List of practice Questions

Let \(S = \left\{ n \in \mathbb{N} : \begin{pmatrix} 0 & i \\ 1 & 0 \end{pmatrix}^n \begin{pmatrix} a & b \\ c & d \end{pmatrix} = \begin{pmatrix} a & b \\ c & d \end{pmatrix}, \forall a, b, c, d \in \mathbb{R} \right\}\), where \(i = \sqrt{-1}\). Then the number of 2-digit numbers in the set S is __________.
The values of a and b, for which the system of equations $2x + 3y + 6z = 8$ $x + 2y + az = 5$ $3x + 5y + 9z = b$ has no solution, are :
Which one of the following compounds will liberate \(CO_2\) when treated with \(NaHCO_3\)?

The given reaction can occur in the presence of: 

(a) Bromine water 
(b) \(Br_2\) in \(CS_2\), 273 K 
(c) \(Br_2/FeBr_3\) 
(d) \(Br_2\) in \(CHCl_3\), 273 K 
Choose the correct answer from the options given below: 
 

Student A and Student B used two screw gauges of equal pitch and 100 equal circular divisions to measure the radius of a given wire. The actual value of the radius of the wire is 0.322 cm. The absolute value of the difference between the final circular scale readings observed by the students A and B is __________. 
$[$Figure shows position of reference '0' when jaws of screw gauge are closed$]$ 
Given pitch = 0.1 cm. 

Match List I with List II. 

Choose the correct answer from the options given below : 
 

Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed then the ratio of the magnitude of impulses imparted to ball 'a' and ball 'b' by the wall along 'X' direction is : 

Two different metal bodies A and B of equal mass are heated at a uniform rate under similar conditions. The variation of temperature of the bodies is graphically represented as shown in the figure. The ratio of specific heat capacities is : 

If \(\alpha, \beta\) are roots of the equation \(x^2 + 5(\sqrt{2})x + 10 = 0, \alpha>\beta\) and \(P_n = \alpha^n - \beta^n\) for each positive integer n, then the value of \(\frac{P_{17}P_{20} + 5\sqrt{2} P_{17}P_{19}}{P_{18}P_{19} + 5\sqrt{2} P_{18}^2}\) is equal to __________.
If the value of \(\left( 1 + \frac{2}{3} + \frac{6}{3^2} + \frac{10}{3^3} + ....... \text{upto } \infty \right)^{\log_{0.25} \left( \frac{1}{3} + \frac{1}{3^2} + \frac{1}{3^3} + ....... \text{upto } \infty \right)}\) is \(l\), then \(l^2\) is equal to __________.
The Boolean expression $(p \implies q) \wedge (q \implies \sim p)$ is equivalent to :
The value of the definite integral $\int_{\pi/24}^{5\pi/24} \frac{dx}{1 + \sqrt[3]{\tan 2x}}$ is :
The sum of all values of $x$ in $[0, 2\pi]$, for which $\sin x + \sin 2x + \sin 3x + \sin 4x = 0$, is equal to :
The number of real roots of the equation $e^{6x} - e^{4x} - 2e^{3x} - 12e^{2x} + e^x + 1 = 0$ is :
Let $f(x) = 3 \sin^4 x + 10 \sin^3 x + 6 \sin^2 x - 3, x \in [-\frac{\pi}{6}, \frac{\pi}{2}]$. Then, $f$ is :
Consider the complete combustion of butane, the amount of butane utilized to produce 72.0 g of water is ________ \(\times 10^{-1}\) g. (in nearest integer)
A home owner uses \(4.00 \times 10^3 \text{ m}^3\) of methane (\(CH_4\)) gas, (assume \(CH_4\) is an ideal gas) in a year to heat his home. Under the pressure of 1.0 atm and 300 K, mass of gas used is \(x \times 10^5\) g. The value of \(x\) is ________. (Nearest integer) (Given R = 0.083 L atm \(K^{-1} mol^{-1}\))
A source of monochromatic radiation of wavelength 400 nm provides 1000 J of energy in 10 seconds. When this radiation falls on the surface of sodium, \(x \times 10^{20}\) electrons are ejected per second. Assume that wavelength 400 nm is sufficient for ejection of electron from the surface of sodium metal. The value of \(x\) is ________. (Nearest integer) (\(h = 6.626 \times 10^{-34} \text{ Js}\))
For the reaction \(A + B \rightleftharpoons 2C\) the value of equilibrium constant is 100 at 298 K. If the initial concentration of all the three species is 1 M each, then the equilibrium concentration of C is \(x \times 10^{-1}\) M. The value of \(x\) is ________. (Nearest integer)
Which one of the following chemical agent is not being used for dry-cleaning of clothes ?
An Organic compound 'A' \(C_4H_8\) on treatment with \(KMnO_4/H^+\) yields compound 'B' \(C_3H_6O\). Compound 'A' also yields compound 'B' an ozonolysis. Compound 'A' is:
The ionic radii of $K^+$, $Na^+$, $Al^{3+}$ and $Mg^{2+}$ are in the order :
In the leaching of alumina from bauxite, the ore expected to leach out in the process by reacting with NaOH is :
At 298.2 K the relationship between enthalpy of bond dissociation (in kJ mol$^{-1}$) for hydrogen ($E_H$) and its isotope, deuterium ($E_D$), is best described by :