The condition that the line $\dfrac{x}{a}\cos\theta+\dfrac{y}{b}\sin\theta=1$ touches the circle $r=2c\cos\theta$ is
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The equation $\dfrac{8}{r}=4-5\cos\theta$ represents
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The tangents at the extremities of a focal chord of a parabola intersect on the directrix at an angle
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Solution of differential equation
$y^2\log y = xy\frac{dy}{dx}+\left(\frac{dy}{dx}\right)^2$ is
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If Laplace transform $L{F(x)}=\frac1{s}e^{-3s}$, then $L{e^{-x}F(3x)}$ is
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If $I=\oint_C e^x,dx+2y,dy-dz$,
where $C$ is the curve $x^2+y^2=4$ and $z=2$, then the value of $I$ is
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The value of the integral
$I=\iint_R e^{x^2+y^2},dy,dx$
where $R$ is the semicircular region bounded by the $x$-axis a…
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In what direction is the derivative of $f(x,y)=x^2-xy+y^2$ at $P(1,-1)$ equal to zero?
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The number of asymptotes of the curve $y^2=ax$ is
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The asymptotes of $\dfrac{a^2}{x^2}+\dfrac{b^2}{y^2}=1$ are
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$\lim_{x\to0}\dfrac{\sin x - x + \frac{x^3}{6}}{x^5}$ is equal to
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Next 10 Questions — AMU MCA 2022
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If the centre of mass of three particles of masses 10, 20 and 30 gram be at the point $(1,-2,3)$, where should a fourth…
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A sphere of mass 0.5 kg and diameter 0.1 m rolls without slipping with a velocity of 0.2 m/s. The total energy of the s…
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The origin of two frames of reference $S$ and $S'$ coincide initially. The frame $S'$ is moving with velocity $(2\mathb…
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A body of mass $m_0$ is placed in a rocket. The rocket is moving with velocity $v=0.8c$. Then, the mass observed by a p…
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Two particles of rest mass $m_0$ approach each other with equal and opposite velocities $v$ in the lab frame. The total…
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If the Thevenin’s theorem is applied to the circuit given below: The current through the $Z_L=6\Omega$ resistor of…
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A circuit consists of a capacitor of 100pF connected in series with a coil of resistance $5\Omega$ and inductance $100\…
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The electrical susceptibility of a material is $44.3\times10^{-12}$ coulomb$^2$/Newton-m$^2$. The value of dielectric c…
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An anti-reflection coating of thickness 0.1μm is to be deposited on a glass plate for normal incidence of light of wave…
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Un-polarized light of intensity $I_0$ passes through a polarizer $P_1$. The light coming out of the polarizer falls on …
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