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Q JEE MAIN
The refractive index of prism is $\mu=\sqrt{3}$ and the ratio of the angle of minimum deviation to the angle of prism is one. The value...
JEE Main Physics Hard
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Q JEE MAINS 2024
Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses...
JEE Main Physics Hard
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Q JEE MAIN
When a dc voltage of 100V is applied to an inductor, a de current of 5A flows through it. When an ac voltage of 200"...
JEE Main Physics Medium
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Q JEE MAINS 2024
Four identical particles of mass $m$ are kept at the four corners of a square. If the gravitational force exerted on one of the masses...
JEE Main Physics Easy
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Q JEE MAIN
A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of energy of...
JEE Main Physics Medium
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Q JEE MAIN
Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point P is $\frac{\mathrm{X} \sigma}{\epsilon_0}$. The...
JEE Main Physics Medium
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Q JEE MAINS 2024
If the wavelength of the first member of Lyman series of hydrogen is λ. The wavelength of the second member will be
JEE Main Physics Easy
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Q JEE MAIN
If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day...
JEE Main Physics Medium
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Q JEE MAIN
In photoelectric experiment energy of 2.48eV irradiates a photo sensitive material. The stopping potential was measured to be 0.5 V. Work function of the photo...
JEE Main Physics Medium
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Q JEE MAINS 2024
A rigid wire consists of a semicircular portion of radius R and two straight sections. The wire is partially immerged in a perpendicular magnetic field...
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Q JEE MAIN
A small ball of mass m and density $\rho$ is dropped in a viscous liquid of density $\rho_0$. After sometime, the ball falls with constant...
JEE Main Physics Medium
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Q JEE MAINS 2024
The refractive index of a prism with apex angle A is cot⁡A/2. The angle of minimum deviation is :
JEE Main Physics Easy
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Q JEE MAIN
An element $\Delta l=\Delta x \hat{i}$ is placed at the origin and carries a large current I=10 A. The magnetic field on the y-axis at...
JEE Main Physics Medium
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Q JEE MAINS 2024
$$ \text { The relation between time ' } t \text { ' and distance ' } x \text { ' is } t=\alpha x^2+\beta...
JEE Main Physics Hard
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Q JEE MAIN
A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed...
JEE Main Physics Medium
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Q JEE MAIN
Four particles A, B, C, D of mass$\frac{m}{2}, m, 2 m, 4 m$, have same momentum, respectively. The particle with maximum kinetic energy is :
JEE Main Physics Easy
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Q JEE MAIN
Two charged conducting spheres of radii a and b are connected to each other by a conducting wire. The ratio of charges of the two...
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Q JEE MAIN
The output Y of following circuit for given inputs is :
JEE Main Physics Medium
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A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other...
JEE Main Physics Medium
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Q JEE MAIN 2024
A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the...
JEE Main Physics Medium
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Q JEE MAIN 2024
A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the...
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Q JEE MAIN
Two planets A and B having masses m1 and m2 move around the sun in circular orbits of $r_1$ and $\mathrm{r}_2$ radii respectively. If angular...
JEE Main Physics Medium
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Q JEE MAIN 2024
A sphere of relative density σ and diameter D has concentric cavity of diameter d. The ratio of D/d, if it just floats on water...
JEE Main Physics Hard
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Q JEE MAIN 2024
A light emitting diode (LED) is fabricated using GaAs semiconducting material whose band gap is 1.42eV. The wavelength of light emitted from the LED is:
JEE Main Physics Easy
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Q JEE MAIN 2024
Given below are two statements: Statement (I): When an object is placed at the centre of curvature of a concave lens, image is formed at...
JEE Main Physics Medium
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Q JEE MAIN
A light string passing over a smooth light pulley connects two blocks of masses $\mathrm{m}_1$ and $\mathrm{m}_2$ (where $\left.m_2>m_1\right)$. If the acceleration of the system...
JEE Main Physics Easy
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Q JEE MAIN 2024
A plane EM wave is propagating along x direction. It has a wavelength of 4 mm. If electric field is in y direction with the...
