List of practice Questions

Let \( g(x) \) be a linear function and \[ f(x) = \begin{cases} g(x), & x \leq 0 \\ \left( \frac{1 + x}{2 + x} \right)^{\frac{1}{x}}, & x > 0 \end{cases} \] is continuous at \( x = 0 \). If \( f'(1) = f(-1) \), then the value of \( g(3) \) is
The frequency distribution of the age of students in a class of 40 students is given below:
\(Age\)151617181920
No. of Students58512xy

If the mean deviation about the median is 1.25, then \(4x + 5y\) is equal to:
Two persons pull a wire towards themselves. Each person exerts a force of $200 \, \text{N}$ on the wire. Young’s modulus of the material of the wire is $1 \times 10^{11} \, \text{N m}^{-2}$. Original length of the wire is $2 \, \text{m}$ and the area of cross-section is $2 \, \text{cm}^2$. The wire will extend in length by ______ $\mu \text{m}$.
Given below are two statements :
Statement (I) : The mean free path of gas molecules is inversely proportional to square of molecular diameter.
Statement (II) : Average kinetic energy of gas molecules is directly proportional to absolute temperature of gas.
In the light of the above statements, choose the correct answer from the option given below:
Number of amine compounds from the following giving solids which are soluble in NaOH upon reaction with Hinsberg's reagent is _____.
amine
Consider a hyperbola \( H \) having its centre at the origin and foci on the \( x \)-axis. Let \( C_1 \) be the circle touching the hyperbola \( H \) and having its centre at the origin. Let \( C_2 \) be the circle touching the hyperbola \( H \) at its vertex and having its centre at one of its foci. If the areas (in square units) of \( C_1 \) and \( C_2 \) are \( 36\pi \) and \( 4\pi \), respectively, then the length (in units) of the latus rectum of \( H \) is:
Match List I with List II
Choose the correct answer from the options given below:
Given below are two statements:
Statement I: The correct order of first ionization enthalpy values of Li, Na, F, and Cl is \( \text{Na} < \text{Li} < \text{Cl} < \text{F} \).
Statement II: The correct order of negative electron gain enthalpy values of Li, Na, F, and Cl is \( \text{Na} < \text{Li} < \text{F} < \text{Cl} \).
In the light of the above statements, choose the correct answer from the options given below:
If the system of equations \[2x + 7y + \lambda z = 3,\]\[3x + 2y + 5z = 4,\]\[x + \mu y + 32z = -1\]has infinitely many solutions, then $(\lambda - \mu)$ is equal to ________.
The incorrect statement regarding the geometrical isomers of 2-butene is:
Assertion: The angular velocity of the moon revolving around the earth is more than that of the earth revolving around the Sun.
Reason: The time taken by the moon to revolve around the earth is less than the time taken by the earth to revolve around the sun.
In the given circuit, the current flowing through the resistance \( 20 \Omega \) is \( 0.3 \, \text{A} \), while the ammeter reads \( 0.9 \, \text{A} \). The value of \( R_1 \) is ______ \( \Omega \).
Resistance diagram
A plane electromagnetic wave propagating in x-direction is described by \( E_y = (200 \, \text{V/m}) \sin(1.5 \times 10^7 t - 0.05 x) \). The intensity of the wave is:
The fragrance of flowers is due to the presence of some steam volatile organic compounds called essential oils. These are generally insoluble in water at room temperature but are miscible with water vapour in vapour phase. A suitable method for the extraction of these oils from the flowers is -
From the vitamins \( A, \, B_1, \, B_6, \, B_{12}, \, C, \, D, \, E, \, \text{and} \, K \), the number of vitamins that can be stored in our body is ______.
Let \(f(x) = \begin{cases} -a & \text{if } -a \leq x \leq 0, \\ x + a & \text{if } 0<x \leq a \end{cases} \) where \(a>0\) and \(g(x) = (f(|x|) - |f(x)|)/2\). Then the function \(g : [-a, a] \to [-a, a]\) is:
Let the sum of two positive integers be 24. If the probability, that their product is not less than $\frac{3}{4}$ times their greatest positive product, is $\frac{m}{n}$, where $\gcd(m, n) = 1$, then $n - m$ equals :
There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is
The quantity of silver deposited when one coulomb charge is passed through\(AgNO_3\)solution:
Conductivity of a photodiode starts changing only if the wavelength of incident light is less than 660 nm. The band gap of the photodiode is found to be \[\frac{X}{8} \, \text{eV}.\]The value of $X$ is:\text{(Given, $h = 6.6 \times 10^{-34} \, \text{Js}$, $e = 1.6 \times 10^{-19} \, \text{C}$)}
Monochromatic light of frequency $6 \times 10^{14}$ Hz is produced by a laser. The power emitted is $2 \times 10^{-3}$ W. How many photons per second on average are emitted by the source.(Given $h = 6.63 \times 10^{-34} \, \text{Js}$)
Match the following : 
(a) \([Cr(H_2O)_6]^{+3}\)(i) \(t^2_{2g}eg^0\)
(b) \([Fe(H_2O)_6]^{+3}\)(ii) \(t^3_{2g}eg^0\)
\((c) [Ni(H_2O)_6]^{+2}\)(iii) \(t^3_{2g}eg^2\)
(d) \([V(H_2O)_6]^{+3}\)(iv) \(t^6_{2g}eg^2\)
Suppose \( 2 - p \), \( p \), \( 2 - \alpha \), \( \alpha \) are the coefficients of four consecutive terms in the expansion of \( (1 + x)^n \). Then the value of \( p^2 - \alpha^2 + 6\alpha + 2p \) equals
A solution of two miscible liquids showing negative deviation from Raoult's law will have:
NaCl reacts with conc. \( H_2SO_4 \) and \( K_2Cr_2O_7 \) to give reddish fumes (B), which react with NaOH to give yellow solution (C). (B) and (C) respectively are: