Let $f(x)$ be continuous whose values are known at $-2,-1,1,2$. If the Lagrange interpolation formula $f(x)=L_1f(-2)+L_2f(-1)+L_3f(1)+L_4f(2)$ is used to approximate $f(0)$, then $L_3$ is
Previous 10 Questions — AMU MCA 2020
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The shortest distance from the point $(1,0,-2)$ to the plane
$x+2y+z=4$ is
Topic: AMU MCA 2020
The general solution of the differential equation
$(D^2 - a^2)^3 y = e^{ax}$, where $D=\frac{d}{dx}$ is
Topic: AMU MCA 2020
The solution of the linear difference equation $y_{k+1}-ay_k=0$, $a\ne 1$ 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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$\lim_{(x,y)\to(0,0)} f(x,y)$ where $f(x,y)=\tan^{-1}\left(\frac{|x|+|y|}{x^2+y^2}\right)$ is
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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…
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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…
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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
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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
Next 10 Questions — AMU MCA 2020
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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
If $x \ge 1$ is the critical region for testing $H_0:\theta=2$ against $H_1:\theta=1$, on the basis of a single observa…
Topic: AMU MCA 2020
The standard deviation of sample means is called
Topic: AMU MCA 2020
If $X$ has an exponential distribution with mean $3$, then the variance of $X$ is
Topic: AMU MCA 2020
A lot consists of 20 defective and 80 non-defective items. Two items are drawn at random without replacement. What is t…
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Suppose random variable $X$ has possible values $1,2,3,\dots$ and $P(X=j)=\frac{1}{2^j}$, $j=1,2,3,\dots$ then $P(X \te…
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Coefficient of correlation is equal to
Topic: AMU MCA 2020
If $X$ has discrete uniform distribution with pmf $f(x)=\frac{1}{8}$ for $x=1,2,\dots,8$, then the mean of the distribu…
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If $P(X=0)=1-P(X=1)$ and $E(X)=3V(X)$, the value of $P(X=0)$ is
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