Sample QuestionsJEE Main 7-April-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.
Let $A B C$ be the triangle such that the equations of lines $A B$ and $A C$ be $3 y-x=2$ and $x+y=2$, respectively, and the points $B$ and $C$ lie on $x$-axis. If $P$ is the orthocentre of the triangle $A B C$, then the area of the triangle PBC is equal to
View full solution →Let the angle $\theta, 0<\theta<\frac{\pi}{2}$ between two unit vectors $\hat{a}$ and $\hat{b}$ be $\sin ^{-1}\left(\frac{\sqrt{65}}{9}\right)$. If the vector $\vec{c}=3 \hat{a}+6 \hat{b}+9(\hat{a} \times \hat{b}), \quad$ then the value of $9(\vec{c} \cdot \hat{a})-3(\vec{c} \cdot \hat{b})$ is
View full solution →Let the line L pass through $(1,1,1)$ and intersect the lines $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-4}{2}=\frac{z}{1}$ . Then, which of the following points lies on the line L?
- A
$(4,22,7)$
- B
$(5,4,3)$
- C
$(10,-29,-50)$
- D
$(7,15,13)$
View full solution →Let the system of equations :
$2 x+3 y+5 z=9$,
$7 x+3 y-2 z=8$,
$12 x+3 y-(4+\lambda) z=16-\mu$,
have infinitely many solutions. Then the radius of the circle centred at $(\lambda, \mu)$ and touching the line $4 \mathrm{x}=3 \mathrm{y}$ is
- A
$\frac{17}{5}$
- B
$\frac{7}{5}$
- C
- D
$\frac{21}{5}$
View full solution →If the area of the region bounded by the curves $y=4-\frac{x^{2}}{4}$ and $y=\frac{x-4}{2}$ is equal to $\alpha$, then $6 \alpha$ equals
View full solution →For $\mathrm{n} \geq 2$, let $S_{n}$ denote the set of all subsets of $\{1,2 \ldots \ldots ., n\}$ with no two consecutive numbers. For example $\{1,3,5\} \in \mathrm{S}_{6}$, but $\{1,2,4\} \notin \mathrm{S}_{6}$. Then $n\left(S_{5}\right)$ is equal to __________.
View full solution →The number of singular matrices of order 2, whose elements are from the set $\{2,3,6,9\}$ is
View full solution →Consider the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ having one of its focus at $\mathrm{P}(-3,0)$. If the latus ractum through its other focus subtends a right angle at P and $a^{2} b^{2}=\alpha \sqrt{2}-\beta, \alpha, \beta \in \mathbb{N}$.
View full solution →The number of relations on the set $\mathrm{A}=\{1,2,3\}$ containing at most 6 elements including (1, 2), which are reflexive and transitive but not symmetric, is __________.
View full solution →The number of points of discontinuity of the function $f(\mathrm{x})=\left[\frac{\mathrm{x}^{2}}{2}\right]-[\sqrt{\mathrm{x}}], \mathrm{x} \in[0,4]$, where $[\cdot]$ denotes the greatest integer function is __________.
View full solution →Two charges $q_{1}$ and $q_{2}$ are separated by a distance of 30 cm. A third charge $q_{3}$ initially at '$C$' as shown in the figure, is moved along the circular path of radius 40 cm from C to D. If the difference in potential energy due to movement of $q_{3}$ from $C$ to $D$ is given by $\frac{q_{3} K}{4 \pi \in_{0}}$, the value of $K$ is :
- A
$8 q_{2}$
- B
$6 q_{2}$
- C
$8 q_{1}$
- D
$6 q_{1}$
View full solution →Two wires A and B are made of same material having ratio of lengths $\frac{L_{A}}{L_{B}}=\frac{1}{3}$ and their diameters ratio $\frac{d_{A}}{d_{B}}=2$. If both the wires are stretched using same force, what would be the ratio of their respective elongations?
- A
$1: 6$
- B
$1: 12$
- C
$3: 4$
- D
$1: 3$
View full solution →An object of mass 1000 g experiences a time dependent force $\overrightarrow{\mathrm{F}}=\left(2 t \hat{\mathrm{i}}+3 \mathrm{t}^{2} \hat{\mathrm{j}}\right) \mathrm{N}$. The power generated by the force at time $t$ is :
- A
$\left(2 t^{2}+3 t^{3}\right) W$
- B
$\left(2 t^{2}+18 t^{3}\right) \mathrm{W}$
- C
$\left(3 t^{3}+5 t^{5}\right) \mathrm{W}$
- D
$\left(2 t^{3}+3 t^{5}\right) \mathrm{W}$
View full solution →A particle of charge $q$, mass $m$ and kinetic energy E enters in magnetic field perpendicular to its velocity and undergoes a circular arc of radius(r). Which of the following curves represents the variation of $r$ with $E$ ?
View full solution →For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is.
