Newton’s Method fails to find the approximate solution of an equation if _____________.

• A) the slope of the tangent line(at any approximated point) is non-zero
• B) the tangent line(at any approximated point) is parallel to x-axis.
• C) None of these
• D) the tangent line (at any approximated point) is not parallel to x-axis.

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

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

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

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

If x = (1^2)+(2^2)+(3^2)+(4^2) + . . . + (30^2), then x = ________.

• A) 9455.
• B) None of these.
• C) 900.
• D) 465.

If $f''(x) < 0\,\forall \,x \in I$, then the graph of $f$ is ___________ on $I$.

• A) concave upward
• B) constant
• C) None of these
• D) concave downward

For the area under the curve f(x) = 2x from x = 0 to x = 8 with mid points approximations for n = 2, what will be the values of xk* ?

• A) 1 and 5
• B) 4 and 6
• C) 3 and 7
• D) 2 and 6

The indefinite integral of ‘sec(x)tan(x)’ is…………….

• A) Cotx +c
• B) Sinx+c
• C) Tanx+c
• D) Secx+c

In the indefinite integral of x(y^2) w.r.t ‘y’ , the independent variable is ……..

• A) xy
• B) y
• C) none of these
• D) x

If [-8,8] is subdivided into ‘16’ equally spaced subintervals, then the LEFT end point of 13th sub-interval will be--------.

• A) 2
• B) 4
• C) 3
• D) 5

What is the estimated area under f(x) = 9 - x2 from x = 0 to x = 4 with mid points for n = 2?

• A) 25
• B) 16
• C) 21
• D) 12

If x=-3 and x=3 are the two critical points of the function: f(x)=81x-3(x^3) then by using the 2nd derivative test, we can conclude that f(x) is relatively maximum at-----

• A) x= -9
• B) x= 3
• C) x=0
• D) x=-3

$${\text{The integral }}\int {{{\sec }^2}(2{x^2})\,.4x\,dx\,} {\text{will be equal to ?}}$$

• A) $${\text{se}}{{\text{c}}^2}(2x) + c$$
• B) $$\tan (2{x^2}) + c$$
• C) $$\sec (2{x^2}).\tan (2{x^2}) + c$$
• D) $$\tan (2x) + c$$

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

• A) Square of n(n+1)(2n+1)/6
• B) Square of n(n+1)/2
• C) Square of n(n+1)/6
• D) Square of (n+1)/2

‘x.ln(x/e)’ is the anti-derivative of ‘lnx’ if and only if the derivative of ‘x.ln(x/e)’ is euqal to --------

• A) x
• B) xln(x/e)
• C) ln(x/e)
• D) lnx

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

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

If f'(r) =0 at some approximation “r” then we cannot proceed on Newton’s method.

• A) False
• B) True
• C)
• D)

Integration of 4Cosx with respect to x is………..

• A) 4Sinx
• B) - 4Sinx
• C)
• D)

If f(x) = Sin(x) + x, then which of the following is true about it

• A) None of these.
• B) Its anti – derivative is Cos(x) + x^2/2 + 10.
• C) Its anti – derivative is –Cos(x) + x^2/2 + 10.
• D) Its anti – derivative is Cos(x) + 1.

Summation of ‘kx’ where k goes from 1 to 5 equals

• A) 15x
• B) None of these
• C) 55
• D) 15k

If ‘n’ goes from 1 to 3 and the summation of ‘na’ = 6a, then the value of ‘a’ is ----------

• A) Undetermined
• B) 6
• C) -6
• D) 1