List of practice Questions

Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
The equation for 2310Ne nucleus which decays by β-emission is:
The enthalpy of atomization of \({CH}_3{NH}_2(g)\) is 2313 kJ mol\(^{-1}\). If \(\Delta_{{C-H}}^{\ominus}\) and \(\Delta_{{N-H}}^{\ominus}\) are 414 and 389 kJ mol\(^{-1}\) respectively, then \(\Delta_{{C-N}}^{\ominus}\) (in kJ mol\(^{-1}\)) will be:
A body is dropped freely from a height of 8 m from the ground. If the coefficient of restitution between the body and the ground is 0.5, then the maximum height reached by the body after second impact with the ground is
If the intensities of two interfering light waves in a medium are I and 4I, then the maximum and minimum intensities are respectively:
What are X and Y respectively in the following set of reactions?
2-Bromobutane $\xrightarrow{{alc. KOH}}$ C$_4$H$_8$ (major)
C$_4$H$_8$ $\xrightarrow{{KMnO}_4/{H}^+}$ X
C$_4$H$_8$ $\xrightarrow{{Baeyer's reagent}}$ Y
Alkaline oxidative fusion of MnO$_2$ gives 'X'. The products formed when 'X' undergoes disproportionation in acid medium are
I) KMnO$_4$
II) MnO$_2$
III) O$_2$
IV) H$_2$O
The work done to take a body of mass 100 kg to the top of a building of height 20 m is (Acceleration due to gravity = 10 m s\textsuperscript{-2})
At T(K) vapour pressure of pure benzene and toluene are 500 and 200 mm Hg respectively. If they form an ideal solution, what is the mole fraction of toluene in a mixture boiling at T(K) at a total pressure of 380 mm Hg ?
At T(K), \( K_c \) value for the dissociation of \( \text{PCl}_5 \) is 0.04.
\[ \text{PCl}_5(g) \rightleftharpoons \text{PCl}_3(g) + \text{Cl}_2(g) \] The number of moles of \( \text{PCl}_5 \) to be added to a 3.0 L flask to get chlorine concentration of 0.15 mol L\(^{-1}\) is (approximately)?
For all \( n \in \mathbb{N} \), which of the following is less than or equal to \( \frac{3^n - 1}{2} \)?
The area of the region lying between the curves \( y = \sqrt{4 - x^2} \), \( y^2 = 3x \) and the Y-axis is:
A thin uniform circular disc rolls with a constant velocity without slipping on a horizontal surface. Its total kinetic energy is

Match the following:

List-I (Metal in drinking water)List-II (Maximum prescribed concentration in ppm)
A) Mn I) \( 0.05 \)
B) ZnII) \( 3.0 \)
C) CdIII) \( 0.005 \)
D) CuIV) \( 5.0 \)
The tangent drawn at an extremity (in the first quadrant) of latus rectum of the hyperbola $$ \frac{x^2}{4} - \frac{y^2}{5} = 1 $$ meets the x-axis and y-axis at $ A $ and $ B $ respectively. If $ O $ is the origin, find $$ (OA)^2 - (OB)^2. $$
Evaluate: $$ \int_0^1 x \sin^{-1} x \, dx $$
A wire of length 20 cm is placed horizontally on the surface of water and is gently pulled up with a force of $1.456 \times 10^{-2}\, N$ to keep the wire in equilibrium. The surface tension of water is
The maximum magnetic field produced by a current of 12 A passing through a copper wire of diameter 1.2 mm is
Identify the incorrect statement regarding the interstitial compounds.
The coefficient of \(x^3\) in the expansion of \(\frac{x^4 + 1}{(x^2 + 1)(x - 1)}\) when it is expressed in terms of positive integral powers of \(x\), is
A line \(L\) passes through point \(P(1, 2)\) and makes an angle of \(60^\circ\) with OX in positive direction. A and B are points on line \(L\), 4 units from P. If O is origin, then area of \(\triangle OAB\) is
If \((2, -1, 3)\) is the foot of the perpendicular drawn from the origin \((0, 0, 0)\) to a plane then the equation of that plane is
If the internal energy of 3 moles of a gas at a temperature of 27 °C is 2250R, then the number of degrees of freedom of the gas is (R - Universal gas constant)
Nature of two oxides of nitrogen X and Y formed in the reaction of sodium nitrite with hydrochloric acid is
What are \( X \) and \( Y \) in the following reaction? $$ \text{nCl/CH}_2 \xrightarrow{X} Y $$