List of top Questions asked in JEE Main

The number of ways to distribute 30 identical candies among four children C₁, C₂, C₃ and C₄ so that C₂ receives atleast 4 and atmost 7 candies, C₃ receives atleast 2 and atmost 6 candies, is equal to:

Numbers are to be formed between 1000 and 3000, which are divisible by 4, using the digits 1, 2, 3, 4, 5 and 6 without repetition of digits. Then the total number of such numbers is ______________.

A line, with the slope greater than one, passes through the point A (4,3) and intersects the line x-y-2=0 at the point B If the length of the line segment AB is $\frac{\sqrt{29}}{3},$ then B also lies on the line :

Let l be a line which is normal to the curve $y = 2x^2 + x + 2$ at a point P on the curve. If the point Q(6, 4) lies on the line l and O is origin, then the area of the triangle OPQ is equal to _________ .

Let $O$ be the origin and $A$ be the point $z _1=1+2 i$. If $B$ is the point $z _2, \operatorname{Re}\left( z _2\right)<0$, such that $OAB$ is a right angled isosceles triangle with $OB$ as hypotenuse, then which of the following is NOT true ?

Sum of squares of modulus of all the complex numbers z satisfying
$\overline{z}=iz^2+z^2–z $
is equal to ________.

If z = x + iy satisfies | z | – 2 = 0 and |z – i| – | z + 5i| = 0, then

Let a function ƒ : N →N be defined by
$f(n) = \left\{ \begin{array}{ll} 2n & n = 2,4,6,8,\ldots \\ n - 1 & n = 3,7,11,15,\ldots \\ \frac{n+1}{2} & n = 1,5,9,13 \end{array} \right.$
then, ƒ is

Let f(x) be a quadratic polynomial such that f(–2) + f(3) = 0. If one of the roots of f(x) = 0 is –1, then the sum of the roots of f(x) = 0 is equal to:

Let f,g : R → R be functions defined by*
$f(x) = \begin{cases} [x], & x < 0 \\ |1 - x|, & x \geq 0 \end{cases}$
and $g(x) = \begin{cases} e^x - x, & x < 0 \\ {(x - 1)^2 - 1}, & x \geq 0 \end{cases}$
Where [x] denotes the greatest integer less than or equal to x. Then, the function fog is discontinuous at exactly:

If
$f(x) = \begin{cases} x + a, & x \leq 0 \\ |x - 4|, & x > 0 \end{cases}$ and $g(x) = \begin{cases} x + 1, & x < 0 \\ (x - 4)^2 + b, & x \geq 0 \end{cases}$
are continuous on R, then (gof) (2) + (fog) (–2) is equal to

Let
$f(x) = \begin{cases} x^3 - x^2 + 10x - 7, & x \leq 1 \\ -2x + \log_2(b^2 - 4), & x > 1 \end{cases}$
Then the set of all values of b, for which f(x) has maximum value at x = 1, is

Let a function f: ℝ → ℝ be defined as :
$\begin{array}{l}f(x) = \left\{\begin{matrix}\int_{0}^{x}(5-|t-3|)dt, & x>4 \\x^2 + bx, & x \le4 \\\end{matrix}\right.\end{array}$
where b ∈ ℝ. If f is continuous at x = 4 then which of the following statements is NOT true?

Let A and B be two events such that

$\begin{array}{l} P\left(B/A\right)\frac{2}{5},\ P\left(A/B\right)=\frac{1}{7}\ \text{and}\ P\left(A\cap B\right)=\frac{1}{9}.\end{array} Consider \begin{array}{l} \left(S1\right)P\left(A’\cup B\right)=\frac{5}{6},\end{array}$

$\begin{array}{l} \left(S2\right)P\left(A’\cap B’\right)=\frac{1}{18}.\end{array}$Then

A six faced die is biased such that
3 × P (a prime number) = 6 × P (a composite number) = 2 × P (1).
Let X be a random variable that counts the number of times one gets a perfect square on some
throws of this die. If the die is thrown twice, then the mean of X is :

Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is :

Given below are two statements : Statement I : On heating with $KHSO _4$, glycerol is dehydrated and acrolein is formed
Statement II : Acrolein has fruity odour and can be used to test glycerol's presence Choose the correct option

Consider the above reaction sequence and identify the product B.

Which will have the highest enol content?

The formulas of A and B for the following reaction sequence are

The number of molecules(s) or ions(s) from the following having non-planar structure is ____.
$NO^-_3, H_2O_2, BF_3, PCl_3, XeF_4, SF_4, XeO_3, PH^+_4, SO3,[Al(OH)_4]^-$

In the above reaction, 5 g of toluene is converted into benzaldehyde with 92% yield. The amount of benzaldehyde produced is______ × 10^–2 g. (Nearest integer).

Which of the given reactions is not an example of disproportionation reaction?

The dark purple colour of $KMnO _4$ disappears in the titration with oxalic acid in acidic medium. The overall change in the oxidation number of manganese in the reaction is :

Choose the correct option for the following reactions