List of top Mathematics Questions asked in JEE Main

The pitch of the screw gauge is $1 mm$ and there are $100$ divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lies $ 8$ divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while $72^{\text {nd }}$ division on circular scale coincides with the reference line. The radius of the wire is

For $a > 0$, let the curves $C_1 : y^2 = ax$ and $C_2 : x^2= ay$ intersect at origin O and a point P. Let the line $x = b (0 < b < a)$ intersect the chord OP and the x-axis at points Q and R, respectively. If the line x = b bisects the area bounded by the curves, $C_1$ and $C_2$, and the area of $\Delta OQR = \frac{1}{2},$ then 'a' satisfies the equation :

The sum of the values of $x$ satisfying the equation, $\sqrt{x}\left(\sqrt{x}-4\right)-3\left|\sqrt{x}-2\right|+6=0 \left(x\,\ge\,0\right),$ is :

If a, b and c are the greatest values of $^{19}C_{p}, \, ^{20}C_{q}$ and $^{21}C_{r}$ respectively, then :

Which of the following statements is a tautology?

Let the latus ractum of the parabola $y^{2}=4x$ be the common chord to the circles $C _{1}$ and $C _{2}$ each of them having radius $2 \sqrt{5}$. Then, the distance between the centres of the circles $C _{1}$ and $C _{2}$ is:

The coefficient of $x^7$ in the expression $\left(1+x\right)^{10}+x\left(1+x\right)^{9}+x^{2}\left(1+x\right)^{8}+...+x^{10}$ is :

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to $50 .$ A box is selected at random and a card is drawn from it. The number on the card is found to be a non-prime number. The probability that the card was drawn from Box I is :

Let $f :(-1, \infty) \rightarrow R$ be defined by $f (0)=1$ and $f ( x )=\frac{1}{ x } \log _{ e }(1+ x ), x \neq 0 .$ Then the function $f$

$\displaystyle\lim_{x \to 0} \left(\frac{3x^{2}+2}{7x^{2}+2}\right)^{\frac {1}{x^2}}$ is equal to :

If a hyperbola passes through the point $P(10,16)$ and it has vertices at $( ? 6,0)$, then the equation of the normal to it at P is :

The inverse function of $f\left(x\right) = \frac{8^{2x}-8^{-2x}}{8^{2x} + 8^{-2x}}, x\epsilon \left(-1, 1\right),$ is __________.

The mean and variance of 7 observations are 8 and $16,$ respectively. If five observations are $2,4,10,12,14,$ then the absolute difference of the remaining two observations is :

If the volume of a parallelepiped whose coterminous edges are $\vec{a}=\hat{i}+\hat{j}+2\,\hat{k}, \vec{b}=2\,\hat{i}+\lambda\,\hat{j}+\hat{k}$ and $\vec{c}=2\,\hat{i}+2\hat{j}+\lambda\hat{k}$ is 35 cu.m, then a value of $\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}-\vec{c}\cdot\vec{a}$ is :

Which one of the following is a tautology ?

Let the ellipse, $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1, a > b,$ pass through the point (2, 3) and have eccentricity equal to $\frac{1}{2}$. Then equation of the normal to this ellipse at $(2,3)$ is :

If $\frac{dy}{dx}=\frac{xy}{x^{2}+y^{2}}; y\left(1\right)=1;$ then a value of $x$ satisfying $y(x) = e$ is :

Let $a_n$ be the $n^{th}$ term of a G.P. of positive terms. If $x=\displaystyle \sum_{n=1}^{100}a_{2n+1}=200$ and $x=\displaystyle \sum_{n=1}^{100}a_{2n}=100$, $x=\displaystyle \sum_{n=1}^{200}a_n$ is equal to :

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in :

If $L=\sin ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right)$ and $M=\cos ^{2}\left(\frac{\pi}{16}\right)-\sin ^{2}\left(\frac{\pi}{8}\right),$ then :

$\displaystyle \lim_{x \to 1}$$\left\{log_{e}\left(e^{x\left(x-1\right)}-e^{x\left(1-x\right)}\right)-log_{e}\left(4x\left(x-1\right)\right)\right\}$ is equal to :

In a game two players $A$ and $B$ take turns in throwing a pair of fair dice starting with player $A$ and total of scores on the two dice, in each throw is noted. $A $ wins the game if he throws a total of $6$ before $B$ throws a total of $7$ and $B$ wins the game if he throws a total of $7 $before $A$ throws a total of six The game stops as soon as either of the players wins. The probability of $A$ winning the game is :

Let A and B be two independent events such that $P\left(A\right) = \frac{1}{3}$ and $P\left(B\right) = \frac{1}{6}.$ Then, which of the following is TRUE ?

If the sum of the series $20+19 \frac{3}{5}+19 \frac{1}{5}+18 \frac{4}{5}+\ldots $ upto $n^ {th }$ term is $488$ and the $n ^ {th }$ term is negative, then :

The probability that a randomly chosen 5 -digit number is made from exactly two digits is :