List of practice Questions

IF $f\left(z\right) = \frac{7-z}{1-z^{2}} $ , where $z = 1 + 2i$, then $|f(z)|$ is equal to :

Let $S=\{1,2,3, \ldots \ldots, 9\}$. For $k=1,2, \ldots \ldots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1}+N_{2}+N_{3}+N_{4}+N_{5}=$

A mercury drop of radius $1 \,cm$ is sprayed into $10^{6}$ drops of equal size. The energy expended in joule is (surface tension of mercury is $460 \times 10^{-3}\,N / m$ ):

The colour of the $X_2$ molecules of group $17$ elements changes gradually from yellow to violet down the group. This is due to

$ n $ identical capacitors are joined in parallel and charged to a potential $ V $ . The charged capacitors are disconnected and then connected in series using insulating handles such that the positive plate of one is connected to the negative plate of the other. The potential difference across the free plates of the combination is

Which of the following is an electrophile ?

Which of the following is an electrophile?

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

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

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

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

$K_a$ 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

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 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 $1.85 \times 10^{-5}$)

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

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

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 :