Let the foci of a hyperbola be $(1,14)$ and $(1,-12)$. If it passes through the point $(1,6)$, then the length of its latus-rectum is :
- A$\frac{25}{6}$
- B$\frac{24}{5}$
- ✓$\frac{288}{5}$
- D$\frac{144}{5}$
Answer: C.
View full solution →Question types
JEE Main 22-Jan-2025 Paper - Shift 1 question types
75 questions across 6 question groups — pick any mix to generate a JEE paper with step-by-step answer keys.
75
Questions
6
Question groups
5
Question types
01
SECTION - A [MATHS - MCQ]
20 Q→02SECTION - B [MATHS - NUMERIC]
5 Q→03SECTION - A [PHYSICS MCQ]
20 Q→04SECTION - B [PHYSICS - NUMERIC]
5 Q→05SECTION - A [CHEMISTY - MCQ]
20 Q→06SECTION - B [CHEMISTY - NUMERIC]
5 Q→Sample Questions
JEE Main 22-Jan-2025 Paper - Shift 1 questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Two balls are selected at random one by one without replacement from a bag containing 4 white and 6 black balls. If the probability that the first selected ball is black, given that the second selected ball is also black, is $\frac{ m }{ n }$, where $\operatorname{gcd}( m , n )=1$, then $m + n$ is equal to :
- ✓14
- B4
- C11
- D13
Answer: A.
View full solution →The area of the region, inside the circle $(x-2 \sqrt{3})^2+y^2=12$ and outside the parabola $y^2=2 \sqrt{3} x$ is
- A$6 \pi-8$
- B$3 \pi-8$
- ✓$6 \pi-16$
- D$3 \pi+8$
Answer: C.
View full solution →- ✓31
- B36
- C37
- D29
Answer: A.
View full solution →Let $f( x )$ be a real differentiable function such that
$f(0)=1$ and $f( x + y )=f( x ) f^{\prime}( y )+f^{\prime}( x ) f( y )$ for all
$x , y \in R$. Then $\sum_{ n =1}^{1 \infty 0} \log _{ e } f( n )$ is equal to :
$f(0)=1$ and $f( x + y )=f( x ) f^{\prime}( y )+f^{\prime}( x ) f( y )$ for all
$x , y \in R$. Then $\sum_{ n =1}^{1 \infty 0} \log _{ e } f( n )$ is equal to :
- A2384
- ✓2525
- C5220
- D2406
Answer: B.
View full solution →Let $\overrightarrow{ c }$ be the projection vector of $\overrightarrow{ b }=\lambda \hat{ i }+4 \hat{ k }, \lambda>0$, on the vector $\vec{a}=\hat{i}+2 \hat{j}+2 \hat{k}$. If $|\vec{a}+\vec{c}|=7$, then the area of the parallelogram formed by the vectors $\vec{b}$ and $\overrightarrow{ c }$ is ___________ .
View full solution →Let $L_1: \frac{x-1}{3}=\frac{y-1}{-1}=\frac{z+1}{0}$ and
$L_2: \frac{x-2}{2}-\frac{y}{0}-\frac{z+4}{\alpha}, \alpha \in R$, be two lines, which intersect at the point $B$. If $P$ is the foot of perpendicular from the point $A (1,1,-1)$ on $L _2$, then the value of $26 \alpha(PB)^2$ is ._________
View full solution →$L_2: \frac{x-2}{2}-\frac{y}{0}-\frac{z+4}{\alpha}, \alpha \in R$, be two lines, which intersect at the point $B$. If $P$ is the foot of perpendicular from the point $A (1,1,-1)$ on $L _2$, then the value of $26 \alpha(PB)^2$ is ._________
Let $A$ be a square matrix of order 3 such that $\operatorname{det}(A)=-2$ and $\operatorname{det}(3 \operatorname{adj}(-6 \operatorname{adj}(3 A)))=2^{n+\pi} \cdot 3^{\operatorname{mn}}$, $m > n$. Then $4 m+2 n$ is equal to $\qquad$ .
View full solution →If $\sum_{ r =0}^5 \frac{{ }^{11} C _{2 r+1}}{2 r +2}=\frac{ m }{ n }, \operatorname{gcd}( m , n )=1$, then $m - n$ is equal to $\qquad$ .
View full solution →Let the function,$
f(x)=\left\{\begin{array}{ll}
-3 a x^2-2, & x<1 \\
a^2+b x, & x \geq 1
\end{array}\right.
$
Be differentiable for all $x \in R$, where $a >1, b \in R$. If the area of the region enclosed by $y=f(x)$ and the line $y=-20$ is $\alpha+\beta \sqrt{3}, \alpha, \beta, \in Z$, then the value of $\alpha+\beta$ is $\qquad$
View full solution →f(x)=\left\{\begin{array}{ll}
-3 a x^2-2, & x<1 \\
a^2+b x, & x \geq 1
\end{array}\right.
$
Be differentiable for all $x \in R$, where $a >1, b \in R$. If the area of the region enclosed by $y=f(x)$ and the line $y=-20$ is $\alpha+\beta \sqrt{3}, \alpha, \beta, \in Z$, then the value of $\alpha+\beta$ is $\qquad$
Given is a thin convex lens of glass (refractive index $\mu$ ) and each side having radius of curvature R . One side is polished for complete reflection. At what distance from the lens, an object be placed on the optic axis so that the image gets formed on the object itself.
- A$R / \mu$
- B$R /(2 \mu-3)$
- C$\mu R$
- ✓$R /(2 \mu-1)$
Answer: D.
View full solution →A parallel-plate capacitor of capacitance $40 \mu F$ is connected to a 100 V power supply. Now the intermediate space between the plates is filled with a dielectric material of dielectric constant $K =2$. Due to the introduction of dielectric material, the extra charge and the change in the electrostatic energy in the capacitor, respectively, are -
- A2 mC and 0.2 J
- B8 mC and 2.0 J
- ✓4 mC and 0.2 J
- D2 mC and 0.4 J
Answer: C.
View full solution →
- A(B), (D) and (E) only
- B(A) and (D) only
- ✓(B), (C) and (E) only
- D(C) and (E) only
Answer: C.
View full solution →- AStatement-I is true but Statement-II is false
- BBoth Statement-I and Statement-II are false
- CBoth Statement-I and Statement-II are true
- ✓Statement-I is false but Statement-II is true
Answer: D.
View full solution →
- ✓2
- B1
- C4
- D3
Answer: A.
View full solution →
The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature $R =2 m$. Another car approaches him from behind with a uniform speed of $90 km / hr$. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the side view mirror is ' a '. The value of 100a is _________ $m / s ^2$.
View full solution →Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is _________ .
The incorrect statements regarding geometrical isomerism are :
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point that cis isomer.
Choose the CORRECT answer from the options given below :
(A) Propene shows geometrical isomerism.
(B) Trans isomer has identical atoms/groups on the opposite sides of the double bond.
(C) Cis-but-2-ene has higher dipole moment than trans-but-2-ene.
(D) 2-methylbut-2-ene shows two geometrical isomers.
(E) Trans-isomer has lower melting point that cis isomer.
Choose the CORRECT answer from the options given below :
- ✓(A), (D) and (E) only
- B(C), (D) and (E) only
- C(B) and (C) only
- D(A) and (E) only
Answer: A.
View full solution →From the magnetic behaviour of $\left[ NiCl _4\right]^{2-}$ (paramagnetic) and $\left[ Ni ( CO )_4\right]$ (diamagnetic), choose the correct geometry and oxidation state.
