If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is 15309 , then the sum of its first nine terms is :
- A760
- B755
- C750
- D757
Question types
JEE Main 7-April-2025 Paper - Shift 2 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 7-April-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.
Let the system of equations
$x+5 y-z=1$
$4 \mathrm{x}+3 \mathrm{y}-3 \mathrm{z}=7$
$24 x+y+\lambda z=\mu$
$\lambda, \mu \in R$, have infinitely many solutions. Then the number of the solutions of this system,
If $\mathrm{x}, \mathrm{y}, \mathrm{z}$ are integers and satisfy $7 \leq \mathrm{x}+\mathrm{y}+\mathrm{z} \leq 77$, is
$x+5 y-z=1$
$4 \mathrm{x}+3 \mathrm{y}-3 \mathrm{z}=7$
$24 x+y+\lambda z=\mu$
$\lambda, \mu \in R$, have infinitely many solutions. Then the number of the solutions of this system,
If $\mathrm{x}, \mathrm{y}, \mathrm{z}$ are integers and satisfy $7 \leq \mathrm{x}+\mathrm{y}+\mathrm{z} \leq 77$, is
- A3
- B6
- C4
- D5
Let $e_{1}$ and $e_{2}$ be the eccentricities of the ellipse $\frac{x^{2}}{b^{2}}+\frac{y^{2}}{25}=1$ and the hyperbola $\frac{x^{2}}{16}-\frac{y^{2}}{b^{2}}=1$, respectively. If $\mathrm{b}<5$ and $\mathrm{e}_{1} \mathrm{e}_{2}=1$, then the eccentricity of the ellipse having its axes along the coordinate axes and passing through all four foci (two of the ellipse and two of the hyperbola) is :
- A$\frac{4}{5}$
- B$\frac{3}{5}$
- C$\frac{\sqrt{7}}{4}$
- D$\frac{\sqrt{3}}{2}$
The number of real roots of the equation $\mathrm{x}|\mathrm{x}-2|+3|\mathrm{x}-3|+1=0$ is :
- A4
- B2
- C1
- D3
Consider the lines $\mathrm{L}_{1}: \mathrm{x}-1=\mathrm{y}-2=\mathrm{z}$ and $\mathrm{L}_{2}: \mathrm{x}-2=\mathrm{y}=\mathrm{z}-1$. Let the feet of the perpendiculars from the point $\mathrm{P}(5,1,-3)$ on the lines $\mathrm{L}_{1}$ and $\mathrm{L}_{2}$ be Q and R respectively. If the area of the triangle $P Q R$ is $A$, then $4 A^{2}$ is equal to :
- A139
- B147
- C151
- D143
The sum of the series
$2 \times 1 \times{ }^{20} \mathrm{C}_{4}-3 \times 2 \times{ }^{20} \mathrm{C}_{5}+4 \times 3 \times{ }^{20} \mathrm{C}_{6}-5 \times 4 \times$ ${ }^{20} \mathrm{C}_{7}+\ldots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}$, is equal to __________ .
View full solution →$2 \times 1 \times{ }^{20} \mathrm{C}_{4}-3 \times 2 \times{ }^{20} \mathrm{C}_{5}+4 \times 3 \times{ }^{20} \mathrm{C}_{6}-5 \times 4 \times$ ${ }^{20} \mathrm{C}_{7}+\ldots+18 \times 17 \times{ }^{20} \mathrm{C}_{20}$, is equal to __________ .
Let the lengths of the transverse and conjugate axes of a hyperbola in standard form be 2a and 2b , respectively, and one focus and the corresponding directrix of this hyperbola be $(-5,0)$ and $5 x+9=0$, respectively. If the product of the focal distances of a point $(\alpha, 2 \sqrt{5})$ on the hyperbola is $p$, then $4 p$ is equal to __________ .
View full solution →For $t>-1$, let $\alpha_{t}$ and $\beta_{t}$ be the roots of the equation $\left((t+2)^{\frac{1}{7}}-1\right) x^{2}+\left((t+2)^{\frac{1}{6}}-1\right) x+\left((t+2)^{\frac{1}{21}}-1\right)=0$. If $\lim _{t \rightarrow-1^{+}} \alpha_{t}=a$ and $\lim _{t \rightarrow-1^{+}} \beta_{t}=b$, then $72(a+b)^{2}$ is equal to __________ .
View full solution →If $\int\left(\frac{1}{\mathrm{x}}+\frac{1}{\mathrm{x}^{3}}\right)\left(\sqrt[23]{3 \mathrm{x}^{-24}+\mathrm{x}^{-26}}\right) \mathrm{dx}$ $=-\frac{\alpha}{3(\alpha+1)}\left(3 x^{\beta}+x^{\gamma}\right)^{\frac{\alpha+1}{\alpha}}+C, x>0$, $(\alpha, \beta, \gamma \in Z)$, where $C$ is the constant of integration, then $\alpha+\beta+\gamma$ is equal to __________ .
View full solution →If the function $f(x)=\frac{\tan (\tan x)-\sin (\sin x)}{\tan x-\sin x}$ is continuous at $\mathrm{x}=0$, then $f(0)$ is equal to __________ .
View full solution →A transparent block A having refractive index $\mu=1.25$ is surrounded by another medium of refractive index $\mu=1.0$ as shown in figure. A light ray is incident on the flat face of the block with incident angle $\theta$ as shown in figure. What is the maximum value of $\theta$ for which light suffers total internal reflection at the top surface of the block ?
- A$\tan ^{-1}(4 / 3)$
- B$\tan ^{-1}(3 / 4)$
- C$\sin ^{-1}(3 / 4)$
- D$\cos ^{-1}(3 / 4)$
An object with mass 500 g moves along x -axis with speed $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The force acting on the object is :
- A8 N
- B5 N
- C6 N
- D4 N
A helicopter flying horizontally with a speed of $360 \mathrm{~km} / \mathrm{h}$ at an altitude of 2 km , drops an object at an instant. The object hits the ground at a point O , 20 s after it is dropped. Displacement of ' O ' from the position of helicopter where the object was released is :
(use acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and neglect air resistance)
(use acceleration due to gravity $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$ and neglect air resistance)
- A$2 \sqrt{5} \mathrm{~km}$
- B4 km
- C7.2 km
- D$2 \sqrt{2} \mathrm{~km}$
Match List-I with List-II.
| List-I | List-II | ||
| (A) | Isothermal | (I) | $\Delta \mathrm{W}$ (work done) $=0$ |
| (B) | Adiabatic | (II) | $\Delta \mathrm{Q}$ (supplied heat) $=0$ |
| (C) | Isobaric | (III) | $\Delta \mathrm{U}$ (change in internal energy) $\neq 0$ |
| (D) | Isochoric | (IV) | $\Delta \mathrm{U}=0$ |
- A(A)-(III), (B)-(II), (C)-(I), (D)-(IV)
- B(A)-(IV), (B)-(I), (C)-(III), (D)-(II)
- C(A)-(IV), (B)-(II), (C)-(III), (D)-(I)
- D(A)-(II), (B)-(IV), (C)-(I), (D)-(III)
Which one of the following forces cannot be expressed in terms of potential energy?
- ACoulomb's force
- BGravitational force
- CFrictional force
- DRestoring force
$M$ and $R$ be the mass and radius of a disc. A small disc of radius $R / 3$ is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc about an axis $A B$ passing through the centre O and perpendicular to the plane of disc is $\frac{4}{x} M^{2}$. The value of $x$ is __________ .
View full solution →The electric field in a region is given by $\vec{E}=(2 \hat{i}+4 \hat{j}+6 \hat{k}) \times 10^{3} N / C$. The flux of the field through a rectangular surface parallel to $x-z$ plane is $6.0 \mathrm{Nm}^{2} \mathrm{C}^{-1}$. The area of the surface is __________ $\mathrm{cm}^{2}$.
View full solution →Two cylindrical rods A and B made of different materials, are joined in a straight line. The ratio of lengths, radii and thermal conductivities of these rods are :
$\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2$ and $\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}$. The free ends of rods A and B are maintained at $400 \mathrm{~K}, 200 \mathrm{~K}$, respectively. The temperature of rods interface is __________ K , when equilibrium is established.
View full solution →$\frac{\mathrm{L}_{\mathrm{A}}}{\mathrm{L}_{\mathrm{B}}}=\frac{1}{2}, \frac{\mathrm{r}_{\mathrm{A}}}{\mathrm{r}_{\mathrm{B}}}=2$ and $\frac{\mathrm{K}_{\mathrm{A}}}{\mathrm{K}_{\mathrm{B}}}=\frac{1}{2}$. The free ends of rods A and B are maintained at $400 \mathrm{~K}, 200 \mathrm{~K}$, respectively. The temperature of rods interface is __________ K , when equilibrium is established.
An inductor of reactance $100 \Omega$, a capacitor of reactance $50 \Omega$, and a resistor of resistance $50 \Omega$ are connected in series with an AC source of 10 V, 50 Hz . Average power dissipated by the circuit is__________ W.
View full solution →A parallel plate capacitor has charge $5 \times 10^{-6} \mathrm{C}$. A dielectric slab is inserted between the plates and almost fills the space between the plates. If the induced charge on one face of the slab is $4 \times 10^{-6} \mathrm{C}$ then the dielectric constant of the slab is __________ .
View full solution →Given below are two statements :
1 M aqueous solution of each of $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{AgNO}_{3}$, $\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2} ; \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ are electrolysed using inert electrodes,
Given : $\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\theta}=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Hg}_{2}^{2+} / \mathrm{Hg}}^{\theta}=0.79 \mathrm{~V}$,
$\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\theta}=0.24 \mathrm{~V}$ and $\mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^{\theta}=-2.37 \mathrm{~V}$
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be $\mathrm{Ag}, \mathrm{Hg}$ and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below
1 M aqueous solution of each of $\mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}, \mathrm{AgNO}_{3}$, $\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2} ; \mathrm{Mg}\left(\mathrm{NO}_{3}\right)_{2}$ are electrolysed using inert electrodes,
Given : $\mathrm{E}_{\mathrm{Ag}^{+} / \mathrm{Ag}}^{\theta}=0.80 \mathrm{~V}, \mathrm{E}_{\mathrm{Hg}_{2}^{2+} / \mathrm{Hg}}^{\theta}=0.79 \mathrm{~V}$,
$\mathrm{E}_{\mathrm{Cu}^{2+} / \mathrm{Cu}}^{\theta}=0.24 \mathrm{~V}$ and $\mathrm{E}_{\mathrm{Mg}^{2+} / \mathrm{Mg}}^{\theta}=-2.37 \mathrm{~V}$
Statement (I) : With increasing voltage, the sequence of deposition of metals on the cathode will be $\mathrm{Ag}, \mathrm{Hg}$ and Cu
Statement (II) : Magnesium will not be deposited at cathode instead oxygen gas will be evolved at the cathode.
In the light of the above statement, choose the most appropriate answer from the options given below
- ABoth statement I and statement II are incorrect
- BStatement I is correct but statement II is incorrect
- CBoth statement I and statement II are correct
- DStatement I is incorrect but statement II is correct
The correct statements from the following are :
(A) $\mathrm{Tl}^{3+}$ is a powerful oxidising agent
(B) $\mathrm{Al}^{3+}$ does not get reduced easily
(C) Both $\mathrm{Al}^{3+}$ and $\mathrm{Tl}^{3+}$ are very stable in solution
(D) $\mathrm{Tl}^{+}$is more stable than $\mathrm{Tl}^{3+}$
(E) $\mathrm{Al}^{3+}$ and $\mathrm{Tl}^{+}$are highly stable
Choose the correct answer from the options given below :
(A) $\mathrm{Tl}^{3+}$ is a powerful oxidising agent
(B) $\mathrm{Al}^{3+}$ does not get reduced easily
(C) Both $\mathrm{Al}^{3+}$ and $\mathrm{Tl}^{3+}$ are very stable in solution
(D) $\mathrm{Tl}^{+}$is more stable than $\mathrm{Tl}^{3+}$
(E) $\mathrm{Al}^{3+}$ and $\mathrm{Tl}^{+}$are highly stable
Choose the correct answer from the options given below :
- A(A), (B), (C), (D) and (E)
- B(A), (B), (D) and (E) only
- C(B), (D) and (E) only
- D(A), (C) and (D) only
The extra stability of half-filled subshell is due to
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another
Identify the correct statements
(A) Symmetrical distribution of electrons
(B) Smaller coulombic repulsion energy
(C) The presence of electrons with the same spin in non-degenerate orbitals
(D) Larger exchange energy
(E) Relatively smaller shielding of electrons by one another
Identify the correct statements
- A(B), (D) and (E) only
- B(A), (B), (D) and (E) only
- C(B), (C) and (D) only
- D(A), (B) and (D) only
Given below are two statements :
In the light of the above statements, choose the most appropriate answer from the options given below :
In the light of the above statements, choose the most appropriate answer from the options given below :
- AStatement I is correct but statement II is incorrect
- BStatement I is correct but statement II is incorrect
- CBoth statement I and statement II are incorrect
- DBoth statement I and statement II are correct
The number of optically active products obtained from the complete ozonolysis of the given compound is :
- A2
- B0
- C1
- D4
Identify the structure of the final product (D) in the following sequence of the reactions :
Total number of $\mathrm{sp}^{2}$ hybridised carbon atoms in product D is.
View full solution →Total number of $\mathrm{sp}^{2}$ hybridised carbon atoms in product D is.
The number of paramagnetic metal complex species among $\left[\mathrm{Co}\left(\mathrm{NH}_{3}\right)_{6}\right]^{3+}, \quad\left[\mathrm{Co}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]^{3-}$, $\left[\mathrm{MnCl}_{6}\right]^{3-},\left[\mathrm{Mn}(\mathrm{CN})_{6}\right]^{3-},\left[\mathrm{CoF}_{6}\right]^{3-},\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3^{--}}$and $\left[\mathrm{FeF}_{6}\right]^{3-}$ with same number of unpaired electrons is__________ .
View full solution →Butane reacts with oxygen to produce carbon dioxide and water following the equation given below
$\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{~g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{CO}_{2}(\mathrm{~g})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
If 174.0 kg of butane is mixed with 320.0 kg of $\mathrm{O}_{2}$, the volume of water formed in litres is __________.(Nearest integer)
[Given : (a) Molar mass of $\mathrm{C}, \mathrm{H}, \mathrm{O}$ are 12, 1, $16 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively, (b) Density of water $\left.=1 \mathrm{~g} \mathrm{~mL}^{-1}\right]$
View full solution →$\mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{~g})+\frac{13}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow 4 \mathrm{CO}_{2}(\mathrm{~g})+5 \mathrm{H}_{2} \mathrm{O}(\mathrm{l})$
If 174.0 kg of butane is mixed with 320.0 kg of $\mathrm{O}_{2}$, the volume of water formed in litres is __________.(Nearest integer)
[Given : (a) Molar mass of $\mathrm{C}, \mathrm{H}, \mathrm{O}$ are 12, 1, $16 \mathrm{~g} \mathrm{~mol}^{-1}$ respectively, (b) Density of water $\left.=1 \mathrm{~g} \mathrm{~mL}^{-1}\right]$
In Dumas' method 292 mg of an organic compound released 50 mL of nitrogen gas $\left(\mathrm{N}_{2}\right)$ at 300 K temperature and 715 mm Hg pressure. The percentage composition of ' N ' in the organic compound is __________ % (Nearest integer)
(Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ )
View full solution →(Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ )
Only litre buffer solution was prepared by adding 0.10 mol each of $\mathrm{NH}_{3}$ and $\mathrm{NH}_{4} \mathrm{Cl}$ in deionised water. The change in pH on addition of 0.05 mol of HCl to the above solution is __________ $\times 10^{-2}$, (Nearest integer)
(Given : $\mathrm{pK}_{\mathrm{b}}$ of $\mathrm{NH}_{3}=4.745$ and $\log _{10} 3=0.477$ )
View full solution →(Given : $\mathrm{pK}_{\mathrm{b}}$ of $\mathrm{NH}_{3}=4.745$ and $\log _{10} 3=0.477$ )
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