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Find the change in internal energy of a gas if its temperature changes by 10K. Moles=10, $C_{p}=7 cal K^{-1}mol^{-1}$, $R=2~cal~K^{-1}mol^{-1}$.

If the domain of the function $\cos^{-1}(\frac{2x-5}{11x-7})+\sin^{-1}(2x^{2}-3x+1)$ is $[a,b]$, then the value of $\frac{1}{ab}$ is:

1 g of $AB_{2}$ is dissolved in 50 g of a solvent such that $\Delta T_{f}=0.689~K.$ When 1 g of AB is dissolved in 50 g of the same solvent, $\Delta T_{f}=1.176~K$. Find the molar mass of $AB_{2}$. (Report to nearest integer).

Two rods of equal length 60 cm each are joined together end to end. The coefficients of linear expansion are $24\times10^{-6\circ}C^{-1}$ and $1.2\times10^{-5\circ}C^{-1}$. Initial temperature $30^{\circ}C$ is increased to $100^{\circ}C$. Find final length (in cm).

A wave propagates whose electric field is given by $\vec{E}=69~\sin(\omega t-kx)\hat{j}$. Find the direction of the magnetic field.

If $f(3)=18$, $f'(3)=0$ and $f''(3)=4$ then the value of $\lim_{x\rightarrow1}\ln(\frac{f(x+2)}{f(3)})^{\frac{18}{(x-1)^{2}}}$ is:

The value of $\int_{\frac{\pi}{6}}^{\pi}\frac{\pi+4x^{11}}{1-\sin(|x|+\frac{\pi}{6})}dx$ is:

If O is the vertex of the parabola $x^{2}=4y,$ Q is a point on the parabola. If C is the locus of the point which divides OQ in the ratio $2:3,$ then the equation of the chord of C which is bisected at the point (1,2) is: (Duplicate Question)

Which of the following resonating structures is the most stable?

Find the volume flow rate in the Venturi meter shown below in which water is flowing. Given $\frac{A}{a}=2$, $A=\sqrt{3}m^{2}$, difference in levels is 5 cm and $\rho=1000~kg~m^{-3}$.

If $A=\{1,2,3,4,5,6\}$ and $B=\{1,2,3,...,9\}$, then the number of strictly increasing functions $f:A\rightarrow B$ such that $f(i)\ne i$ for all $i$ is:

If the mean and variance of observations $x, y, 12, 14, 4, 10, 2$ is 8 and 16 respectively, where $x>y$, then the value of $3x-y$ is:

Ellipse E: $\frac{x^{2}}{36}+\frac{y^{2}}{16}=1$. A hyperbola is confocal with the ellipse and the eccentricity of the hyperbola is equal to 5. If the principal axis of the hyperbola is the x-axis, then the length of the latus rectum of the hyperbola is:

Consider the following reaction: $Ca+2HCl \rightarrow CaCl_2+H_2$. If 14g of calcium reacts with excess HCl, choose the incorrect option.

80 mL of an organic compound is mixed with 264 mL of $O_{2}$ and ignited. It gives 224 mL of gaseous mixture at NTP. After passing through KOH, 64 mL of gas remains. The organic compound is:

If the electric field of an EM wave is given by $60[\sin(3\times10^{14}t)+\sin(12\times10^{14}t)]$ at $x=0$ and it falls on a photosensitive material having work function $2.8 eV$, find the maximum kinetic energy (in eV) of the ejected electrons.

Find the moment of inertia of the system formed using two identical rods about the given axis of rotation as shown in the figure. Each rod has mass M and length L.

If $x^{2}+x+1=0$ then evaluate $(x+\frac{1}{x})^{4}+(x^{2}+\frac{1}{x^{2}})^{4}+...+(x^{25}+\frac{1}{x^{25}})^{4}$

Observe the following reaction sequence: $(P)\xrightarrow{NH_{3}, \Delta}(Q)\xrightarrow{Br_{2}/KOH}(R)$. Which of the following is the correct structure for P, Q and R? (Refer to image)

An air-filled capacitor of capacitance $C$ is filled with a dielectric $(k=3)$ of width $\frac{d}{3}$, where $d$ is the separation between the plates. The new capacitance is: