If $y=\sqrt{\frac{1-x}{1+x}}$, then $(1-x^2)\frac{dy}{dx}+y$ is

1

The function $f(x)=\sqrt{|x|-x}$ is continuous for

Topic: AMU MCA 2017

2

If $y=e^{x}+e^{x+e^{x}}+e^{x+e^{x+e^{x}}}+\dots$, then $\frac{dy}{dx}$ is equal to

Topic: AMU MCA 2017

3

The total revenue in rupees received from the sale of $x$ units of a product is given by $R(x)=5x^2+20x+7$. The margina…

Topic: AMU MCA 2017

4

Differentiate y = sin⁻¹((1 - x²)/(1 + x²)), 0 < x < 1 with respect to x.

Topic: AMU MCA 2017

5

The area of the region bounded by the two parabolas $y=x^2$ and $y=x$ is

Topic: AMU MCA 2017

6

The integral $\int e^x (1+\tan x)\sec x , dx$ equals

Topic: AMU MCA 2017

7

$\int \frac{\sin^2 x - \cos^2 x}{\sin^2 x \cos^2 x} dx$ is equal to

Topic: AMU MCA 2017

8

$\int_{1}^{\sqrt{3}} \frac{dx}{1+x^2}$ equals

Topic: AMU MCA 2017

9

The general solution of differential equation $\frac{dy}{dx}+2xy=2e^{-x^2}$ is

Topic: AMU MCA 2017

10

The function $y=c_1\cos x+c_2\sin x$ is a solution of the D.E. where $c_1$ and $c_2$ are real numbers

Topic: AMU MCA 2017

1

If the system of equations$2x+ay+6z=8$$x+2y+bz=5$$x+y+3z=4$has a unique solution then

Topic: AMU MCA 2017

2

If $a, b, c$ are roots of the equation $x^3 + px + q = 0$, then the value of $\begin{vmatrix} a & b & c \\ b & c & a …

Topic: AMU MCA 2017

3

If $y = \sin(mx)$, then the value of the determinant $\begin{vmatrix} y & y_1 & y_2 \\ y_3 & y_4 & y_5 \\ y_6 & y_7 …

Topic: AMU MCA 2017

4

If $A=\begin{bmatrix}2 & 3 \\ 5 & -2\end{bmatrix}$ be such that $A^{-1}=\lambda A$. Then, the value of $\lambda$ is

Topic: AMU MCA 2017

5

If $A=\begin{bmatrix}\alpha & 0 \\ 1 & 1\end{bmatrix}$ and $B=\begin{bmatrix}1 & 0 \\ 5 & 1\end{bmatrix}$ and $A^2=B$, …

Topic: AMU MCA 2017

6

$\sin^{-1}\left(\frac{8}{17}\right) + \sin^{-1}\left(\frac{3}{5}\right)$ is equal to

Topic: AMU MCA 2017

7

If $\cos^{-1} \sqrt{p} + \cos^{-1} \sqrt{1 - p} + \cos^{-1} \sqrt{1 - q} = \frac{3\pi}{4}$, then the value of $q$ is:

Topic: AMU MCA 2017

8

The function $f(x) = \cos x$ is strictly decreasing on:

Topic: AMU MCA 2017

9

If $^nP_4 = 20 \times ^nP_2$. Then, the value of $n$ is:

Topic: AMU MCA 2017

10

If $\sin^{-1} x - \cos^{-1} x = \frac{\pi}{6}$, then the value of $x$ is:

Topic: AMU MCA 2017