List of practice Questions

Progestasert is an IUD which makes the uterus unsuitable and cervix hostile the sperms as they are

Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $'\theta'$ with the vertical. If wires have mass $\lambda$ per unit length then, the value of $I$ is : ( $g =$ gravitational acceleration)

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}}$. Measured value of $L$ is $20.0\, cm$ known to $1\, mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\, s$ using a wrist watch of $1\, s$ resolution. The accuracy in the determination of $g$ is

A $25\, cm$ long solenoid has radius $2\, cm$ and $500$ total number of turns. It carries a current of $15\, A$. If it is equivalent to a magnet of the same size and magnetization $|\bar{M}|$ (magnetic moment/volume), then $|\bar{M}|$ is :

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is

Let k be a non-zero real number. If $f(x) = \begin{cases} \frac{\left(e^x-1\right)^2}{sin\left(\frac{x}{k}\right)log\left(1+\frac{x}{4}\right)}, & \text{x $\ne$ 0} \\[2ex] 12, & \text{x = 0} \end{cases}$ is a continuous function, then the value of $k$ is :

The de - Broglie wavelength associated with the electron in the $n = 4$ level is :

A colour blind man marries a woman with normal sight who has no history of colour blindness in her family. What is the probability of their grandson being colour blind ?

Tannins give positive test for all of the following EXCEPT
(P) Goldebeater skin test
(Q) Phenazone
(R) Biuret test
(S) FeCl

The $pH$ of a solution obtained by mixing of $100\, mL$ of a $HCl$ solution of $pH = 2$ with $400\, mL$ of another $HCl$ solution of $pH = 3$ will be

The work done by electric field during the displacement of a negatively charged particle towards a fixed positively charged particle is $9\, J$. As a result the distance between the charges has been decreased by half. What work is done by the electric field over the first half of this distance?

The conductivity of an electrolyte is very low as compared to a metal at room temperature. The number density of free ions in electrolyte is much smaller as compared to number density of free electrons in metals. Further, ions drift much more slowly, being heavier.

At $t = 0$, the function $f \left(t\right) = \frac{sin\,t}{t}$ has

If p : It rains today, q : I go to school, r : I shall meet my friends and s : I shall go for a movie, then which of the following is the proportion? If it does not rain or if I do not go to school, then I shall meet my friend and go for a movie.

If $(2, 7, 3)$ is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6\,x -12\,y -2\,z + 20 = 0$, then the coordinates of the other end of the diameter are

The value of $ \displaystyle \sum^{30}_{r = 16} (r + 2)(r - 3)$ is equal to :

A complex number $z$ is the said to be unimodular if $|z|=1 .$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z_{1}-2 z_{2}}{2-z_{1} z_{2}}$ is unimodular and $z _{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

The solution of the differential equation $ydx - (x + 2y^2)dy = 0$ is $x = f(y)$. If $f(- 1) = 1$, then $f(1)$ is equal to :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :

The term independent of $x$ in the binomial expansion of $\left(1-\frac{1}{x}+3x^{5}\right)\left(2x^{2}-\frac{1}{x}\right)^{8}$ is :

The mean of the data set comprising of $16$ observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is

The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$

In a $\Delta ABC$, the lengths of the two larger sides are $10$ and $9$ units, respectively. If the angles are in AP, then the length of the third side can be

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=k r^{a}$, where $k$ and a are constants and $r$ is the distance from its center. If the electric field at $r =\frac{R}{2}$ is times that at $r = R$, the value of $a$ is