JEE Main Physics Medium
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Q JEE MAIN
Young's modulus is determined by the equation given by $\mathrm{Y}=49000 \frac{\mathrm{~m}}{\ell} \frac{\text { dyne }}{\mathrm{cm}^2}$ where M is the mass and l is the extension...
JEE Main Physics Medium
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Q JEE MAIN
A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :
JEE Main Physics Medium
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Q JEE MAIN 2024
A particle moving in a straight line covers half the distance with speed 6 m/s. The other half is covered in two equal time intervals...
JEE Main Physics Medium
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Q JEE MAIN
The correct truth table for the following logic circuit is :
JEE Main Physics Medium
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Q JEE MAIN
A clock has 75" " cm,60" " cm long second hand and minute hand respectively. In 30 minutes duration the tip of second hand will...
JEE Main Physics Medium
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Q JEE MAIN
Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than...
JEE Main Physics Easy
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Q JEE MAIN
Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II : Current in a...
JEE Main Physics Hard
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Q JEE MAIN
Match List I with List II Choose the correct answer from the options given below...
JEE Main Physics Hard
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Q JEE MAIN 2024
Two forces $\vec{F}_1$ and $\vec{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the...
JEE Main Physics Medium
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Q JEE MAIN
In the given circuit, the terminal potential difference of the cell is :
JEE Main Physics Medium
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Q JEE MAIN
The specific heat at constant pressure of a real gas obeying $\mathrm{PV}^2=\mathrm{RT}$ equation is :
JEE Main Physics Hard
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Q JEE MAIN 2024
An elastic spring under tension of 3 N has a length a . Its length is b under tension 2 N . For its length...
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Q JEE MAIN 2024
A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as:
JEE Main Physics Easy
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Q JEE MAIN
The value of unknown resistance (x) for which the potential difference between B and D will be zero in the arrangement shown, is :
JEE Main Physics Medium
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Q JEE MAIN
$\sigma$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point on the surface of...
JEE Main Physics Medium
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Q JEE MAIN 2024
Three capacitors of capacitances 25μF,30μF and 45μF are connected in parallel to a supply of 100 V. Energy stored in the above combination is E....
JEE Main Physics Hard
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Q JEE MAIN 2024
Two wavelengths $\lambda_1$ and $\lambda_2$ are used in Young's double slit experiment $\lambda_1=450 \mathrm{~nm}$ and $\lambda_2=650 \mathrm{~nm}$. The minimum order of fringe produced by $\lambda_2$...
JEE Main Physics Medium
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Q JEE MAIN
While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1" " mm and circular scale reading is...
JEE Main Physics Hard
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Q JEE MAIN 2024
In the experiment to determine the galvanometer resistance by half-deflection method, the plot of 1/θ vs the resistance (R) of the resistance box is shown...
JEE Main Physics Medium
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Q JEE MAIN 2024
A soap bubble is blown to a diameter of 7 cm . 36960erg of work is done in blowing it further. If surface tension of...
JEE Main Physics Medium
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Q JEE MAIN
Which of the following phenomena does not explain by wave nature of light. (A) reflection (B) diffraction (C) photoelectric effect (D) interference (E) polarization Choose...
JEE Main Physics Easy
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Q JEE MAIN 2024
Twelve wires each having resistance $2 \Omega$ are joined to form a cube. A battery of 6 V emf is joined across point a and...
JEE Main Physics Medium
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Q JEE MAIN 2024
An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20μF is ..............V.
JEE Main Physics Medium
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Q JEE MAIN 2024
A alternating current at any instant is given by $\mathrm{i}=\left[6+\sqrt{56} \sin \left(100 \pi \mathrm{t}+\frac{\pi}{3}\right)\right] \mathrm{A}$. The rms value of the current is $\_\_\_\_$ A.
JEE Main Physics Easy
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Q JEE MAIN 2024
If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is ............ × 〖10〗^(-2) MeV. (Given 1u=931MeV/c^2, atomic...
JEE Main Physics Medium
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Q JEE MAIN
Three bodies A,B and C have equal kinetic energies and their masses are 400g,1.2kg and 1.6kg respectively. The ratio of their linear momenta is :
JEE Main Physics Easy
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Q JEE MAIN
Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~ms}^{-1}$ The relative permeability of the medium is 2.0. The relative permittivity will...
