List of top Questions asked in JEE Main

For the reaction given below:
\(CoCl_3.xNH_3 + AgNO_3 (aq) →\)
If two equivalents of AgCl precipitate out, then the value of x will be____.

The number of chiral alcohol(s) with molecular formula C₄H₁₀O is ____.

In the given reaction

the number of sp² hybridised carbon(s) in compound ‘X’ is _____.

In the given reaction,

The number of π electrons present in the product ‘P’ is_____.

The structure of protein that is unaffected by heating is

Let α be a root of the equation 1 + x² + x⁴ = 0. Then the value of α¹⁰¹¹ + α²⁰²² – α³⁰³³ is equal to

Let
A=\(\begin{bmatrix} 2 & -1 \\ 0 & 2 \end{bmatrix}\)
If B = I – ⁵C₁(adjA) + ⁵C₂(adjA)² – …. – ⁵C₅(adjA)⁵, then the sum of all elements of the matrix B is

Using the rules for significant figures, the correct answer for the expression
\(\frac{0.02858 × 0.112}{ 0.5702}\)
will be

The sum of the infinite series
\(1 + \frac{5}{6} + \frac{12}{6^2} + \frac{22}{6^3} + \frac{35}{6^4} +\frac{51}{6^5} + \frac{70}{6^6}+…..\)
is equal to

The potential energy of a particle of mass \(4 kg\) in motion along the x-axis is given by \(U = 4(1- cos 4x) J\). The time period of the particle for small oscillation \((sin θ ≃ θ)\) is \((\frac{π}{K})\) s. The value of \(K\) is ..........

Let f : R → R be a function defined by:
\(ƒ(x) = (x-3)^{n_1} (x-5)^{n_2} , n_1, n_2 ∈ N\)
Then, which of the following is NOT true?

Let f be a real valued continuous function on [0, 1] and
\(f(x) = x + \int_{0}^{1} (x - t) f(t) \,dt\)
Then, which of the following points (x, y) lies on the curve y = f(x)?

If
\(\int_{0}^{2} (\sqrt{2x} - \sqrt{2x - x^2}) \,dx = \int_{0}^{1} \left(1 - \sqrt{1 - y^2} - \frac{y^2}{2}\right) \,dy + \int_{1}^{2} (2 - \frac{y^2}{2}) \,dy + I\)
then I equal is

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about ____ W.

If y = y (x) is the solution of the differential equation
\((1 + e^{2x})\frac{dy}{dx} + 2(1 + y^2)e^x = 0\)
and y(0) = 0, then
\(6 \left( y'(0) + \left( \log_e\left(\sqrt{3}\right) \right)^2 \right)\)
is equal to

Let P : y² = 4ax, a > 0 be a parabola with focus S. Let the tangents to the parabola P make an angle of π/4 with the line y = 3x + 5 touch the parabola P at A and B. Then the value of a for which A, B and S are collinear is

For the given circuit the current through battery of 6 V just after closing the switch S will be _____ A.

Let a triangle ABC be inscribed in the circle
\(x² - \sqrt2(x+y)+y² = 0\)
such that ∠BAC= π/2. If the length of side AB is √2, then the area of the ΔABC is equal to :

An object O is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the figure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ____ cm.

In an experiment with a convex lens, the plot of the image distance (ν′) against the object distance (μ′) measured from the focus gives a curve ν′μ′ = 225. If all the distances are measured in cm. The magnitude of the focal length of the lens is _______ cm.

In an experiment to find acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillations with a watch of 1 s resolution. If measured value of length is 10 cm known to 1 mm accuracy, the accuracy in the determination of g is found to be x %. The value of x is _________ .

Let
\(\frac{x-2}{3} = \frac{y+1}{-2} = \frac{z+3}{-1}\)
lie on the plane px – qy + z = 5, for some p, q ∈ ℝ. The shortest distance of the plane from the origin is :

The distance of the origin from the centroid of the triangle whose two sides have the equations
x – 2y + 1 = 0 and 2x – y – 1 = 0 and whose orthocenter is (7/3, 7/3) is :

In a carnot engine, the temperature of reservoir is 527°C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is _____ \(× 10^6\) J.

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____ .