List of top Questions asked in JEE Main

Let the mirror image of a circle c₁ :x² + y² – 2x – 6y + α = 0 in line y = x + 1 be c₂ : 5x²+ 5y² + 10gx + 10fy + 38 = 0. If r is the radius of circle c₂, then α + 6r² is equal to _________.

The coefficient of x¹⁰¹ in the expression (5 + x)⁵⁰⁰ + x(5 + x)⁴⁹⁹ + x²(5 + x)⁴⁹⁸ + ……+ x⁵⁰⁰, x > 0, is

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of 5 μC are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be:

A water drop of radius 1 μm falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is \(1.8 \times 10^{–5} Nsm^{–2}\) and its density is negligible as compared to that of water \((10^6 gm^{–3})\). Terminal velocity of the water drop is

Let the area of the triangle with vertices \(A(1, α), B(α, 0)\) and \(C(0, α)\) be \(4\) sq. units. If the points \((α, –α), (–α, α)\) and \((α^2, β)\) are collinear, then \(β\) is equal to

Sugar moiety in DNA and RNA molecules, respectively are

Let

\(a→=α\^{i}+3\^{j}−\^{k}, \overrightarrow{b}=3\^{i}−β\^{j}+4\^{k} and \overrightarrow{c}=\^{i}+2\^{j}−2\^{k }\)

where α,β∈R, be three vectors. If the projection of

\(\overrightarrow{a} on \overrightarrow{c} is \frac{10}{3} and \overrightarrow{b}×\overrightarrow{c}=−6\^{i}+10\^{j}+7\^{k}, \)

then the value of α+β 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

A monoatomic gas at pressure P and volume V is suddenly compressed to one eighth of its original volume. The final pressure at constant entropy will be :

Let \(X\) be a random variable having binomial distribution \(B(7, p)\). If \(P(X = 3) = 5P(X = 4)\), then the sum of the mean and the variance of \(X\) is:

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be ______%.

The number of 7-digit numbers which are multiples of 11 and are formed using all the digits 1, 2, 3, 4, 5, 7 and 9 is _____.

The remainder on dividing 1 + 3 + 3² + 3³ + … + 3²⁰²¹ by 50 ____ is

The area (in sq. units) of the region enclosed between the parabola y² = 2x and the line x + y = 4 is _______.

Let a circle C : (x – h)² + (y – k)² = r², k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.

The speed of light in media ‘A’ and ‘B’ are 2.0 × 10¹⁰ cm/s and 1.5 × 10¹⁰ cm/s respectively. A ray of light enters from the medium B to A at an incident angle ‘θ’. If the ray suffers total internal reflection, then

The number of values of a ∈ N such that the variance of 3, 7, 12, a, 43 – a is a natural number is :

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60°. The pole subtends an angle 30° at the top of the tower. Then the height of the tower is :

Let f and g be twice differentiable even functions on (–2, 2) such that
\(ƒ(\frac{1}{4})=0, ƒ(\frac{1}{2})=0, ƒ(1) =1\) and \(g(\frac{3}{4}) = 0 , g(1)=2\)
.Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If \(r_d\) and \(r_p\) are the radii of their circular paths respectively, then the ratio \(\frac{r_d}{r_p}\) will be \(\sqrt x:1\) where \(x\) is__________

Which of the following statement is a tautology?

If the sum of the coefficients of all the positive powers of x, in the Binomial expansion of \(\left(x^n+\frac{2}{x^5}\right)^7\) is 939, then the sum of all the possible integral values of n is ____________.

If \(y(x) = (x^x)^x, \quad x > 0\), then \(\frac{d^2x}{dy^2} + 20\) at \(x = 1\) is equal to __________.

The spin-only magnetic moment value of an octahedral complex among \(CoCl_3⋅4NH_3\), \(NiCl_2⋅6H_2O\) and \(PtCl_4⋅2HCl\), which upon reaction with excess of \(AgNO_3\) gives 2 moles of \(AgCl\) is _____ B.M. (Nearest Integer)

A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced at STP is ____ cm³. (Nearest integer)

[Given : Faraday constant F = 96500 C mol^–1 at STP, molar volume of an ideal gas is 22.7 L mol^–1]