List of top Mathematics Questions asked in JEE Main

The tangent at the point \((2, -2)\) to the curve, \(x^2y^2 - 2x = 4(1 - y)\) does not pass through the point :

If \(y = \left[x + \sqrt{x^2 - 1}\right]^{15} + \left[x - \sqrt{x^2 - 1}\right]^{15}\), then \((x^2 - 1)\dfrac{d^2y}{dx^2} + x\dfrac{dy}{dx}\) is equal to :

\(\displaystyle\lim_{x \to 3} \frac{\sqrt{3x} - 3}{\sqrt{2x - 4} - \sqrt{2}}\) is equal to :

If all the words, with or without meaning, are written using the letters of the word QUEEN and are arranged as in English dictionary, then the position of the word QUEEN is :

The number of real values of \(\lambda\) for which the system of linear equations
\(2x + 4y - \lambda z = 0\)
\(4x + \lambda y + 2z = 0\)
\(\lambda x + 2y + 2z = 0\)
has infinitely many solutions, is :

Let \(A\) be any \(3 \times 3\) invertible matrix. Then which one of the following is not always true ?

Let \(p(x)\) be a quadratic polynomial such that \(p(0) = 1\). If \(p(x)\) leaves remainder 4 when divided by \(x - 1\) and it leaves remainder 6 when divided by \(x + 1\); then :

Let \(f(x) = 2^{10}\cdot x + 1\) and \(g(x) = 3^{10}\cdot x - 1\). If \((f\circ g)(x) = x\), then \(x\) is equal to :

A hyperbola passes through the point \(P\left(\sqrt{2},\sqrt{3}\right)\) and has foci at \((\pm2,0)\). Then the tangent to this hyperbola at P also passes through the point :

If the image of the point \(P(1,-2,3)\) in the plane \(2x+3y-4z+22=0\) measured parallel to the line \(\frac{x}{1}=\frac{y}{4}=\frac{z}{5}\) is Q, then PQ is equal to:

For three events A, B and C,
P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = \(\frac{1}{4}\)
and P(All the three events occur simultaneously) = \(\frac{1}{16}\).
Then the probability that at least one of the events occurs, is :

The following statement \((p\to q)\to\left[(\sim p\to q)\to q\right]\) is :

Let \(\vec{a}=2\hat{i}+\hat{j}-2\hat{k}\) and \(\vec{b}=\hat{i}+\hat{j}\). Let \(\vec{c}\) be a vector such that \(|\vec{c}-\vec{a}|=3\), \(|(\vec{a}\times\vec{b})\times\vec{c}|=3\) and the angle between \(\vec{c}\) and \(\vec{a}\times\vec{b}\) is \(30^\circ\). Then \(\vec{a}\cdot\vec{c}\) is equal to :

Let k be an integer such that the triangle with vertices \((k,-3k)\), \((5,k)\) and \((-k,2)\) has area 28 sq. units. Then the orthocentre of this triangle is at the point :

If \(A=\begin{bmatrix}2&-3\\-4&1\end{bmatrix}\), then adj\((3A^2+12A)\) is equal to

If \(5\left(\tan^2x-\cos^2x\right)=2\cos2x+9\), then the value of \(\cos4x\) is :

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:

If S is the set of distinct values of 'b' for which the following system of linear equations
\(x+y+z=1\)
\(x+ay+z=1\)
\(ax+by+z=0\)
has no solution, then S is :

The function \(f:R\to\left[-\frac{1}{2},\frac{1}{2}\right]\) defined as \(f(x)=\frac{x}{1+x^2}\), is

An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is :

A box contains $15$ green and $10$ yellow balls. If $10$ balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is :

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the y-axis passes through the point :

For any three positive real numbers a, b and c, $9(25a^2 + b^2) + 25 (c^2 - 3ac) = 15b (3a + c)$. Then :

Let $a, b, c \, \in \, R$. If $f(x) = ax^2 + bx + c$ is such that $a + b + c = 3$ and $f (x + y) = f (x) + f (y) + xy, \forall \, x, y \, \in \, R,$ then $\displaystyle\sum^{10}_{n = 1} f(n)$ is equal to :

$\displaystyle\lim_{x \to \frac{\pi}{2}} \frac{\cot x - \cos x}{\left(\pi - 2x\right)^{3}} $ equals :