List of practice Questions

Let $f$ be a non-negative function defined on the interval [0,1].if $\int_0^x \sqrt{1-(f'(t))^2}dt = \int_0^x f(t) dt , 0 \le x \le 1$ and $f (0) = 0$, then
In a $\triangle$ ABC w ith fixed base BC, the vertex A moves such that cos B + cos C = 4 $ sin^2 \frac{A}{2}$. If a, b and c denote th e lengths of th e sides of th e triangle opposite to the angles A, B and C respectively, then
A line with positive direction cosines passes through the point $P (2, -1, 2)$ and makes equal angles with the coordinate axes. The line meets the plane $2x + y+ z = 9$ at point $Q$. The length of the line segment $PQ$ equals
If the force acting on a body is inversely proportional to its speed, then its kinetic energy is
In inelastic collision
A sphere is rolling without slipping on a fixed horizontal plane surface In the figure, A is the point of contact. B is the centre of the sphere and C is its topmost point. Then,
C$_v$ and C$_p$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respectively. Then,
Ablockofbase $l0 cm\times10 cm$ and height 15 cm is kept on an inclined plane. The coefficient of friction between them is $\sqrt3$. The inclination $\theta$ of this inclined plane from the horizontal plane is gradually increased from 0$^{\circ}$. Then
A student performed the experiment to measure the speed of sound in air using resonance air-column method. Two resonances in the air-column were obtained by lowering the water level. The resonance with the shorter air-column is the first resonance and that with the longer air column is the second resonance. Then,
A ball is dropped from a height of $20\, m$ above the surface of water in a lake. The refractive index of water is$\frac{4}{3}$ A fish fish inside the lake, in the line of fall of the ball, is looking at the ball. At an instant, when the ball is 12.8 m above the water surface, the fish sees the speed of ball as ($Take g = 10\,m/s^2$)
Which of the following provides most evident proof of evolution?
The vitamin which is essential for blood clotting is
The vacuole is lined by a membrane called
$t$-butyl chloride preferably undergo hydrolysis by
Synsacrum of fowl consists of about
In which form does the food transported in plants?
In Pheretima, septa are absent between which segments?
In Mollusca, eye is present over a stalk, called
In frog heart, there are cardiac muscles which consists of fibres called
If root of a flowering plant has $24$ chromosomes, then its gamete has how many chromosomes?
$H - O - H$ bond angle in $H _{2} O$ is $104.5^{\circ}$ and not $109^{\circ} 28'$ because of
Diwali rocket is ejecting $50\, g$ of gasses at a velocity of $400 \,m/s$ . The accelerating force on the rocket will be
Contractile vacuole in protozoan Amoeba is meant for
Clamp connections are observed in
Chromosome complement with $2n - 1$ is called