List of practice Questions

The sides of a triangle are in the ratio $ 1 : \sqrt 3 : 2 $, then the angles of the triangle are in the ratio
If f(x) is differentiable and $\int_0^{t^2}x f(x) dx =\frac{2}{5}t^5,$ then $f\bigg(\frac{4}{25}\bigg)$ equals
If y is a function of x and $\log (x + y) = 2xy$, then the value of y ' (0) is
If one of the diameters of the circle $x^2 + y^2 - 2x - 6y + 6 = 0$ is a chord to the circle with centre (2,1), then the radius of the circle is
If $^{n-1}C_r =(k^2 -3) \, ^nC_{r+1}$then k belongs to
Given both $\theta and \phi are acute angles and sin \theta=\frac{1}{2}, cos \phi=\frac{1}{3},$ then the value of $\theta+\phi $ belongs to
An infinite GP has first term x and sum 5, then x belongs to
If one root is square of the other root of the equation $x^2+px+q=0,$ then the relation between p and q is
If $\omega (\ne 1)$ be a cube root of unity and $(1 + \omega^2)^n = (1 + \omega^4)^n,$ then the least positive value of n is
An ideal gas expands isothermally from a volume $V_1$ to $ V_2$and then compressed to original volume $V_1$ adiabatically. Initial pressure is p$_1$ and final pressure is p$_3$. The total work done is W. Then,
After 280 days, the activity of a radioactive sample is 6000 dps. The activity reduces to 3000 dps after another 140 days. The initial activity of the sample in dps is
Acetaldehyde cannot show
A source of sound of frequency 600 Hz is placed inside water. The speed of sound in water is 1500m/s and in air it is 300 m/s. The frequency of sound recorded by an observer who is standing in air is
A sodium salt of an unknown anion when treated with $ MgCl_2 $ gives white precipitate only on boiling. The anion is
A particle is placed at the origin and a force F = kx is acting on it (where k is a positive constant). If U (0) = 0, the graph of U (x) versus x will be (where U is the potential energy function)
Triple fusion in angiosperms is the fusion of second sperm with
Liquid oxygen at 50 K is heated to 300 K at constant pressure of 1 atm. The rate of heating is constant. Which of the following graphs represent the variation of temperature with time?
2-Hexyne gives trans-2-hexene on treatment with
Which of the following has -O-O- linkage?
$(NH_4)_2Cr_2 O_7$ on heating gives a gas which is also given by
Spontaneous adsorption of a gas on solid surface is an exothermic process, because
When $I^-$ is oxidised by $MnO_4^-$ in alkaline medium, $I^-$ converts into
The correct statement(s) for orthoboric acid is/'are
Which of the following is an antigibberellin?
Which one of the following is vestigial organ of human?