MCA Entrance Previous Year Question Bank

Which of the following is false about

${\lim }_{y\to 0}\frac{\sqrt{1+\sqrt{1+y^4}}-\sqrt{2}}{y^4}$

(A) limit exist and equal to $\frac{1}{4\sqrt{2}}$

(B) limit does not exist

(C) limit exist and equal to $\frac{1}{2\sqrt{2}}$

(D) limit exist and equal to $\frac{1}{2\sqrt{2}(\sqrt{2}+1)}$

If the curve 𝑎𝑦+𝑥²=7 and 𝑥³=𝑦, cut orthogonally at (1, 1), then the value of a is -

The point(s) at which function $f(x)=\{\begin{array}{llc}\frac{x}{|x|};& x& lt;0\\ -1;& x\ge 0& \end{array}$ is continuous is/are

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A:${\int }_{-3}^3(x^3+5),dx=30$

Reason R:$f(x)=x^3+5$ is an odd function.

In the light of the above statements, choose the correct answer from the options given below:

Which of the following is true: A. Two vectors are said to be identical if their difference is zero. B. Velocity is not a vector quantity. C. Projection of one vector on another is not an application of dot product. D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function. Choose the most appropriate answer from the options given below:

Match List I with List II

Choose the correct answer from the options given below:

Which of the following functions is differentiable at x = 0?

If the parametric equation of a curve is given by $x=e^{t}cost$ and $y=e^{t}sint$ then the tangent to the curve at the point t = π/4 makes the angle with the axis of x is

$$\text{if }f(x)=\{\begin{array}{ll}x\sin \left(\frac{1}{x}\right),& x\ne 0\\ 0,& x=0\end{array}\text{, then }f(x)\text{ is }$$