List of practice Questions

A deflection magnetometer is adjusted in the usual way. When a magnet is introduced, the deflection observed is $\theta$, and the period of oscillation of the needle in the magnetometer is $T$. When the magnet is removed, the period of oscillation is $T_0$. The relation between $T$ and $T_0$ is

The equilibrium constant for the reaction $N _{2( g )}+ O _{2( g )} \rightleftharpoons 2 NO _{( g )}$ is $4 \times 10^{-4}$ at $2000\,K$. In presence of a catalyst the equilibrium is attained ten times faster. Therefore the equilibrium constant in presence of catalyst of $2000\, K$ is

The reaction quotient '$Q$' is useful in predicting the direction of the reaction. Which of the following is incorrect ?

Dissolving $NaCN$ in de-ionized water will result in a solution having

Identify the Br??sted acid in the following equation: $PO _{4}^{3-}+ H _{2} O (l) \longrightarrow HPO _{4}^{2-}(a q)+ OH ^{-}(a q)$

The number of grams/weight of $NH_4Cl$ required to be added to 3 liters of $0.01\, M\, NH_3$ to prepare the buffer of $pH=9.45$ at temperature $298\, K$ ($K_b$ for $NH_3$ is $1.85 \times 10^{-5}$)

For the reaction $2 HI (g) \rightleftharpoons H _{2}(g)+ I _{2}(g)$ the degree of dissociation $(\alpha)$ of HI(g) is related to equilibrium constant $K_p$ by the expression:

For the reaction, $H_{2} + I_{2} {\rightleftharpoons} 2HI, K= 47.6.$ If the initial number of moles of each reactant and product is 1 mole then at equilibrium

The second dissociation constant of fumaric acid is greater than maleic acid. Higher the dissociation constant of acid, more is the acidic character.

$K_a$ for $HCN$ is $5 \times 10^{-10}$ at $25^{\circ}C$. For maintaining a constant $pH\, = \,9$, the volume of $5\, M \,KCN$ solution required to be added to $10 \,mL$ of $2\, M HCN$ solution is

Two identical balls P and Q are projected with same speeds in vertical plane from same point O with making projection angles with horizontal $30^{\circ} $ and $60^{\circ} $ respectively and they fall directly on plane AB at points P' and Q' respectively. Which of the following statement is true about distances as given in options?

The length of the semi-latus rectum of an ellipse is one thrid of its major axis, its eccentricity would be

The differential equation of all parabolas whose axis is $y-axis$ is

Two cars moving in opposite directions approach each other with speed of $22\, m/s$ and $16.5\, m/s$ respectively. The driver of the first car blows a horn having a frequency $400\, Hz$. The frequency heard by the driver of the second car is [velocity of sound $340\, m/s$] :

Two blocks $A$ and $B$ of masses $3\,m$ and $m$ respectively are connected by a massless and inextensible string. The whole system is suspended by a massless spring as shown in figure. The magnitudes of acceleration of $A$ and $B$ immediately after the string is cut, are respectively :

A body of mass $50\, kg$. is suspended using a spring balance inside a lift at rest. If the lift starts falling freely, the reading of the spring balance is

The particular solution of the differential equation $xdy + 2ydx = 0$, when $x = 2, y = 1$ is

In blue green algae, photo synthesis takes place in :

Two particles P and Q are moving on a circle. At a certain instant of time both the particles are diametrically opposite and P has tangential acceleration $8 \, m/s^2$ and centripetal acceleration $5 \, m/s^2$ whereas Q has only centripetal acceleration of $1 \, m/s^2$. At that instant acceleration (in $m/s^2)$ of P with respect to Q is :

A current carrying wire in its neighbourhood produces

A conducting circular loop of radius r carries a constant current z. It is placed in a uniform magnetic field $\vec{B}_{0}$ such that $\vec{B}_{0}$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is

For given L-R circuit, growth of current as function of time t is shown in graph. Which of the following option represents value of time constant most closely for the circuit?

A 10gm bullet moving directly upward at 1000 m/s strikes and passes through the center of mass of a 10 kg block initially at rest .The bullet emerges from the block moving directly upward at 400 m/s. What will be velocity of the block just after the bullet comes out of it ?

There are two identical springs each of spring constant k. Here springs, pulley and rods are massless and block has mass m. What is the extension of each spring at equilibrium ?

A bead of mass m can slide without friction on a fixed circular horizontal ring of radius 3R having centre at the point C. The bead is attached to one of the ends of spring of spring constant k. Natural length of spring is R and the other end of the spring is fixed at point O as shown in figure. Bead is released from position A, what will be kinetic energy of the bead when it reaches at point B ?