List of practice Questions

An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1 st, 2 nd, 3 rd and 4 th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?
An $A.P.$ has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is $13$, then the common difference is
If the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is
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
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:
Four point charges (with equal magnitude of charge of $5\, C$; but with different signs) are placed at four corners of a square of side $10\, m.$ Assuming that the square is centered at the origin and the configuration of the charges are as given in the figure, the potential and the magnitude of electric field at the origin, respectively are [ Note : $k = \frac{1}{4 \pi \varepsilon_0}$]
The apparent frequency observed by a moving observer away from a stationary source is $20\%$ less than the actual frequency. If the velocity of sound in air is $330 \; ms^{-1}$ , then the velocity of the observer is
The current $ I $ through $ 10\,\Omega $ resistor in the circuit given below is
The dimensional formula for rate of doing work is