- A
$5: 36$
- B
$5: 27$
- C
$3: 4$
- D
$27: 5$
View full solution →View full solution →A wire of length 10 cm and diameter 0.5 mm is used in a bulb. The temperature of the wire is $1727^{\circ} \mathrm{C}$ and power radiated by the wire is 94.2 W. Its emissivity is $\frac{x}{8}$ where $x=$ __________
(Given $\sigma=6.0 \times 10^{-8} \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-4}, \pi=3.14$ and assume that the emissivity of wire material is same at all wavelength.)
View full solution →A container contains a liquid with refractive index of 1.2 up to a height of 60 cm and another liquid having refractive index 1.6 is added to height H above first liquid. If viewed from above, the apparent shift in the position of bottom of container is 40 cm. The value of H is __________ cm.
(Consider liquids are immisible)
$A, B$ and $C$ are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure.
The moment of inertia of the given system about $P Q$ is $\frac{x}{15} I$, where $I$ is the moment of inertia of the disc about its diameter. The value of $x$ is __________ . View full solution →The reactions which cannot be applied to prepare an alkene by elimination, are
Choose the correct answer from the option given below :
An octahedral complex having molecular composition $Co.5 \mathrm{NH}_{3}.\mathrm{Cl}. \mathrm{SO}_{4}$ has two isomers A and B. The solution of A gives a white precipitate with $\mathrm{AgNO}_{3}$ solution and the solution of B gives white precipitate with $\mathrm{BaCl}_{2}$ solution. The type of isomerism exhibited by the complex is,
View full solution →Given below are two statements :
Statement I : D-(+)-glucose + D-(+) fructose $\xrightarrow{-\mathrm{H}_{2} \mathrm{O}}$ sucrose
sucrose $\xrightarrow{\text { Hydrolysis }}$ D-(+)-glucose + D-(+) fructose
Statement II : Invert sugar is formed during sucrose hydrolysis.
In the light of the above statements, choose the correct answer from the options given below -
- A
Both Statement I and Statement II are true.
- B
Statement I is false but Statement II are true.
- C
Statement I is true but Statement II is false.
- D
Both Statement I and Statement II are false.
View full solution →A person's wound was exposed to some bacteria and then bacteria growth started to happen at the same place. The wound was later treated with some antibacterial medicine and the rate of bacterial decay (r) was found to be proportional with the square of the existing number of bacteria at any instance. Which of the following set of graphs correctly represents the 'before' and 'after' situation of the application of the medicine?
[Given : $\mathrm{N}=\mathrm{No}$. of bacteria, $\mathrm{t}=$ time, bacterial growth follows I$^{\text {st }}$ order kinetics.]
View full solution →Match the LIST-I with LIST-II.LIST-I
Molecule/ion | LIST-II
Bond pair : lone pair
(on the central atom) |
| A. | $\mathrm{ICl}_{2}^{-}$ | I. | 4 : 2 |
| B. | $\mathrm{H}_{2} \mathrm{O}$ | II. | 4 : 1 |
| C. | $\mathrm{SO}_{2}$ | III. | 2 : 3 |
| D. | $\mathrm{XeF}_{4}$ | IV. | 2 : 2 |
Choose the correct answer from the options given below : View full solution →The number of paramagnetic complex among
$\left[ FeF _6\right]^{3-}, \left[ Fe ( CN )_6\right]^{3-}, \left[ Mn ( CN )_6\right]^{3-}, \left[ Co \left( C _2 O _4\right)_3\right]^{3-}$, $\left[ MnCl _6\right]^{3-}$ and $\left[ CoF _6\right]^{3-}$, which involved $d ^2 sp ^3$ hybridization is __________ .
View full solution →The percentage dissociation of a salt $\left(\mathrm{MX}_{3}\right)$ solution at given temperature (van't Hoff factor $\mathrm{i}=$ $2)$ is. __________ % (Nearest integer)
View full solution →1 Faraday electricity was passed through $\mathrm{Cu}^{2+}(1.5$ $\mathrm{M}, 1 \mathrm{~L}) / \mathrm{Cu}$ and 0.1 Faraday was passed through $\mathrm{Ag}^{+}(0.2 \mathrm{M}, 1 \mathrm{~L}) / \mathrm{Ag}$ electrolytic cells. After this the two cells were connected as shown below to make an electrochemical cell. The emf of the cell thus formed at 298 K is-
$\begin{aligned} \text { Given : } & E _{ Cu ^2 / Cu }^0=0.34 V \\ & E _{ Ag ^{+} / Ag }^0=0.8 V \\ \frac{2.303 RT }{ F } & =0.06 V\end{aligned}$ View full solution →View full solution →An organic compound weighing 500 mg, produced 220 mg of $\mathrm{CO}_{2}$. on complete combustion. The percentage composition of carbon in the compound is __________ $\%$. (nearest integer)
(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1}$ of $\mathrm{C}: 12, \mathrm{O}: 16$)
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