List of practice Questions

The number of integers, greater than $7000$ that can be formed, using the digits $3,5,6,7,8$ without repetition, is
Let $A$ be a $3 \times 3$ matrix such that $|\operatorname{adj}(\operatorname{adj}(\operatorname{adj} A ))|=12^4$ Then $\mid A ^{-1}$ adj $A \mid$ is equal to
If the system of equations $ x+2 y+3 z=3$ $ 4 x+3 y-4 z=4 $ $ 8 x+4 y-\lambda z=9+\mu$ has infinitely many solutions, then the ordered pair $(\lambda, \mu)$ is equal to :
In AM modulation, a signal is modulated on a carrier wave such that maximum and minimum amplitude are found to be $6 V$ and $2 V$ respectively The modulation index is
The electric current in a circular coil of 2 turns produces a magnetic induction $B _1$ at its centre The coil is unwound and is rewound into a circular coil of 5 turns and the same current produces a magnetic induction $B _2$ at its centre The ratio of $\frac{ B _2}{ B _1}$ is :

A drop of liquid of density ρ is floating half immersed in a liquid of density σ and surface tension 7.5×10−4 Ncm−1. The radius of drop in cm will be : ( Take : g=10 m/s2)

Two billiard balls of mass $005\, kg$ each moving in opposite directions with $10 \, ms ^{-1}$ collide and rebound with the same speed If the time duration of contact is $t =0005 \, s$, then what is the force exerted on the ball due to each other?

For a free body diagram shown in the figure, the four forces are applied in the ' $x$ ' and ' $y$ ' directions What additional force must be applied and at what angle with positive $x$-axis so that the net acceleration of body is zero?

Capacitance of an isolated conducting sphere of radius $R_1$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius $R_2$ connected to earth The ratio of their radii $\left(\frac{ R _2}{ R _1}\right)$ is:
For an object placed at a distance $24\, m$ from a lens, a sharp focused image is observed on a screen placed at a distance $12\, cm$ from the lens A glass plate of refractive index $15$ and thickness $1 \,cm$ is introduced between lens and screen such that the glass plate plane faces parallel to the screen By what distance should the object be shifted so that a sharp focused image is observed again on the screen?
Light wave travelling in air along $x$-direction is given by $E_y=540 \sin \pi \times 10^4(x-c t) Vm ^{-1}$ Then, the peak value of magnetic field of wave will be (Given $c =3 \times 10^8 ms ^{-1}$ )
When you walk through a metal detectorcarrying a metal object in your pocket, itraises an alarm This phenomenon works on
An electron with energy $01\, keV$ moves at right angle to the earth's magnetic field of $1 \times 10^{-4} Wbm ^{-2}$ The frequency of revolution of the electron will be (Take mass of electron $=90 \times 10^{-31} kg$ )
A current of $15 \,mA$ flows in the circuit asshown in figure The value of potentialdifference between the points $A$ and $B$ will be
The length of a seconds pendulum at a height h=2R from earth surface will be :
(Given : R= Radius of earth and acceleration due to gravity at the surface of earth g=π2ms−2)
Sound travels in a mixture of two moles of helium and $n$ moles of hydrogen If rms speed of gas molecules in the mixture is $\sqrt{2}$ times the speed of sound, then the value of $n$ will be
Let $\eta_1$ is the efficiency of an engine at $T _1=447^{\circ} C$ and $T _2=147^{\circ} C$ while $\eta_2$ is the efficiency at $T _1=947^{\circ} C$ and $T _2=47^{\circ} C$ The ratio $\frac{\eta_1}{\eta_2}$ will be :
An object is taken to a height above the surface of earth at a distance $\frac{5}{4} R$ from the centre of the earth Where radius of earth, $R =6400 km$ The percentage decrease in the weight of the object will be
A bag of sand of mass $98\, kg$ is suspended by a rope A bullet of $200\, g$ travelling with speed $10\, ms ^{-1}$ gets embedded in it, then loss of kinetic energy will be
A ball is projected from the ground with a speed $15\, ms ^{-1}$ at an angle $\theta$ with horizontal so that its range and maximum height are equal, then'tan $\theta$ ' will be equal to
The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1\%,2\% and $3 \%$ respectively The maximum percentage error in the detection of the dissipated heat will be:
Hydrogen atom from excited state comes to the ground by emitting a photon of wavelength $\lambda$ The value of principal quantum number 'n' of the excited state will be :(R : Rydberg constant)

Match List I with List II :
 

List-I (molecule)List-II (hybridization; shape)
AXeO3​isp3d ; linear
BXeF2​iisp3; pyramidal
CXeOF4​iiisp3d3; distorted octahedral
DXeF6​ivsp3d2 ;square pyramidal


Choose the correct answer from the options given below:

Two solutions $A$ and $B$ are prepared by dissolving $1 g$ of non-volatile solutes $X$ and $Y$ respectively in $1 \,kg$ of water The ratio of depression in freezing points for $A$ and $B$ is found to be $1: 4$ The ratio of molar masses of $X$ and $Y$ is :
$Ka _1, Ka _2$ and $Ka _3$ are the respective ionization constants for the following reactions (a), (b) and (c)
(a) $H _2 C _2 O _4 \rightleftharpoons H ^{+}+ HC _2 O _4^{-}$
(b) $HC _2 O _4^{-} \rightleftharpoons H ^{+}+ HC _2 O _4^{2-}$
(c) $H _2 C _2 O _4 \rightleftharpoons 2 H ^{+}+ C _2 O _4^{2-}$
The relationship between $K _{ a _1}, K _{ a _2}$ and $K _{ a _3}$ is given as