Sample QuestionsJEE Main 23-Jan-2025 Paper - Shift 2 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
$\lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}$ is equal to:
- A
$\frac{2}{\sqrt{3 e }}$
- B
$\frac{2 e }{\sqrt{3}}$
- C
$\frac{2 e }{3}$
- ✓
$\frac{2}{3 \sqrt{e}}$
Answer: D.
View full solution →If $I=\int_0^{\frac{\pi}{2}} \frac{\sin ^{\frac{3}{2}} x}{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x} d x$, then $\int_0^{21} \frac{x \sin x \cos x}{\sin ^4 x+\cos ^4 x} d x$ equals:
- ✓
$\frac{\pi^2}{16}$
- B
$\frac{\pi^2}{4}$
- C
$\frac{\pi^2}{8}$
- D
$\frac{\pi^2}{12}$
Answer: A.
View full solution →If the square of the shortest distance between the lines $\frac{x-2}{1}=\frac{y-1}{2}=\frac{z+3}{-3}$ and $\frac{x+1}{2}=\frac{y+3}{4}=\frac{z+5}{-5}$ is $\frac{ m }{ n }$, where $m , n$ are coprime numbers, then $m + n$ is equal to:
Answer: B.
View full solution →The number of complex numbers $z$, satisfying $|z|=1$ and $\left|\frac{ z }{\overline{ Z }}+\frac{\overline{ z }}{ z }\right|=1$, is :
Answer: D.
View full solution →Let $A =\left[ a _{ ij }\right]$ be a $3 \times 3$ matrix such that $A \left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]=\left[\begin{array}{l}0 \\ 0 \\ 1\end{array}\right], A \left[\begin{array}{l}4 \\ 1 \\ 3\end{array}\right]=\left[\begin{array}{l}0 \\ 1 \\ 0\end{array}\right]$ and $A \left[\begin{array}{l}2 \\ 1 \\ 2\end{array}\right]=\left[\begin{array}{l}1 \\ 0 \\ 0\end{array}\right]$, then $a _{23}$ equals:
Answer: A.
View full solution →The roots of the quadratic equation $3 x ^2- px + q =0$ are $10^{\text {th }}$ and $11^{\text {th }}$ terms of an arithmetic progression with common difference $\frac{3}{2}$. If the sum of the first 11 terms of this arithmetic progression is 88 , then $q -2 q$ is equal to __________ .
View full solution →The variance of the numbers $8,21,34,47, \ldots, 320$, is __________.
View full solution →The focus of the parabola $y^2=4 x+16$ is the centre of the circle C of radius 5 . If the values of $\lambda$, for which $C$ passes through the point of intersection of the lines $3 x-y=0$ and $x+\lambda y=4$, are $\lambda_1$ and $\lambda_2, \lambda_1<\lambda_2$, then $12 \lambda_1+29 \lambda_2$ is equal to __________.
View full solution →Let $\alpha, \beta$ be the roots of the equation $x^2-a x-b=0$ with $\operatorname{Im}(\alpha)<\operatorname{Im}(\beta)$. Let $P_n=\alpha^n-\beta^n$. If $P_3=-5 \sqrt{7} i, \quad P_4=-3 \sqrt{7} i, \quad P_5=11 \sqrt{7} i \quad$ and $P_6=45 \sqrt{7} i$, then $\left|\alpha^4+\beta^4\right|$ is equal to __________ .
View full solution →The number of ways, 5 boys and 4 girls can sit in a row so that either all the boys sit together or no two boys sit together, is __________.
A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x _2$ under the tension of 7 N . For the elongation of $\left(5 x_1-2 x_2\right)$, the tension in the spring will be,
Answer: C.
View full solution →A concave mirror of focal length $f$ in air is dipped in a liquid of refractive index $\mu$. Its focal length in the liquid will be :
- A
$\frac{f}{\mu}$
- B
$\frac{f}{(\mu-1)}$
- C
$\mu f$
- ✓
$f$
Answer: D.
View full solution →
Using the given P-V diagram, the work done by an ideal gas along the path ABCD is -
- A
$4 P_0 V_0$
- B
$3 P _0 V_0$
- C
$-4 P_0 V_0$
- ✓
$-3 P _0 V_0$
Answer: D.
View full solution →A plane electromagnetic wave of frequency20 MHz travels in free space along the $+x$ direction. At a particular point in space and time, the electric field vector of the wave is $E _{ y }=9.3 Vm ^{-}$ ${ }^1$. Then, the magnetic field vector of the wave at that point is-
- A
$B _{ z }=9.3 \times 10^{-8} T$
- B
$B _{ z }=1.55 \times 10^{-8} T$
- C
$B _{ z }=6.2 \times 10^{-8} T$
- ✓
$B_z=3.1 \times 10^{-8} T$
Answer: D.
View full solution →What is the current through the battery in the circuit shown below?
Answer: C.
View full solution →In a series LCR circuit, a resistor of $300 \Omega$, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is $\qquad$ $\times 10^4$ radians $s ^{-1}$.
View full solution →A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance $2.5 \mu F$. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be __________ $Vs ^{-1}$.
