List of top Questions asked in JEE Main

For forces are acting at a point P in equilibrium as shown in the figure. The ratio of force F₁ to F₂ is 1 : x where x =___.

In the circuit, the logical value of A = 1 or B = 1 when potential at A or B is 5 V and the logical value of A = 0 or B = 0 when potential at A or B is 0 V. The truth table of the given circuit will be:

Let
ƒ : R → R
be defined as f(x) = x -1 and
g : R - { 1, -1 } → R
be defined as
g(x) = \(\frac{x²}{x² - 1}\)
Then the function fog is :

A wire of length L and radius r is clamped rigidly at one end. When the other end of the wire is pulled by a force F, its length increases by 5 cm. Another wire of the same material of length 4L and radius 4r is pulled by a force 4F under same conditions. The increase in length of this wire is ___ cm.

\(∫^5_0\,cos(π(x-[\frac{x}{2}]))dx \), where [t] denotes greatest integer less than or equal to t, is equal to

If the system of equations αx + y + z = 5, x + 2y + 3z = 4, x + 3y +5z = β has infinitely many solutions, then the ordered pair (α, β) is equal to:

Let PQ be a focal chord of the parabola y² = 4x such that it subtends an angle of π/2 at the point (3, 0). Let the line segment PQ be also a focal chord of the ellipse \(E:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a^2>b^2.\) If e is the eccentricity of the ellipse E, then the value of \(\frac{1}{e^2}\) is equal to

Let the tangent to the circle C₁: x² + y² = 2 at the point M(–1, 1) intersect the circle C₂: (x – 3)² + (y – 2)² = 5, at two distinct points A and B. If the tangents to C₂ at the points A and B intersect at N, then the area of the triangle ANB is equal to

If A =\(\sum_{n=1}^{\infty}\)\(\frac{1}{( 3 + (-1)^n)^n}\) and B = \(\sum_{n=1}^{\infty}\)\(\frac{(-1)^n}{( 3 + (-1)^n)^n}\) ,
then A/B is equal to :

Let the mean and the variance of 5 observations x₁, x₂, x₃, x₄, x₅ be \(\frac{24}{5} \) and \(\frac{194}{25}\), respectively. If the mean and variance of the first 4 observations are \(\frac{7}{2}\) and a, respectively, then (4a + x₅) is equal to

A unit scale is to be prepared whose length does not change with temperature and remains 20 cm, using a bimetallic strip made of brass and iron each of different length. The length of both components would change in such a way that difference between their lengths remains constant. If length of brass is 40 cm and length of iron will be ___ cm.

The volume charge density of a sphere of radius 6 m is 2μC cm^-3. The number of lines of force per unit surface area coming out from the surface of the sphere is _______ × 10¹⁰ NC^-1.

In the given figure, the value of V₀will be ______ V.

\(\lim_{{x \to 0}} \limits\) \(\frac{cos(sin x) - cos x }{x^4}\) is equal to :

Eight copper wire of length l and diameter d are joined in parallel to form a single composite conductor of resistance R. If a single copper wire of length 2l have the same resistance (R) then its diameter will be ________ d.

Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable, and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to

Consider a cuboid of sides 2x, 4x and 5x and a closed hemisphere of radius r. If the sum of their surface areas is a constant k, then the ratio x : r, for which the sum of their volumes is maximum, is

The area of the region bounded by y² = 8x and y² = 16(3 – x) is equal to

If \(∫\frac{1}{x}\) \(√{\frac{1-x}{1+x}}\) dx = \(g(x) + c,g(1) = 0\) , then g \((\frac{1}{2})\)
is equal to

If y = y(x) is the solution of the differential equation
\(x\) \(\frac{dy}{dx}\) \(+ 2y =\) \(xe^x , y(1) = 0\)
then the local maximum value of the function
\(z(x) = x²y(x) - e^x , x ∈ R\)
is