The coefficients $a, b, c$ in the quadratic equation $a x^2+b x+c=0$ are chosen from the set $\{1,2,3,4,5,6,7,8\}$. The probability of this equation having repeated...
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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...
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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:
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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,...
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The integral $\int_0^{\frac{\pi}{4}} \frac{136 \sin x}{3 \sin x+5 \cos x} d x$ is equal to :
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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...
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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...
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If the wavelength of the first member of Lyman series of hydrogen is λ. The wavelength of the second member will be
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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...
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The number of critical points of the function $f(x)=(x-2)^{2 / 3}(2 x+1)$ is:
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$\int_0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x$ is equal to $\_\_\_\_$
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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 :
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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...
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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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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...
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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...
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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 :
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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
$\_\_\_\_$ .
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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...
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The refractive index of a prism with apex angle A is cotA/2. The angle of minimum deviation is :
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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...
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The sum of all the solutions of the equation $(8)^{2 x}-16 \cdot(8)^x+48=0$ is is:
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If the system of equations
has infinitely many solutions, then $\lambda^4-\mu$ is equal to:
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$$ \text { The relation between time ' } t \text { ' and distance ' } x \text { ' is } t=\alpha x^2+\beta...
JEE MainPhysicsHard
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A train starting from rest first accelerates uniformly up to a speed of 80 km/h for time t, then it moves with a constant speed...
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The value of $k \in \mathbb{N}$ for which the integral $I_n=\int_0^1\left(1-x^k\right)^n d x, n \in \mathbb{N}$, satisfies $147 I_{20}=148 I_{21}$ is:
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If $f(x)=\left\{\begin{array}{cc}x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0, & x=0\end{array}\right.$, then
JEE MainMathematicsMedium
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Four particles A, B, C, D of mass$\frac{m}{2}, m, 2 m, 4 m$, have same momentum, respectively. The particle with maximum kinetic energy is :
JEE MainPhysicsEasy
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QJEE MAIN 2024
For the function f(x)=sinx+3x-2x2+x, where x0,2, consider the following two statements : (I) f is increasing in 0,2. (II) f' is decreasing in 0,2. Between...
JEE MainMathematicsHard
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There are 5 points $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \mathrm{P}_4, \mathrm{P}_5$ on the side AB , excluding A and B , of a triangle ABC . Similarly...
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Let $\vec{a}, \vec{b}$ and $\overrightarrow{\mathrm{c}}$ be three non-zero vectors such that $\vec{b}$ and $\vec{c}$ are non-collinear if $\vec{a}+5 \vec{b}$is collinear with$\vec{c}, \vec{b}+6 \vec{c}$ is collinear...
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If the system of equations $$ \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 MainMathematicsEasy
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QJEE 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 :
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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...
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The pressure and volume of an ideal gas are related as (Constant). The work done when the gas is taken from state to state is...
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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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