List of top Questions asked in JEE Main

Who was known as “Father of modern concrete”?

Dominion tower is designed by

The dome of Rashtrapati Bhawan is influenced by which of the following:

ARCHITECT ACT 1972 was enforced in which month

Choose the correct option among the following by looking at the image given above:

Lintel is related to:

Cavity Walls are used for

Vertical elements in a building are:-

KANDARIYA MAHADEV TEMPLE is situated in which state of India?

Which of the following is not a sustainable development goal targeted to be achieved by 2030?

Let \(\mathrm{A}_{1}=[1]\), \(\mathrm{A}_{2}=\left[\begin{array}{ll}2 & 3 \\ 4 & 5\end{array}\right]\), \(\mathrm{A}_{3}=\left[\begin{array}{ccc}6 & 7 & 8 \\ 9 & 10 & 11 \\ 12 & 13 & 14\end{array}\right], \ldots\) Then the sum of the diagonal elements of \(\mathrm{A}_{20}\) is ________.

Let \([\mathrm{t}]\) denote the greatest integer less than or equal to t. Then the value of \(10-10 \int_{-2}^{2}\left[x+x^{3}\right] dx\) is ________.

Let \(A=\frac{1}{\sqrt{2}}\left[\begin{array}{cc}1 & 1 \\ -1 & 1\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & 0 \\ 0 & -1\end{array}\right]\). If \(k, l \in \mathbb{N}\) be such that \(A^{k} B^{l}=I\), then the minimum value of \(k+l\) is ________.

The remainder when \((556)^{40}\) is divided by 7 is ________.

If the shortest distance between the lines \(3x+2y-4z-5=0=5x-7y-17z+2\) and \(\frac{x-2}{3}=\frac{y-1}{-5}=\frac{z+1}{2}\) is \(\frac{10}{\sqrt{k}}\), then \(k\) is equal to ________.

The number of 7 digits integers formed by using the digits 2, 3, 4, 5 only and having the sum of digits equal to 18 is ________.

Let \(f(x)\) be a polynomial of degree 5 such that \(\lim_{x \to 0} \frac{f(x)}{x^{2}}=1\), \(f(-1)=-1\), \(f(x)-14x\) has an extrema at \(x=1\) and \(f(x)-10x\) has an extrema at \(x=-1\). Then \(f(2)\) is equal to ________.

For \(p \in \mathbb{N}\), if the angle between pair of tangents drawn to the ellipse \(3x^{2}+2y^{2}=5\) from the point \((1, p)\) is \(\tan^{-1}\left(\frac{12}{\sqrt{5}}\right)\), then the distance of the vertex of the parabola \(y=x^{2}-px+p+1\) from the point \((-7,8)\) is equal to ________.

\(\left(\sin 5^{\circ} \sin 55^{\circ} \sin 65^{\circ} \sin 75^{\circ}\right)^{-1}\) is equal to ________.

Let P be a polygon with \(n\) vertices such that the line segment joining any two points of P remains entirely in P. If the number of diagonals of P is \(n+25\), then \(n\) is equal to ________.

If an unbiased die, marked with \(-3,-2,-1,0,1,2\) on its faces, is thrown four times, then the probability of getting \(-1\) as the sum of outputs is :

If the angle between the line \(l: \frac{x-1}{2}=\frac{y+1}{1}=\frac{z-2}{2}\) and the plane \(\mathrm{P}: \lambda x+4y-7=0,\ \lambda \neq 0\), is \(\operatorname{cosec}^{-1}\left(\frac{3}{2}\right)\), then the sum of co-ordinates of the point where line \(l\) crosses the plane P is :

Given \({}^{n}C_{r}=\frac{n!}{r!(n-r)!}\), \(0 \leq r \leq n\) and n is a non-negative integer. Then a possible value of k for which the equality
\({}^{50}C_{k-1}+\sum_{r=1}^{50}{}^{100-r}C_{k-2}={}^{100}C_{49}\) holds, is

Let three distinct normal be drawn to the parabola \(y^{2}+4y-6x-8=0\) from a point \((a, \mathrm{b})\) on the axis of the parabola. Then :

If the circles \(x^{2}+y^{2}-2 x-4 y+4=0\) and \(x^{2}+y^{2}-6 x-10 y+20+2 \sqrt{13}=0\) touch each other at the point \((a, \mathrm{b})\), then \((3 a-2 \mathrm{b})^{2}\) is equal to :