JEE Main Physics Medium
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Q JEE MAIN 2024
A body moves on a frictionless plane starting from rest. If S_n is distance moved between t=n-1 and t =n and S_(n-1) is distance moved...
JEE Main Physics Medium
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Q JEE MAIN
To project a body of mass m from earth's surface to infinity, the required kinetic energy is (assume, the radius of earth is $\mathrm{R}_{\mathrm{E}}, \mathrm{g}=$...
JEE Main Physics Medium
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Q JEE MAIN 2024
The density and breaking stress of a wire are 6× 〖10〗^4 " " kg/m^3 and 1.2×〖10〗^8 " " N/m^2 respectively. The wire is suspended from...
JEE Main Physics Medium
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Q JEE MAIN 2024
Three blocks M_1,M_2,M_3 having masses 4 kg,6 kg and 10 kg respectively are hanging from a smooth pully using rope 1,2 and 3 as shown...
JEE Main Physics Easy
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Q JEE MAIN 2024
The magnetic field existing in a region is given by $\vec{B}=0.2(1+2 x) \hat{k} T$. A square loop of edge 50 cm carrying 0.5 A current...
JEE Main Physics Easy
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Q JEE MAIN 2024
If the shortest distance between the lines L_1:r ⃗=(2+λ)i ˆ+(1-3λ)j ˆ+(3+4λ)k ˆ,λ∈R L_2:r ⃗=2(1+μ)i ˆ+3(1+μ)j ˆ+(5+μ)k ˆ,μ∈R is m/√n, where gcd⁡(m,n)=1, then the value of...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $A$ and $B$ be two square matrices of order 3 such that $|A|=3$ and $|B|=2$. Then $\left|A^T A(\operatorname{adj}(2 A))^{-1}(\operatorname{adj}(4 B))(\operatorname{adj}(A B))^{-1} A A^T\right|$ is...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $A=\left[\begin{array}{lll}2 & a & 0 \\ 1 & 3 & 1 \\ 0 & 5 & b\end{array}\right]$. If $A^3=4 A^2-A-21 I$, where 1 is...
JEE Main Mathematics Hard
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Q JEE-Main 2024
The function $f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in R$ is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let λ,μ∈R. If the system of equations 3x+5y+λz=3 7x+11y-9z=2 97x+155y-189z=μ has infinitely many solutions, then μ+2λ is equal to :
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10$. The number of points of local maxima of $f$ in interval $(0,2 \pi)$ is:
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $f(x)$ be a positive function such that the area bounded by $y=f(x), y=0$ from $x=0$ to $x=a>0$ is $\mathrm{e}^{-\mathrm{a}}+4 \mathrm{a}^2+\mathrm{a}-1$. Then the differential equation,...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
The integral $\int_0^{\frac{\pi}{4}} \frac{136 \sin x}{3 \sin x+5 \cos x} d x$ is equal to :
JEE Main Mathematics Easy
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Q JEE-Main 2024
The mean and standard deviation of 20 observations are found to be 10 and 2, respectively. On respectively, it was found that an observation by...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
The number of critical points of the function $f(x)=(x-2)^{2 / 3}(2 x+1)$ is:
JEE Main Mathematics Easy
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Q JEE-Main 2024
$\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x$ is equal to $\_\_\_\_$
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If the function $f(x)=\frac{\sin 3 x+\alpha \sin x-\beta \cos 3 x}{x^3}, x \in R$, is continuous at $x=0$, then $f(0)$ is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $\mathrm{P}(\mathrm{x}, \mathrm{y}, \mathrm{z})$ be a point in the first octant, whose projection in the xy -plane is the point Q . Let $\mathrm{OP}=\gamma$; the...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $A=\{1,3,7,9,11\}$ and $B=\{2,4,5,7,8,10,12\}$. Then the total number of one-one maps $f: A \rightarrow B$, such that $f(1)+f(3)=14$, is :
JEE Main Mathematics Easy
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Q JEE-Main 2024
If $\mathrm{A}(3,1,-1), \mathrm{B}\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), \mathrm{C}(2,2,1)$ and $\mathrm{D}\left(\frac{10}{3}, \frac{2}{3}, \frac{-1}{3}\right)$ are the vertices of a quadrilateral ABCD , then its area is $\_\_\_\_$ .
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let the circles $C_1:(x-\alpha)^2+(y-\beta)^2=r_1^2$ and $C_2:(x-8)^2+\left(y-\frac{15}{2}\right)^2=r_2^2$ touch each other externally at the point $(6,6)$. If the point $(6,6)$ divides the line segment joining the centres...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is is:
JEE Main Mathematics Easy
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Q JEE MAIN 2024N
If the system of equations has infinitely many solutions, then $\lambda^4-\mu$ is equal to:
JEE Main Mathematics Easy
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Q JEE MAIN 2024
The value of $k \in \mathbb{N}$ for which the integral $I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}$, satisfies $147 I_{20}=148 I_{21}$ is:
JEE Main Mathematics Medium
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Q JEE-Main 2024
If $f(x)=\left\{\begin{array}{cc}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$, then
JEE Main Mathematics Medium
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Q JEE MAIN 2024
For the function f(x)=sin⁡x+3x-2x2+x, where x0,2, consider the following two statements :
(I) f is increasing in 0,2.
(II) f' is decreasing in 0,2. Between...
JEE Main Mathematics Hard
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Q JEE MAIN 2024
There are 5 points $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \mathrm{P}_4, \mathrm{P}_5$ on the side AB , excluding A and B , of a triangle ABC . Similarly...
JEE Main Mathematics Easy
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Q JEE MAIN
Let $\vec{a}, \vec{b}$ and $\overrightarrow{\mathrm{c}}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a}+5 \vec{b}$is collinear with$\vec{c}, \vec{b}+6 \vec{c}$ is collinear...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
If the system of equations $$ \begin{aligned} & x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0 \\ & \mathrm{x}+(\cos \alpha) \mathrm{y}+(\sin \alpha) \mathrm{z}=0 \\ & \mathrm{x}+(\sin...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If y=y(x) is the solution of the differential equation dydx+2y=sin⁡(2x),y(0)=34, then y8 is equal to :
JEE Main Mathematics Easy
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Q JEE MAIN 2024
One of the points of intersection of the curves $y=1+3 x-2 x^2$ and $y=\frac{1}{x}$ is $\left(\frac{1}{2}, 2\right)$. Let the area of the region enclosed by...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let the sum of the maximum and the minimum values of the function $f(x)=\frac{2 x^2-3 x+8}{2 x^2+3 x+8}$ be $\frac{m}{n}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$. Then $\mathrm{m}+\mathrm{n}$...
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Q JEE MAIN 2024
If the solution $y=y(x)$ of the differential equation $\left(x^4+2 x^3+3 x^2+2 x+2\right) d y-\left(2 x^2+2 x+3\right) d x=0$ satisfies $y(-1)=-\frac{\pi}{4}$, then $y(0)$ is equal to:
JEE Main Mathematics Hard
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Q JEE MAIN 2024
Let a rectangle ABCD of sides 2 and 4 be inscribed in another rectangle PQRS such that the vertices of the rectangle ABCD lie on...
JEE Main Mathematics Hard
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Q JEE MAIN 2024
The vertices of a triangle are A(-1,3),B(-2,2) and C(3,-1). A new triangle is formed by shifting the sides of the triangle by one unit inwards....
JEE Main Mathematics Hard
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Q JEE MAIN 2024
Three urns A, B and C contain 7 red, 5 black; 5 red, 7 black and 6 red, 6 black balls, respectively. One of the...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let d be the distance of the point of intersection of the lines x+63=y2=z+11 and x-74=y-93=z-42 from the point (7,8,9). Then d2+6 is equal to...
JEE Main Mathematics Hard
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Q JEE MAIN 2024
Let $f: \mathrm{R} \rightarrow \mathrm{R}$ be a function given by $$ f(x)=\left\{\begin{array}{cl} \frac{1-\cos 2 x}{x^2} & , x<0 \\ \alpha & , x=0, \text {...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $\alpha=1^2+4^2+8^2+13^2+19^2+26^2+\cdots \ldots$ upto 10 terms and $\beta=\sum_{n=1}^{10} n^4$. If $4 \alpha-\beta=55 k+40$, then k is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If the function $f(x)=\left\{\begin{array}{cl}\frac{1}{|x|} & , \\ a x^2+2 b, & |x| \geq 2\end{array}\right.$ is differentiable on R , then $48(\mathrm{a}+\mathrm{b})$ is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be a function defined by $$ \begin{aligned} & f(x)=\frac{4^x}{4^x+2} \text { and } \\ & M=\int_{f(a)}^{f(1-a)} x \sin ^4(x(1-x)) d...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $\alpha, \beta \in N$ be roots of equation $x^2-70 x+\lambda=0$, where $\frac{\lambda}{2}, \frac{\lambda}{3} \notin \mathrm{~N}$. If $\lambda$ assumes the minimum possible value, then $\frac{(\sqrt{\alpha-1}+\sqrt{\beta-1})(\lambda+35)}{|\alpha-\beta|}$...
JEE Main Mathematics Easy
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Q JEE-Main 2024
Let $A=\{1,2,3, \ldots 20\}$. Let $R_1$ and $R_2$ two relation on A such that $\mathrm{R}_1=\{(\mathrm{a}, \mathrm{b}): \mathrm{b}$ is divisible by a$\}$ $\mathrm{R}_2=\{(\mathrm{a}, \mathrm{b}): \mathrm{a}$ is...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let A={1,2,3,4} and R={(1,2),(2,3),(1,4)} be a relation on A. Let S be the equivalence relation on A such that R⊂S and the number of elements...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}|=1,|\vec{b}|=4$ and $\vec{a} \cdot \vec{b}=2$. If $\vec{c}=(2 \vec{a} \times \vec{b})-3 \vec{b}$ and the angle between $\vec{b}$...
JEE Main Mathematics Easy
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Q JEE-Main 2024
Let the line of the shortest distance between the lines $\mathrm{L}_1: \vec{r}=(\hat{\imath}+2 \hat{\jmath}+3 \hat{k})+\lambda(\hat{\imath}-\hat{\jmath}+\hat{k})$ and $\mathrm{L}_2: \overrightarrow{\mathrm{r}}= (4 \hat{\imath}+5 \hat{\jmath}+6 \hat{k})+\mu(\hat{\imath}+\hat{\jmath}-\hat{k})$ intersect $L_1$ and $L_2$...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let $y=y(x)$ be the solution of the differential equation $\left(1-x^2\right) d y=\left[x y+\left(x^3+2\right) \sqrt{3\left(1-x^2\right)}\right] d x,-1< x<1, y(0)=0$. If $y\left(\frac{1}{2}\right)=\frac{m}{n}, m$ and $n$ are coprime...
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Q JEE-Main 2024
If $\int_{-\pi / 2}^{\pi / 2} \frac{8 \sqrt{2} \cos x d x}{\left(1+e^{\sin x}\right)\left(1+\sin ^4 x\right)}=\alpha \pi+\beta \log _e(3+2 \sqrt{2})$, where $\alpha, \beta$ are integers, then...
JEE Main Mathematics Easy
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Q JEE MAIN 2024
Let the foci and length of the latus rectum of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1, a>b$ be $( \pm 5,0)$ and $\sqrt{50}$, respectively. Then, the square of...
JEE Main Mathematics Easy
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Q JEE-Main 2024
Let $\mathrm{P}=\{\mathrm{z} \in \mathbb{C}:|\mathrm{z}+2-3 \mathrm{i}| \leq 1\}$ and $\mathrm{Q}=\{\mathrm{z} \in \mathbb{C}: \mathrm{z}(1+\mathrm{i})+\overline{\mathrm{z}}(1-\mathrm{i}) \leq-8\}$. Let in $\mathrm{P} \cap \mathrm{Q},|\mathrm{z}-3+2 \mathrm{i}|$ be maximum and minimum at $z_1$...
JEE Main Mathematics Hard
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Q JEE MAIN 2024
If $\alpha$ denotes the number of solutions of $|1-\mathrm{i}|^{\mathrm{x}}=2^{\mathrm{x}}$ and $\beta=\left(\frac{|z|}{\arg (z)}\right)$, where $\mathrm{z}=\frac{\pi}{4}(1+\mathrm{i})^4\left(\frac{1-\sqrt{\pi} \mathrm{i}}{\sqrt{\pi}+\mathrm{i}}+\right. \left.\frac{\sqrt{\pi}-\mathrm{i}}{1+\sqrt{\pi} \mathrm{i}}\right), \mathrm{i}=\sqrt{-1}$, then the distance of the point $...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
The value 9∫_0^9 [√(10x/(x+1))]dx, where [t] denotes the greatest integer less than or equal to t, is
JEE Main Mathematics Easy
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Q JEE-Main 2024
Let the line $\mathrm{L}: \sqrt{2} \mathrm{x}+\mathrm{y}=\alpha$ pass through the point of the intersection P (in the first quadrant) of the circle $x^2+y^2=3$ and the parabola...
JEE Main Mathematics Medium
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Q JEE-Main 2024
In the expansion of $(1+x)\left(1-x^2\right)\left(1+\frac{3}{x}+\frac{3}{x^2}+\frac{1}{x^3}\right)^5, x \neq 0$, the sum of the coefficient of $x^3$ and $x^{-13}$ is equal to
JEE Main Mathematics Medium
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Q JEE-Main 2024
Let $\{x\}$ denote the fractional part of $x$ and $f(x)=\frac{\cos ^{-1}\left(1-\{x\}^2\right) \sin ^{-1}(1-\{x\})}{\{x\}-\{x\}^3}, x \neq 0$. If $L$ and R respectively denotes the left hand...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $Q$ and $R$ be the feet of perpendiculars from the point $P(a, a, a)$ on the lines $x=y, z=1$ and $x=-y, z=$ -1 respectively....
JEE Main Mathematics Easy
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Q JEE MAIN 2024
If d_1 is the shortest distance between the lines x+1=2y=-12z,x=y+2=6z-6 and d_2 is the shortest distance between the lines (x-1)/2=(y+8)/(-7)=(z-4)/5,(x-1)/2=(y-2)/1=(z-6)/(-3), then the value of (32√3...
JEE Main Mathematics Medium
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Q JEE-Main 01.02.24_(S1)
Let 3,7,11,15,….,403 and 2,5,8,11,…,404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to
JEE Main Mathematics Easy
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Q JEE MAIN 2024
The total number of words (with or without meaning) that can be formed out of the letters of the word 'DISTRIBUTION' taken four at a...
JEE Main Mathematics Medium
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Q JEE MAIN 2024
Let $S=(-1, \infty)$ and $f: S \rightarrow \mathbb{R}$ be defined as $f(x)=\int_{-1}^x\left(e^t-1\right)^{11}(2 t-1)^5(t-2)^7(t-3)^{12}(2 t-10)^{61} d t$ Let $p=$ Sum of square of the values of...
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Q JEE MAIN 2024
A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in...
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If the Coefficient of $x^{30}$ in the expansion of $\left(1+\frac{1}{x}\right)^6\left(1+x^2\right)^7\left(1-x^3\right)^8 ; x \neq 0$ is $\alpha$, then $|\alpha|$ equals
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If the integral $525 \int_0^{\frac{\pi}{2}} \sin 2 x \cos ^{\frac{11}{2}} x\left(1+\cos ^{\frac{5}{2}} x\right)^{\frac{1}{2}} d x$ is equal to $(n \sqrt{2}-64)$, then $n$ is equal to
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K_a for CH_3 COOH is 1.8×〖10〗^(-5) and K_b for NH_4 OH is 1.8×〖10〗^(-5). The pH of ammonium acetate solution will be
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Consider the following reaction: 3PbCl_2+2(NH_4 )_3 PO_4→Pb_3 (PO_4 )_2+6NH_4 Cl If 72mmol of PbCl_2 is mixed with 50mmol of (NH_4 )_3 PO_4, then amount of...
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Among the following oxide of p - block elements, number of oxides having amphoteric nature is Cl_2 O_7,CO,PbO_2,〖" " N〗_2 O,NO,Al_2 O_3,SiO_2,〖" " N〗_2 O_5,...
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Lowest Oxidation number of an atom in a compound A_2 " " B is -2 . The number of an electron in its valence shell...
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Total number of deactivating groups in aromatic electrophilic substitution reaction among the following is
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Number of colourless lanthanoid ions among the following is…. Eu^(3+),Lu^(3+),Nd^(3+),La^(3+),Sm^(3+)
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The number of molecules/ion/s having trigonal bipyramidal shape is PF_5,BrF_5,PCl_5,[PtCl_4 ]^(2-),BF_3,Fe(CO)_5
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The ratio of ( ^14 C)/( ^12 C) in a piece of wood is 1/8 part that of atmosphere. If half life of ^14 C...
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Total number of essential amino acid among the given list of amino acids is ______
Arginine, Phenylalanine, Aspartic acid, Cysteine, Histidine, Valine, Proline
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Number of ambidentate ligands among the following is $\_\_\_\_$
$ \mathrm{NO}_2^{-}, \mathrm{SCN}^{-}, \mathrm{C}_2 \mathrm{O}_4^{2-}, \mathrm{NH}_3, \mathrm{CN}^{-}, \mathrm{SO}_4^{2-}, \mathrm{H}_2 \mathrm{O} $
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The number of white coloured salts among the following is (A) SrSO_4 (B) Mg(NH_4 ) PO_4 (c) BaCrO_4 (D) Mn(OH)_2 (E) PbSO_4 (F) PbCrO_4 (G)...
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The total number of species from the following in which one unpaired electron is present, is N_2,O_2,C_2^-,O_2^-,O_2^(2-),H_2^+,CN^-,He_2^+
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The potential for the given half cell at 298" " K is (-)………...×〖10〗^(-2) " " V. 2H^+ _"aq) " +2e^-→H_2 (" " g) [H^+ ]=1M,P_(H_2...
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Molarity (M) of an aqueous solution containing xg of anhyd. CuSO_4 in 500" " mL solution at 32 ^∘ C is 2×10^(-1) M. Its molality...
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Number of optical isomers possible for 2 – chlorobutan
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When equal volume of 1 MHCl and $1 \mathrm{MH}_2 \mathrm{SO}_4$ are separately neutralised by excess volume of 1 M NaOH solution. X and ykJ of...
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The standard reduction potentials at 298" " K for the following half cells are given below : ■(&Cr_2 O_7^(2-)+14H^++6e^-→2Cr^(3+)+7H_2 O,E^∘=1.33" " V@Fe^(3+) (aq)+3e^-→Fe&E^∘=-0.04" " V@Ni^(2+)...
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How many compounds among the following compounds show inductive, mesomeric as well as hyperconjugation effects?
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Given below are two statements : Statement I : The rate law for the reaction A+B→C is rate (r)=k[A]^2 [" " B]. When the concentration...
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The heat of solution of anhydrous $\mathrm{CuSO}_4$ and $\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}$ are $-70 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and $+12 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The heat of...
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$0.05 \mathrm{MCuSO}_4$ when treated with $0.01 \mathrm{MKK}_2 \mathrm{Cr}_2 \mathrm{O}_7$ gives green colour solution of $\mathrm{Cu}_2 \mathrm{Cr}_2 \mathrm{O}_7$. The [SPM: Semi Permeable Membrane] Due to osmosis...
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Identify the incorrect statements regarding primary standard of titrimetric analysis (A) It should be purely available in dry form. (B) It should not undergo chemical...
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On reaction of Lead Sulphide with dilute nitric acid which of the following is not formed ?
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Identify the product A and product B in the following set of reactions.
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Identify major product " X " formed in the following reaction :
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Compare the energies of following sets of quantum numbers for multielectron system.
(A) n=4,1=1 (B) n=4,1=2
(C) n=3,1=1 (D) n=3,1=2
(E) n=4,1=0
Choose the correct...
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For the given reaction, choose the correct expression of $\mathrm{K}_{\mathrm{C}}$ from the following :- $\mathrm{Fe}_{(\mathrm{aq})}^{3+}+\mathrm{SCN}_{(\mathrm{aq})}^{-} \rightleftharpoons\left(\mathrm{FeSCN)}_{(\mathrm{aq})}^{2+}\right.$
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Given below are two statements: Statement (I) : The NH_2 group in Aniline is ortho and para directing and a powerful activating group. Statement (II)...
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Choose the correct option for free expansion of an ideal gas under adiabatic condition from the following :
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Match List - I with List -II. Choose the correct answer from options given below:
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Given below are two statements : Statement (I) : Potassium hydrogen phthalate is a primary standard for standardisation of sodium hydroxide solution. Statement (II) :...
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In Kjeldahl's method for estimation of nitrogen, CuSO_4 acts as :
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What is the structure of C ?
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The electronic configuration of $\mathrm{Cu}($ □ II) is $3 \mathrm{~d}^9$ whereas that of $\mathrm{Cu}(\mathrm{I})$ is $3 \mathrm{~d}^{10}$. Which of the following is correct?
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Identify the logic operation performed by the given circuit
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Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): The total number...
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Given below are two statements : one is labelled as Assertion (A) : and the other is labelled as Reason (R). Assertion (A) : Both...
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Arrange the bonds in order of increasing ionic character in the molecules. LiF,K_2 O,N_2,SO_2 and CIF_3.
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The parameter that remains the same for molecules of all gases at a given temperature is :
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For the given compounds, the correct order of increasing $\mathrm{pK}_{\mathrm{a}}$ value
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Ionic reactions with organic compounds proceed through: (A) Homolytic bond cleavage (B) Heterolytic bond cleavage (C) Free radical formation (D) Primary free radical (E) Secondary...
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Which of the following compound will most easily be attacked by an electrophile?
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Given below are two statements one is labelled as Assertion (A) and the other is labelled as Reason (R): Assertion $(\mathrm{A})$ - $\mathrm{S}_{\mathrm{N}} 2$ reaction...
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Which of the following complex is homoleptic?
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Number of molecules/species from the following having one unpaired electron is $\mathrm{O}_2, \mathrm{O}_2^{-1}, \mathrm{NO}, \mathrm{CN}^{-1}, \mathrm{O}_2^{2-}$
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Given below are two statements.
Statement (I): The oxidation state of an element in a particular compound is the charge acquired by its atom on...
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The number of different chain isomers for $\mathrm{C}_7 \mathrm{H}_{16}$ is $\_\_\_\_$ .
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Given below are two statements: Statement (I) : Aminobenzene and aniline are same organic compounds. Statement (II) : Aminobenzene and aniline are different organic compounds....
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Relative stability of the contributing structures is :
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2.5 g of a non-volatile, non-electrolyte is dissolved in 100 g of water at $25^{\circ} \mathrm{C}$. The solution showed boiling point elevation by $2^{\circ} \mathrm{C}$....
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Identify A and B in the following sequence of reaction
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Consider the following transformation involving first order elementary reaction in each step at constant temperature as shown below.
$...
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The F-ions make the enamel on teeth much harder by converting hydroxyapatite (the enamel on the surface of teeth) into much harder fluoroapatite having the...
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In which one of the following pairs the central atoms exhibit $\mathrm{sp}^2$ hybridization?
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): PH_3 has lower boiling...
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Correct order of basic strength of Pyrrole
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Given below are two statements: Statement (I): A solution of [Ni(H_2 O)_6 ]^(2+) is green in colour. Statement (II): A solution of [Ni(CN)_4 ]^(2-) is...
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In the following sequence of reaction, the major products B and C respectively are :
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Consider the following reaction $\mathrm{MnO}_2+\mathrm{KOH}+\mathrm{O}_2 \rightarrow \mathrm{~A}+\mathrm{H}_2 \mathrm{O}$ Product ' $A$ ' in neutral or acidic medium disproportionate to give products ' $B$ ' and...
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