
1. A.4 square units
2. B.8 square units
3. C.12 square units
4. D.16 square units
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Answer: B
Q832012 · 19 Aug 2012
What is $\int (\frac{1}{c o s ^{2} x} - \frac{1}{s i n ^{2} x}) d x$ equal to? where c is the constant of integration
1. A. $2 cosec 2 x + c$
2. B. $- 2 cot 2 x + c$
3. C. $2 sec 2 x + c$
4. D. $- 2 tan 2 x + c$
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Answer: A
Q752012 · 15 Apr 2012
What is $\int (x^{2} + 1)^{\frac{5}{2}} x d x$ equal to? where c is a constant of integration.
1. A. $(x^{2} + 1)^{\frac{7}{2}} + c$
2. B. $\frac{2}{7} (x^{2} + 1)^{\frac{7}{2}} + c$
3. C. $\frac{1}{7} (x^{2} + 1)^{\frac{7}{2}} + c$
4. D.None of the above
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Answer: C
Q762012 · 15 Apr 2012
If $f (x) = x^{2} - 6 x + 8$ and there exists a point c in the interval $[2, 4]$ such that $f^{'} (c) = 0$ , then what is the value of c?
1. A.2.5
2. B.2.8
3. C.3
4. D.3.5
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Answer: C
Q772012 · 15 Apr 2012
1. A.4
2. B.5
3. C.6
4. D.8
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Answer: D
Q782012 · 15 Apr 2012
1. A. $3 \times 1$
2. B. $1 \times 1$
3. C. $1 \times 3$
4. D. $3 \times 3$
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Answer: B
Q792012 · 15 Apr 2012
What is $\int_{- π /2}^{π /2} ∣ sin x ∣ d x$ equal to ?
1. A.2
2. B.1
3. C. $π$
4. D.0
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Answer: A
Q802012 · 15 Apr 2012
The area bounded by the curve $x = f (y)$ , the y-axis and the two lines $y = a$ and $y = b$ is equal to :
1. A. $\int_{a}^{b} y d x$
2. B. $\int_{a}^{b} y^{2} d x$
3. C. $\int_{a}^{b} x d y$
4. D.None of the above
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Answer: C
Q812012 · 15 Apr 2012
If $y = \frac{x + 1}{x - 1}$ , then what is $\frac{d y}{d x}$ equal to ?
1. A. $\frac{- 2}{x - 1}$
2. B. $\frac{- 2}{( x - 1 ) ^{2}}$
3. C. $\frac{2}{( x - 1 ) ^{2}}$
4. D. $\frac{2}{x - 1}$
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Answer: B
Q832012 · 15 Apr 2012
Consider the following : 1. $\int ln 10 d x = x + c$ 2. $\int 1 0^{x} d x = 1 0^{x} + c$ where c is the constant of integration. Which of the above is/are correct ?
1. A.1 only
2. B.2 only
3. C.Both 1 and 2
4. D.Neither 1 nor 2
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Answer: D