View full solution →At steady state the charge on the capacitor, as shown in the circuit below, is $\qquad$ $\mu C$.
View full solution →A satellite of mass $\frac{M}{2}$ is revolving around earth in a circular orbit at a height of $\frac{R}{3}$ from earth surface. The angular momentum of the satellite is $M \sqrt{\frac{G M R}{x}}$. The value of $x$ is __________ , where M and $R$ are the mass and radius of earth, respectively. (G is the gravitational constant)
View full solution →An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension $0.095 J / m ^2$ and density $10^3 kg / m ^3$. The difference between pressure inside the bubble and atmospheric pressure _________ $N / m ^2$. $\left(\right.$ Take $\left.g=10 m / s ^2\right)$
View full solution →Consider the following reactions
$K _2 Cr _2 O _7 \xrightarrow[- H _2 O ]{ KOH }[ A ] \xrightarrow[- H _2 O ]{ H _2 SO _4}[B]+ K _2 SO _4$
The products [A] and [B], respectively are :
- A
$K _2 Cr ( OH )_6$ and $Cr _2 O _3$
- B
$K _2 CrO _4$ and $Cr _2 O _3$
- ✓
$K _2 CrO _4$ and $K _2 Cr _2 O _7$
- D
$K _2 CrO _4$ and CrO
Answer: C.
View full solution →Given below are two statements about X-ray spectra of elements :
Statement (I) : A plot of $\sqrt{v}(v=$ frequency of X-rays emitted) vs atomic mass is a straight line.
Statement (II) : A plot of $v(v=$ frequency of X-rays emitted) vs atomic number is a straight line. In the light of the above statements choose the correct answer from the options given below :
- A
Statement I is true but Statement II is false
- B
Both Statement I and Statement II are true
- ✓
Both Statement I and Statement II are false
- D
Statement I is false but Statement II is true
Answer: C.
View full solution →Consider a binary solution of two volatile liquid components 1 and $2 x _1$ and $y _1$ are the mole fractions of component 1 in liquid and vapour phase, respectively. The slope and intercept of the linear plot of $\frac{1}{x_1}$ vs $\frac{1}{y_1}$ are given respectively as :
- ✓
$\frac{ P _1^0}{ P _2^0}, \frac{ P _2^0- P _1^0}{ P _2^0}$
- B
$\frac{ P _2^0}{ P _1^0}, \frac{ P _1^0- P _2^0}{ P _2^0}$
- C
$\frac{ P _1^0}{ P _2^0}, \frac{ P _1^0- P _2^0}{ P _2^0}$
- D
$\frac{ P _2^0}{ P _1^0}, \frac{ P _2^0- P _1^0}{ P _2^0}$
Answer: A.
View full solution →Identify the products $[A]$ and $[B]$, respectively in the following reaction :
Answer: C.
View full solution →pH of water is 7 at $25^{\circ} C$. If water is heated to $80^{\circ} C$, it's pH will :
Answer: A.
View full solution →A compound ' X ' absorbs 2 moles of hydrogen and ' X ' upon oxidation with $KMnO _4 \mid H ^{+}$gives
The total number of $\sigma$ bonds present in the compound ' X ' is __________. View full solution →The bond dissociation enthalpy of $X _2 \Delta H _{\text {bond }}^{\circ}$ calculated from the given data is __________ $kJ mol ^{-1}$. (Nearest integer)
$\begin{array}{l} M ^{+} X ^{-}( s ) \rightarrow M ^{+}( g )+ X ^{-}( g ) \Delta H _{\text {lattice }}^{\circ}=800 kJ mol ^{-1} \\ M ( s ) \rightarrow M ( g ) \Delta H _{\text {sub }}^{\circ}=100 kJ mol ^{-1} \\ M ( g ) \rightarrow M ^{+}( g )^{-}+ e ^{-}( g ) \Delta H _{ i }^{\circ}=500 kJ mol ^{-1}\end{array}$
$
\begin{array}{l}
X(g)+e^{-}(g) \rightarrow X^{-}(g) \Delta H_{eg}^{\circ}=-300 kJ mol^{-1} \\
M(s)+\frac{1}{2} X_2(g) \rightarrow M^{+} X^{-}(s) \Delta H_{f}^{\circ}=-400 kJ mol^{-1}
\end{array}
$
[Given : $M ^{+} X ^{-}$is a pure ionic compound and X forms a diatomic molecule $X_2$ is gaseous state]
View full solution →When 81.0 g of aluminium is allowed to react with 128.0 g of oxygen gas, the mass of aluminium oxide produced in grams is __________. (Nearest integer)
Given :
Molar mass of Al is $27.0 g mol ^{-1}$
Molar mass of O is $16.0 g mol ^{-1}$
View full solution →Consider the following sequence of reactions.
Total number of $sp ^3$ hybridised carbon atoms in the major product C formed is __________ . View full solution →0.01 mole of an organic compound $( X )$ containing $10 \%$ hydrogen, on complete combustion produced $0.9 g H _2 O$. Molar mass of $( X )$ is _________) $g mol ^{-1}$.
View full solution →
