List of practice Questions

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

The power of $x$ in the term with the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is:

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $ \Delta ABC $ is at $(3, 2, 1)$, then the equation of the plane is

How many four digit numbers $abcd$ exist such that $a$ is odd, $b$ is divisible by $3$, $c$ is even and $d$ is prime?

If $\tan^{-1} x$ + $\tan^{-1} y$ = $\frac{2\pi}{3 }$ , then $\cot^{-1} x$ + $\cot^{-1} y$ is equal to

If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to

The position of a particle is given by $ r =\hat{i}+2\hat{j}-\hat{k} $ and its linear momentum is given by $ p = 3\hat{i}+4\hat{j}-2\hat{k} $ . Then its angular momentum, about the origin is perpendicular to

In a group of 6 boys and 4 girls, a team consisting of four children is formed such that the team has atleast one boy. The number of ways of forming a team like this is

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $0.2$. When $T_2$ is reduced by $50\, K$, its efficiency increases to $0.4$. Then $T_1$ and $T_2$ are respectively

A glass tube of length $ 1.0\, m $ is completely filled with water. A vibrating tuning fork of frequency $ 500 \,Hz $ is kept over the mouth of the tube and the water is drained out slowly at the bottom of the tube. If velocity of sound in air is $ 330\,m{{s}^{-1}}, $ then the total number of resonances that occur will be

An electron enters uniform electric field maintained by parallel plates and of value $ EV{{m}^{-1}} $ with a velocity $ v\text{ }m{{s}^{-1}}, $ the plates are separated by a distance $ d $ metre, then acceleration of the electron in the field is:

An electron, placed in an electric field, experiences a force F of $1\, N.$ What are the magnitude and direction of the electric field E at the point where the electron is located $(e = 1.6 \times 10^{-19} C)$ ?

$CO^-$ ion moving with kinetic energy of $20\, keV$ dissociates into $O^-$ and $C$ which move along the parent ion direction. Assuming no energy is released during dissociation, the kinetic energy of the daughters $(K.E)_{O^-}$ and $(K.E)_C$ are related as

Find the total capacitance and total charge on the capacitors

For an ideal gas, the specific heat at constant pressure $C_P$ is greater than the specific heat at constant volume $C_V$ . This is because

A $ 2\mu C $ charge moving around a circle with a frequency of $ 6.25\times {{10}^{12}}Hz $ produces a magnetic field $6.28\, T$ at the centre of the circle. The radius of the circle is

A common emitter amplifier gives an output of $ 3 \,V $ for an input of $ 0.01 \,V $ . If $ \beta $ of the transistor is $100$ and the input resistance is $ 1\text{ }k\Omega , $ then the collector resistance is

1 mole of $FeSO_4$ (atomic weight of Fe is $55.84 \, g \, mol^{-1}$) is oxidized to $Fe_2(SO_4)_3$. Calculate the equivalent weight of ferrous ion

An alloy of transition metal containing a non transition metal as a constituent is

Gd$(64)$ has _____ unpaired electrons with sum of spin _____

Propanal on reaction with dilute sodium hydroxide forms:

A dye that imparts different colours to the fabric with different metal ions is called

An important industrial solvent, also a laboratory reagent called 2-butanone is nothing but:

An invert sugar is