If PSP' and QSQ' be two perpendicular focal chords of parabola $y^2 = 4x$, then $\frac{1}{SP \cdot SP'} + \frac{1}{SQ \cdot SQ'}$ equals

1

Let $T : \mathbb{R}^2 \to \mathbb{R}^3$ defined by $T(x,y) = (-x-y, 3x+8y, 9x-11y)$. Then the rank and nullity of $T$ a…

Topic: AMU MCA 2020

2

The direction cosines of the line which is equally inclined to the axes is

Topic: AMU MCA 2020

3

The equation of the cone reciprocal to $x^2 + 2y^2 + 3z^2 = 0$ is

Topic: AMU MCA 2020

4

The general solution of $y = 2x \frac{dy}{dx} + y\left(\frac{dy}{dx}\right)^2$ is

Topic: AMU MCA 2020

5

If $A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}$ satisfies the matrix equation $A^2 - kA + 2I = 0$, then the val…

Topic: AMU MCA 2020

6

Let $T$ be a linear operator on $\mathbb{R}^3$ defined by $T(x,y,z) = (2x,; x-y,; 5x + 4y + z)$ Then $T^{-1}$ is

Topic: AMU MCA 2020

7

An integrating factor for $(\cos y \sin 2x)dx + (\cos^2 y - \cos^2 x)dy = 0$

Topic: AMU MCA 2020

8

Which of the following is not true?

Topic: AMU MCA 2020

9

The solution of $\frac{dx}{x^2 - yz - z^2} = \frac{dy}{2xy} = \frac{dz}{2xz}$ is given by

Topic: AMU MCA 2020

10

Let $V$ be a 3-dimensional vector space with $A$ and $B$ its subspaces of dimensions $2$ and $1$ respectively. If $A \c…

Topic: AMU MCA 2020

1

The equation of axis of the conic $\sqrt{ax} + \sqrt{by} = 1$ is

Topic: AMU MCA 2020

2

If the Trapezoidal rule with interval $[0,1]$ is exact for approximating the integral $\int_{0}^{1} (x^3 - cx^2)\,dx$,…

Topic: AMU MCA 2020

3

If $S$ is the set of all real numbers except $-1$ and $*$ is defined by $a * b = a + b + ab$, then the inverse of $2 *…

Topic: AMU MCA 2020

4

Equation of the cone with vertex at origin and direction cosines of generators satisfying $l^2 + 2m^2 - 3n^2 = 0$ is g…

Topic: AMU MCA 2020

5

Let $f(x,y,z) = e^{\sqrt{1 - x^2 - y^2}}$. Then the range of $f$ is

Topic: AMU MCA 2020

6

Let $G$ be a group having elements $a$ and $b$ such that $O(a)=4$, $O(b)=2$ and $a^3 b = ba$. Then $O(ab)$ is

Topic: AMU MCA 2020

7

The value of $\iint_R y\sin(ny)\,dA$, where $R=[1,2]\times[0,\pi]$ is

Topic: AMU MCA 2020

8

The volume of the solid in the first octant bounded by the cylinder $z=9-y^2$ and the plane $x=2$ is

Topic: AMU MCA 2020

9

The volume of the solid that lies under the paraboloid $z=x^2+y^2$ above the $xy$-plane, and inside the cylinder $x^2+y…

Topic: AMU MCA 2020

10

Consider the series $x_{n+1}=\frac{x_n}{2}+\frac{9}{8x_n}$, $x_0=0.5$ obtained from the Newton-Raphson method. The seri…

Topic: AMU MCA 2020