List of practice Questions

In a \(\Delta ABC\). with usual notation, match the items in List - I with the items in List - II and choose the correct option.

List I		List II
(A)	\(r_1r_2\sqrt{\bigg(\frac{4R-r_1-r_2}{r_1+r_2}\bigg)}\)	1	\(b\)
(B)	\(\frac{r_2(r_3+r_1)}{\sqrt{r_1r_2+r_2r_3+r_3r_1}}\)	2	\(a^2,b^2,c^2 are \;in \;AP\)
(C)	\(\frac{a}{c}=\frac{sin(A-B)}{sin(B-C)}\)	3	\(\triangle\)
(D)	\(bc\;cos^2\frac{A}{2}\)	4	\(R\; r_1r_2r_3\)
		5	\(s(s-a)\)

Molal depression constant for a solvent is $4.0\, kg\, mol^{-1}$. The depression in the freezing point of the solvent for $0.03\, mol\, kg^{-1}$ solution of $ {K2SO4}$ is : (Assume complete dissociation of the electrolyte)

NaH is an example of :

$ {NO_2}$ required for a reaction is produced by the decomposition of $ {N2O5}$ in $ {CCl4}$ as per the equation $ { 2N2O5(g) -> 4NO2(g) + O2(g).}$ The initial concentration of $ {N2O5}$ is $3.00\, mol$ $ {L^{-1}}$ and it is $2.75\, mol$ $ {L^{-1}}$ after $30$ minutes. The rate of formation of $ {NO2}$ is :

One mole of an ideal gas passes through a process where pressure and volume obey the relation $P =P_{o} \left[1- \frac{1}{2} \left(\frac{V_{0}}{V}\right)^{2}\right] $ .Here $P_o$ and $V_o$ are constants. Calculate the change in the temperature of the gas if its volume changes from $V_o$ to $2 V_o$ .

Peptization is a :

Seven capacitors, each of capacitance $2 \mu F$, are to be connected in a configuration to obtain an effective capacitance of $\left(\frac{6}{13}\right)\mu F$. Which of the combinations, shown in figures below, will achieve the desired value ?

Sodium metal on dissolution in liquid ammonia gives a deep blue solution due to the formation of:

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If $99$ more identical balls are addded to the total number of balls used in forming the equilaterial triangle, then all these balls can be arranged in a square whose each side contains exactly $2$ balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is :

Suppose that $20$ pillars of the same height have been erected along the boundary of a circular stadium. If the top of each pillar has been connected by beams with the top of all its non-adjacent pillars, then the total number beams is :

Surface of certain metal is first illuminated with light of wavelength $\lambda_1 =350 \; nm$ and then, by light of wavelength $\lambda_2=54\, \; nm$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of $2$. The work function of the metal (in eV) is close to : (Energjr of photon = $\frac{1240}{\lambda (in \; nm)} eV$)

Temperature difference of \(120^{\circ}C\) is maintained between two ends of a uniform rod \(AB\) of length \(2L\). Another bent rod \(PQ\), of same cross section as \(AB\) and length \(\frac{3L}{2}\) , is connected across \(AB\) (See figure). In steady state, temperature difference between \(P\) and \(Q\) will be close to :

The $71^{st}$ electron of an element $X$ with an atomic number of $71$ enters into the orbital :

The amorphous form of silica is :

The amount of sugar $ {(C_{12}H_{22}O_{11})}$ required to prepare $2\, L$ of its $0.1\, M$ aqueous solution is :

The amphoteric hydroxide is :

The area (in s units) of the smaller of the two circles that touch the parabola, $y^2 = 4x$ at the point $(1, 2)$ and the x-axis is :

The combination of plots which does not represent isothermal expansion of an ideal gas is:

The compound that inhibits the growth of tumors is :

One plano-convex and one plano-concave lens of same radius of curvature $'R'$ but of different materials are joined side by side as shown in the figure. If the refractive index of the material of $1$ is $\mu_1$ and that of $2$ is $\mu_2$, then the focal length of the combination is :

The contrapositive of the statement "If you are born in India, then you are a citizen of India", is :

The correct decreasing order for acid strength is :

The correct order of hydration enthalpies of alkali metal ions is -

The effect of lanthanoid contraction in the lanthanoid series of elements by and large means :

The energy required to take a satellite to a height $'h'$ above Earth surface (radius of Earth = $6.4 \times 10^3 \; km) $ is $E_1$ and kinetic energy required for the satellite to be in a circular orbit at this height is $E_2$. The value of $h$ for which $E_1 $ and $E_2$ are equal, is: