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Temperature of an ideal gas, initially at $27^{\circ} \mathrm{C}$, is raised by $6^{\circ} \mathrm{C}$. The rms velocity of the gas molecules will,

asked Dec 14, 2021 in Kinematics by kritika (90.1k points)

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A liquid of bulk modulus $k$ is compressed by applying an external pressure such that its density increases by $0.01 \%$. The pressure applied on the liquid is

asked Dec 14, 2021 in Kinematics by kritika (90.1k points)

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A uniform capillary tube of length / and inner radius $r$ with its upper end sealed is submerged vertically into water. The outside pressure is $\mathrm{p}_{0}$ and surface tension of water is $\gamma$. When a length $\mathrm{x}$ of the capillary is submerged into water, it is found that water levels inside and outside the capillary coincide. The value of $x$ is

asked Dec 14, 2021 in Kinematics by kritika (90.1k points)

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A uniform string of length $L$ and mass $M$ is fixed at both ends while it is subject to a tension $T$. It can vibrate at frequencies $(v)$ given by the formula (where $n=1,2,3, \ldots .$.)

asked Dec 14, 2021 in Kinematics by kritika (90.1k points)

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The velocity of a particle executing a simple harmonic motion is $13 \mathrm{~ms}^{-1}$, when its distance from the equilibrium position (Q) is $3 \mathrm{~m}$ and its velocity is $12 \mathrm{~ms}^{-1}$, when it is $5 \mathrm{~m}$ away from $\mathrm{Q}$. The frequency of the simple harmonic motion is

asked Dec 14, 2021 in Kinematics by kritika (90.1k points)

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test test test test

asked Dec 14, 2021 in Kinematics by deepak01 (12.2k points)

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Let $f(x)=\cos \left(\frac{\pi}{x}\right), x \neq 0$ then assuming $k$ as an integer,

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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A hyperbola, having the transverse axis of length $2 \sin \theta$ is confocal with the ellipse $3 x^{2}+4 y^{2}=12$. Its equation is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The area of the triangle formed by the intersection of a line parallel to $x$-axis and passing through $P(h, k)$, with the lines $y=x$ and $x+y=2$ is $h^{2}$. The locus of the point $P$ is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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In a third order matrix $\mathrm{A}, \mathrm{a}_{i j}$ denotes the element in the $\mathrm{i}$-th row and $\mathrm{j}$-th column. $$ \text { If } \begin{aligned} a_{i} &=0 \text { for } i=j \\ &=1 \text { for } i>j \\ &=-1 \text { for } i<j \end{aligned} $$ Then the matrix is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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On the occasion of Dipawali festival each sutdent of a class sends greeting cards to others. If there are 20 students in the class, the number of cards sends by students is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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If the equation $x^{2}-c x+d=0$ has roots equal to the fourth powers of the roots of $x^{2}+a x+b=0$, where $a^{2}>4 b$, then the roots of $x^{2}-4 b x+2 b^{2}-c=0$ will be

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The area of the region lying above $x$-axis, and included between the circle $x^{2}+y^{2}=2 a x \&$ the parabola $y^{2}=a x$, $a>0$ is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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A particle is in motion along a curve $12 y=x^{3}$. The rate of change of its ordinate exceeds that of abscissa in

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let $I=\int_{0}^{1} \frac{x^{3} \cos 3 x}{2+x^{2}} d x$. Then

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Consider the parabola $y^{2}=4 x .$ Let $P$ and $Q$ be points on the parabola where $P .(4,-4) \& Q(9,6) .$ Let $R$ be a point on the arc of the parabola between $\mathrm{P} \& \mathrm{Q}$. Then the area of $\triangle \mathrm{PQR}$ is largest when

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The equation $x \log x=3-x$

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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The normals to the curve $y=x^{2}-x+1$, drawn at the points with the abscissa $x_{1}=0, x_{2}=-1$ and $x_{3}=\frac{5}{2}$

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let $f(x)=\left\{\begin{array}{cl}-2 \sin x, & \text { if } x \leq-\frac{\pi}{2} \\ A \sin x+B, & \text { if }-\frac{\pi}{2}<x<\frac{\pi}{2} . \text { Then } \\ \cos x, & \text { if } x \geq \frac{\pi}{2}\end{array}\right.$

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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Let $A$ be the centre of the circle $x^{2}+y^{2}-2 x-4 y-20=0 .$ Let $B(1,7)$ and $D(4,-2)$ be two points on the circle such that tangents at $B$ and $D$ meet at $C$. The area of the quadrilateral $A B C D$ is

asked Dec 13, 2021 in Sets, relations and functions by kritika (90.1k points)

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