List of practice Questions

If $ \omega \ne 1 $ is a cube root of unity, then the value of $ \left| \begin{matrix} 1+2{{\omega }^{100}}+{{\omega }^{200}} \\ 1 \\ \omega \\\end{matrix}\begin{matrix} {{\omega }^{2}} \\ 1+{{\omega }^{100}}+2{{\omega }^{200}} \\ {{\omega }^{2}} \\\end{matrix}\begin{matrix} 1 \\ \omega \\ 1+{{\omega }^{100}}+2{{\omega }^{200}} \\\end{matrix} \right| $ is equal to

If the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is

If the semi-major axis of an ellipse is 3 and the latus rectum is $\frac{16}{9},$ then the standard equation of the ellipse is

If $ \theta $ is semi vertical angle of a cone of maximum volume and given slant height, then $ tan\theta $ is equal to

The area bounded by the parabola $ {{y}^{2}}=8x $ and its latus rectum in sq unit is

The least integer satisfying $\frac{396}{10}-\frac{19-x}{10} < \frac{376}{10}-\frac{19-9x}{10}$ is

The value of the integral $\displaystyle \int_0^1$ $\frac{x^{3}}{1+x^{8}} dx$ is equal to

$\left(\frac{1+\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)}{1+\cos \left(\frac{\pi}{12}\right) - i \sin\left(\frac{\pi}{12}\right)}\right)^{72}$ is equal to

The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is

If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to

If A\B = {a, b}, B\A = {c, d} and A\B = {e, f}, then the set B is equal to

If $^n$C$_2$ + $^n$C$_3$ = $^6$C$_3$ and $^n$C$_x$ = $^n$C$_3$, x ? 3, then the value of x is equal to

The number of diagonals in a hexagon is

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

A ground receiver receives a signal at $5\, MHz$, transmitted by a ground transmitter at a height of $320\, m$, which is $110\, km$ away from it. Then it can communicate through (radius of earth $R \,= \,6400 \,km$)

A metallic bar of coefficient of linear expansion $10^{-5} K^{-1}$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The percentage increase in its length is

An experiment measures quantities $a$, $b$ and $c$, and quantity $X$ is calculated from $X= ab^2/c^3$. If the percentage error in $a$, $b$ and $c$ are $\pm 1\%$, $\pm 3\%$ and $\pm 2\%$, respectively, then the percentage error in $X$ will be

A battery of $6\,V$ and internal resistance $2 \Omega$ is connected to a silver voltameter. If the current of $1.5\, A$ flows through the circuit, the resistance of the voltameter is

If $m$ represents the mass of each molecule of a gas and $T$, its absolute temperature, then the root mean square velocity of the gaseous molecule is proportional to

A carbon resistor is marked with the ring coloured brown, black, green and gold. The resistance in ohm is

A Carnot engine is operating between a hot body and cold body maintained at temperature $T_1$ and $T_2$ respectively. Consider the following three cases : The temperature of the hot body is changed to $T_1 + \Delta T$ and cold body is at $T_2$ : The temperature of the hot body is at $T_1$ and cold body is changed to $T_2 + \Delta T$ : The temperature of the hot body is at $T_1$ and cold body is changed to $T_2 - \Delta T$

A linear harmonic oscillator with force constant 3.210N m and amplitude 0.01 m has a

The change in potential of the half-cell $Cu^{2+}|Cu$, when aqueous $Cu^{2+}$ solution is diluted $100$ times at $298 \,K$ ? $\left( \frac{2.303 RT}{F} = 0.06 \right)$

The number of lone pair and bond pair of electrons on the sulphur atom in sulphur dioxide molecule are respectively

The standard electrode potentials of $ A{{g}^{+}}/Ag $ is $ +0.80\text{ }V $ and $ C{{u}^{+}}/Cu $ is $ +0.34\text{ }V $ . These electrodes are connected through a salt bridge and if: