[Math Processing Error]$$Area\,\,of\,\,the\,\,\,region\,\,bounded\,\,by\,\,the\,\,curves\,\,y = x^2 + 2\,\,,\,\,y = \,\, - x\,\,\,\,;\,\,x = 0\,\,and\,\,x = 1\,\,is$$

• A) [Math Processing Error]$$None\,\,of\,\,these$$
• B) [Math Processing Error]$$\frac{3} {{16}}$$
• C) [Math Processing Error]$$\frac{5} {{16}}$$
• D) [Math Processing Error]$$\frac{17} {{6}}$$

[Math Processing Error]$${\text{If }}f{\text{ is continuous at every point of }}[a,b]{\text{ and }}F{\text{ is anti - derivative of }}f{\text{ on }}[a,b]{\text{, then}}$$

• A) [Math Processing Error]$$\int_a^b {f(x)} dx = F(a) - F(b)$$
• B) none of these
• C) [Math Processing Error]$$\int_a^b {f(x)} dx = F(b) - F(a)$$
• D) [Math Processing Error]$$\int_a^b {f(x)} dx = F(a) + F(b)$$

The value of [Math Processing Error]∫1∞dxx2_____.$\int\limits_1^\infty {\frac{{dx}}{{{x^2}}}} \,\_\_\_\_\_.$

• A) 4
• B) 0
• C) 1
• D) 3

[Math Processing Error]$$If\,f(x)\, = \,\sqrt x ,\,\,then\,\,\int\limits_1^2 {\pi \,[f(x)} ]^2 \,dx\,\,is\,\, - - - - - - -$$

• A) [Math Processing Error]$$\frac{7 \pi } {2}$$
• B) [Math Processing Error]$$\frac{5 \pi } {2}$$
• C) [Math Processing Error]$$\frac{3 \pi } {2}$$
• D) [Math Processing Error]$$\frac{\pi } {2}$$

If the function and limits of definite integral are the same and variable of integration are changed, i.e [Math Processing Error]∫abf(x)dx=∫abf(t)dt$$\int_a^b {f(x)} dx = \int_a^b {f(t)} dt$$ Then the answer would be

• A) do not changed
• B) changed
• C)
• D)

1+2+3+…+339 equals _____.

• A) 338(340)/6
• B) 338(339)/6
• C) 339(340)/2
• D) 338(340)/2

\[\text{The vertical asymptote of the function }f(x)=\frac{3{{x}^{2}}+1}{2-x}\text{ is}\]

• A) -2
• B) 0
• C) $\infty $
• D) 2

The symbol $\int {}$ was introduced by___________and is called integral sign.

• A) Leibnitz
• B) Lagrange
• C) Cauchy
• D) Newton

What is the estimated area under f(x) = 2x from x = 0 to x = 4 with mid points for n = 2?

• A) 10
• B) 8
• C) 18
• D) 16

$\text{A line }y={{y}_{\text{0}}}\text{ is called a horizontal asymptote for the graph of function }f\text{ if}$

• A) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)={{y}_{0}}$
• B) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=0$
• C) $\underset{x\to 0}{\mathop{\lim }}\,f(x)={{y}_{0}}$
• D) $\underset{x\to +\infty }{\mathop{\lim }}\,f(x)=\infty$

The maximum and minimum values of the function
f(x)=1/x does not lie in the interval [-1,1] because -------

• A) f(x) is discontinuous in [-1,1]
• B) f(x) is not one-to-one
• C) f(x) is differentiable in [-1,1]
• D) f(x) is continuous in [-1,1]

Integration of 3x^2 with respect to x is…………

• A) x^2
• B) x^3
• C) x
• D) x^4

If f(x) = Sec^ (2) x + x^3, then which of the following is NOT true about it.

• A) Its anti – derivative is Tan(x) + x^4/4 + 12.
• B) None of these.
• C) Its anti – derivative is Tan(x) + x^4/4 + 15.
• D) Its anti – derivative is Tan(x) + x^4/4 + 10.

Which of the following is the sum of 3k+1 where k goes from 0 to 2?

• A) 39
• B) 27
• C) 30
• D) 33

Sum of n-terms of a series whose nth term is ‘n’ = ---

• A) (n+1)/2
• B) n(n+1)/2
• C) n(n+1)
• D) n(n-1)/2

The indefinte integral of ‘cos (x) – sin (x)’ is………………

• A) cos (x) +sin (x)+c
• B) cos (x) .sin (x) +c
• C) -cos (x) + sin (x) +c
• D) -cos (x) – sin (x)+c

12+22+32+…+192 equals _____.

• A) 19(20)(21)/6
• B) 19(20)(31)/6
• C) 19(20)(37)/6
• D) 19(20)(39)/6

$${\text{The}}\,{\text{value}}\,{\text{of}}\,c\,{\text{in}}\,{\text{Rolle's}}\,{\text{Theorem}}\,{\text{for}}\,{\text{the}}\,{\text{function}}\,f(x) = {e^x}\sin x,\,\,x \in [0,\pi ]\,{\text{is}}\_\_\_\_\_\_\_\_\_\_.$$

• A) $$\frac{\pi }{4}$$
• B) $$\frac{{3\pi }}{2}$$
• C) $$\frac{\pi }{6}$$
• D) $$\frac{{3\pi }}{4}$$

summation of (3) ;where ( j varies from 1 to 4) indicates to add ………to itself 4 times.

• A) 2
• B) 3
• C) 4
• D) 1

The estimated area under f(x) = x^2 + 2 from
x = 1 to x = 5 with right end points for
n = 2 is ________.

• A) 28.
• B) 76.
• C) 30.
• D) 50.