List of practice Questions

If $C$ and $R$ denote capacitance and resistance, the dimensional formula of $CR$ is
Formalin is an aqueous solution of
A boat which has a speed of $5\, km/h$ in still water crosses a river of width $1\, km$ along the shortest possible path in $15\, min$. The velocity of the river water in $km/h$ is
The $ pK_a$ of acetyl salicylic acid (aspirin) is 3.5. The pH of gastric juice in human stomach is about 2-3 and the pH in the small intestine is about 8. A spirin will be
The oxidation number of phosphorus in Ba(H$_2PO_2 )_2$ is
The number of structural and configurational isomers of a brorno compound, $C_5 H_9 Br,$ formed by the addition of HBr to 2-pentyne respectively, are
Sum of the first n terms of the series $\frac{1}{2} + \frac{3}{4} + \frac{7}{8} + \frac{15}{16} + ...$ is equal to
Potassium manganate $(K_2MnO_4)$ is formed when
One hundred identical coins, each with probability p, of showing up heads are tossed once. If $0 < p < 1$ and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is
For two given events $A$ and $B, P(A \cap B) $ is
The equations of the tangents drawn from the origin to the circle $x^2 + y^2 + 2 rx + 2hy + h^2 = 0, $ are
Prove that the value of the integral, $\int\limits_0^{2a} [f(x)/ f(x) + f(2a-x)] dx$ is equal to a
The value of the expression $\sqrt{3} cosec 20^\circ -sec 20^\circ $is equal to
If the first and the $ (2n - 1)th$ term of an $AP, GP$ and $HP$ are equal and their nth terms are $a, b$ and $c$ respectively, then
If $ y^2 = P (x) $ is a polynomial of degree 3, then $2 \frac{d}{dx} \bigg(y^3 \frac{d^2 \, y}{ dx^2}\bigg) $ equals
If one mole of a monoatomic gas ($\gamma$ = 5/ 3) is mixed with one mole of a diatomic gas ($\gamma$ = 7 / 5), the value of $\gamma$ for the mixture is
The orbital diagram in which Aufbau principle is violated is
A cylinder of radius R made of a material of thermal conductivity $K_1$, is surrounded by a cylindrical shell of inner radius R and outer radius 2R made of a material of thermal conductivity K$_2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is
The wavelength of a spectral line for an electronic transition is inversely related to
A bottle of dry ammonia and a bottle of dry hydrogen chloride connected through a long tube are opened simultaneously at both ends the white ammonium chloride ring first formed will be
A satellite $S$ is moving in an elliptical orbit around the earth. The mass of the satellite is very small compared to the mass of the earth. Then,
Water potential is equal to
Let $I$ be the moment of inertia of a uniform square plate about an axis $AB$ that passes through its centre and is parallel to two of its sides. $CD$ is a line in the plane of the plate that passes through the centre of the plate and makes an angle $\theta$ with $AB$. The moment of inertia of the plate about the axis $CD$ is then equal to
The coefficient of restitution $e$, for a perfectly elastic collision is
The molecule that has linear structure is