- A$\left[ NiCl _4\right]^{2-}: Ni ^{ II }$, square planar $\left[ Ni ( CO )_4\right]$ : $Ni (0)$, square planar
- ✓$\left[ NiCl _4\right]^{2-}: Ni ^{\prime \prime}$, tetrahedral $\left[ Ni ( CO )_4\right]: Ni (0)$, tetrahedral
- C$\left[ NiCL _4\right]^{2-}: Ni ^{\text {II }}$, tetrahedral $\left[ Ni ( CO )_4\right]$ : $Ni ^{\text {ill }}$, square planar
- D$\left[ NiCl _4\right]^{2-}: Ni (0)$, tetrahedral $\left[ Ni ( CO )_4\right]: Ni (0)$, square planar
Answer: B.
View full solution →The products formed in the following reaction sequence are :
- A
- B
- ✓
- D
Answer: C.
View full solution →Arrange the following solutions in order of their increasing boiling points.
(i) $10^{-4} M NaCl$
(ii) $10^{-4} M$ Urea
(iii) $10^{-3} M NaCl$
(iv) $10^{-2} M NaCl$
(i) $10^{-4} M NaCl$
(ii) $10^{-4} M$ Urea
(iii) $10^{-3} M NaCl$
(iv) $10^{-2} M NaCl$
- ✓(ii) < (i) < (iii) < (iv)
- B(ii) < (i) $\cong$ (iii) < (iv)
- C(i) < (ii) < (iii) < (iv)
- D(iv) $<$ (iii) < (i) < (ii)
Answer: A.
View full solution →In which of the following complexes the CFSE, $\Delta_0$ will be equal to zero?
- A$\left[ Fe \left( NH _3\right)_6\right] Br _2$
- B$\left[ Fe ( en )_3\right] Cl _3$
- C$K _4\left[ Fe ( CN )_6\right]$
- ✓$K _3\left[ Fe ( SCN )_6\right]$
Answer: D.
View full solution →Consider the following sequence of reactions :
Molar mass of the product formed (A) is _________ $g mol ^{-1}$.
View full solution →Molar mass of the product formed (A) is _________ $g mol ^{-1}$.
$A \rightarrow B$
The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 kJ mol ^{-1}$ and the frequency factor is $10^{20}$, the time required for $50 \%$, molecules of A to become B is _________ picoseconds (nearest integer).
$
\left[R=8.314 J K^{-1} mol^{-1}\right]
$
View full solution →The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is $191.48 kJ mol ^{-1}$ and the frequency factor is $10^{20}$, the time required for $50 \%$, molecules of A to become B is _________ picoseconds (nearest integer).
$
\left[R=8.314 J K^{-1} mol^{-1}\right]
$
The number of molecules/ions that show linear geometry among the following is _________ .
$
SO_2, BeCl_2, CO_2, N_3^{-}, NO_2, F_2 O, XeF_2, NO_2^{+}, I_3^{-}, O_3$
View full solution →$
SO_2, BeCl_2, CO_2, N_3^{-}, NO_2, F_2 O, XeF_2, NO_2^{+}, I_3^{-}, O_3$
In Carius method for estimation of halogens, 180 mg of an organic compound produced 143.5 mg of AgCl . The percentage composition of chlorine in the compound is _________ $\%$.
[Given : molar mass in $g mol ^{-1}$ of Ag : 108, $Cl =35.5]$
View full solution →[Given : molar mass in $g mol ^{-1}$ of Ag : 108, $Cl =35.5]$
Some $CO _2$ gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of $CO _2$ gas was later passed through an aqueous solution of $Ca ( OH )_2$. The excess unreacted $Ca ( OH )_2$ was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of $CO _2$ was x , then x is _________ $cm ^3$ (nearest integer).
[Given : The entire amount of $CO _2(g)$ reacted with exactly half the initial amount of $Ca ( OH )_2$ present in the aqueous solution.]
View full solution →[Given : The entire amount of $CO _2(g)$ reacted with exactly half the initial amount of $Ca ( OH )_2$ present in the aqueous solution.]
Generate a JEE Main 22-Jan-2025 Paper - Shift 1 paper free
Pick question groups from the list above, set marks and difficulty, and export a branded PDF with step-by-step answer keys. First 3 chapters free — no signup.