List of top Questions asked in JEE Main

The final product ‘C’ in the following series of reactions

Which of the following is NOT an example of synthetic detergent?
Sugar moiety in DNA and RNA molecules, respectively are
Which of the following compound does not contain sulphur atom?

Given below are two statements.

Statement I : Phenols are weakly acidic.

Statement II : Therefore they are freely soluble in NaOH solution and are weaker acids than alcohols and water.

Choose the most appropriate option.

Choose the correct answer :

1. The probability that a randomly chosen 2 × 2 matrix with all the entries from the set of first 10 primes, is singular, is equal to :

Let the solution curve of the differential equation \(x\frac{dy}{dx}-y=\sqrt{y^2+16x^2},\)  y(1) = 3 be y = y(x). Then y(2) is equal to 
If the mirror image of the point (2, 4, 7) in the plane 3x – y + 4z = 2 is (a, b, c), then 2a + b + 2c is equal to

Let ƒ R ⇒ R be a function defined by

Let ƒ : R ⇒ R be a function defined by

where [t] is the greatest integer less than or equal to t. Let m be the number of points where ƒ is not differentiable and 

Then the ordered pair (m, I) is equal to :

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

The area enclosed by y2 = 8x and y = √2x that lies outside the triangle formed by \(y=√2x,x=1,y=2√2\), is equal to 

If the system of linear equations

2x + y – z = 7

x – 3y + 2z = 1

x + 4y + δz = k, where δ, k ∈ R

has infinitely many solutions, then δ + k is equal to:

Let α and β be the roots of the equation x2 + (2i – 1) = 0. Then, the value of |α2 + β2| is equal to
Let Δε{∧,∨,⇒,⇔} be such that (p∧q)Δ((p∨q)⇒q) is a tautology. Then ∆is equal to 
Let A = [aij] be a square matrix of order 3 such that aij = 2j–i, for all i, j = 1, 2, 3. Then, the matrix A2 + A3 + … + A10 is equal to 
Let a set A = A1 ⋃ A2 ⋃ …⋃ Ak, where Ai ⋂ Aj = Φ for i ≠ j, 1 ≤ i, j ≤ k. Define the relation R from A to A by R = {(x, y) : y ∈ Ai if and only if x ∈ Ai, 1 ≤ i ≤ k}. Then, R is
Let \((a_n)^∞_{n=0}\) be a sequence such that a0=a1=0 and \(a_{n+2}=2a_{n+1}−a_n+1\) for all n⩾0. Then, \(∑^∞_{n=2} \frac{a_n}{7^n}\) is equal to
The distance between the two points A and A′ which lie on y = 2 such that both the line segments AB and A′B (where B is the point (2, 3)) subtend angle π/4 at the origin, is equal to
A wire of length 22 m is to be cut into two pieces. One of the pieces is to be made into a square and the other into an equilateral triangle. Then, the length of the side of the equilateral triangle, so that the combined area of the square and the equilateral triangle is minimum, is
A small square loop of wire of side l is placed inside a large square loop of wire L(L>>l). As shown in figure, both loops are coplanar and their centers coincide at point O. The mutual inductance of the system is:
small square loop of wire of side
If the constant term in the expansion of\( (3x^3−2x^2+\frac{5}{x^5})^{10}\)  is 2k·l, where l is an odd integer, then the value of k is equal to
The rms value of the conduction current in a parallel plate capacitor is 6.9 μA. The capacity of this capacitor, if it is connected to 230 V ac supply with an angular frequency of 600 rad/s, will be :
Time taken by light to travel in two different materials A and B of refractive indices μA and μB of same thickness is t1 and t2 respectively. If t2 – t1 = 5 × 10–10 s and the ratio of μA to μB is 1 : 2. Then, the thickness of material, in meter is: (Given vA and vB are velocities of light in A and B materials, respectively.)
The momentum of an electron revolving in nth orbit is given by: (Symbols have their usual meanings)
The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by: