The volume of the solid in the first octant bounded by the cylinder $z=9-y^2$ and the plane $x=2$ is
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The value of $\iint_R y\sin(ny)\,dA$, where $R=[1,2]\times[0,\pi]$ is
Topic: AMU MCA 2020
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
Let $f(x,y,z) = e^{\sqrt{1 - x^2 - y^2}}$. Then the range of $f$ is
Topic: AMU MCA 2020
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
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 *…
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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
The equation of axis of the conic $\sqrt{ax} + \sqrt{by} = 1$ is
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If PSP' and QSQ' be two perpendicular focal chords of parabola $y^2 = 4x$, then $\frac{1}{SP \cdot SP'} + \frac{1}{SQ \…
Topic: AMU MCA 2020
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
The direction cosines of the line which is equally inclined to the axes is
Topic: AMU MCA 2020
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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
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
$\lim_{(x,y)\to(0,0)} f(x,y)$ where $f(x,y)=\tan^{-1}\left(\frac{|x|+|y|}{x^2+y^2}\right)$ is
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The value of $\int_C (y^2\,dx + x^2\,dy)$, where $C$ is the triangle given by $x=0$, $x+y=1$, $y=0$ is
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The solution of the linear difference equation $y_{k+1}-ay_k=0$, $a\ne 1$ is
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The general solution of the differential equation
$(D^2 - a^2)^3 y = e^{ax}$, where $D=\frac{d}{dx}$ is
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The shortest distance from the point $(1,0,-2)$ to the plane
$x+2y+z=4$ is
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Let $f(x)$ be continuous whose values are known at
$-2,-1,1,2$. If the Lagrange interpolation formula
$f(x)=L_1f(-2)+…
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In the analysis of data of a randomized block design with 5 blocks and 4 treatments, the error degrees of freedom is:
Topic: AMU MCA 2020
The following LPP
Maximize $z = x_1 + x_2$
Subject to
$x_1 + x_2 \le 1$
$-3x_1 + x_2 \ge 3$
$x_1, x_2 \ge 0$
Topic: AMU MCA 2020
