List of top Mathematics Questions asked in JEE Main

The values of \(\lambda\) and \(\mu\) for which the system of linear equations
\(x+y+z=2\)
\(x+2y+3z=5\)
\(x+3y+\lambda z=\mu\)
has infinitely many solutions are, respectively:

The region represented by
\(\{z=x+iy\in C : |z|-\mathrm{Re}(z)\le 1\}\) is also given by the inequality :
\(\{z=x+iy\in C : |z|-\mathrm{Re}(z)\le 1\}\)

If \(\displaystyle\sum_{i=1}^{n}(x_i-a)=n\) and \(\displaystyle\sum_{i=1}^{n}(x_i-a)^2=na\) \((n, a>1)\) then the standard deviation of n observations \(x_1, x_2, \ldots, x_n\) is :

Let a, b, c, d and p be any non zero distinct real numbers such that
\((a^2+b^2+c^2)p^2-2(ab+bc+cd)p+(b^2+c^2+d^2)=0\). Then :

If \(\alpha\) and \(\beta\) be two roots of the equation \(x^2-64x+256=0\). Then the value of
\(\left(\dfrac{\alpha^3}{\beta^5}\right)^{1/8}+\left(\dfrac{\beta^3}{\alpha^5}\right)^{1/8}\)
is :

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

The position of a moving car at time t is given by \(f(t)=at^2+bt+c,\ t>0\), where a, b and c are real numbers greater than 1. Then the average speed of the car over the time interval \([t_1,\ t_2]\) is attained at the point :

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

The area (in sq. units) of the region
\(A=\{(x, y) : |x|+|y|\le 1,\ 2y^2\ge |x|\}\)

Let m and M be respectively the minimum and maximum values of
\(\begin{vmatrix}\cos^2 x & 1+\sin^2 x & \sin 2x\\ 1+\cos^2 x & \sin^2 x & \sin 2x\\ \cos^2 x & \sin^2 x & 1+\sin 2x\end{vmatrix}\)
Then the ordered pair (m, M) is equal to :

In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is __________.

The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^6\) in powers of \(x\), is ______.

If the lines \(x + y = a\) and \(x - y = b\) touch the curve \(y = x^2 - 3x + 2\) at the points where the curve intersects the x-axis, then \(\dfrac{a}{b}\) is equal to _______.

If the sum of the first 20 terms of the series
\(\log_{(7^{1/2})}x + \log_{(7^{1/3})}x + \log_{(7^{1/4})}x + \ldots\)
is \(460\), then \(x\) is equal to :

Let the vectors \(\vec{a}, \vec{b}, \vec{c}\) be such that \(|\vec{a}| = 2\), \(|\vec{b}| = 4\) and \(|\vec{c}| = 4\). If the projection of \(\vec{b}\) on \(\vec{a}\) is equal to the projection of \(\vec{c}\) on \(\vec{a}\) and \(\vec{b}\) is perpendicular to \(\vec{c}\), then the value of \(|\vec{a} + \vec{b} - \vec{c}|\) is ___________.

Let \(A = \{a, b, c\}\) and \(B = \{1, 2, 3, 4\}\). Then the number of elements in the set \(C = \{f : A \to B \mid 2 \in f(A)\text{ and } f\text{ is not one-one}\}\) is ______.

If the line \(y = mx + c\) is a common tangent to the hyperbola
\(\dfrac{x^2}{100} - \dfrac{y^2}{64} = 1\)
and the circle \(x^2 + y^2 = 36\), then which one of the following is true?

Which of the following points lies on the tangent to the curve
\(x^4 e^y + 2\sqrt{y+1} = 3\) at the point \((1, 0)\)?

If for some \(\alpha \in \mathbb{R}\), the lines
\(L_1 : \dfrac{x+1}{2} = \dfrac{y-2}{-1} = \dfrac{z-1}{1}\)
and
\(L_2 : \dfrac{x+2}{\alpha} = \dfrac{y+1}{5-\alpha} = \dfrac{z+1}{1}\)
are coplanar, then the line \(L_2\) passes through the point :

If \(a + x = b + y = c + z + 1\), where \(a, b, c, x, y, z\) are non-zero distinct real numbers, then
\(\begin{vmatrix} x & a+y & x+a \\ y & b+y & y+b \\ z & c+y & z+c \end{vmatrix}\)
is equal to :

The statement
\((p \to (q \to p)) \to (p \to (p \vee q))\) is :

If the mean and the standard deviation of the data \(3, 5, 7, a, b\) are \(5\) and \(2\) respectively, then \(a\) and \(b\) are the roots of the equation :

Let \(y=y(x)\) be the solution of the differential equation \( \cos x\,\frac{dy}{dx}+2y\sin x=\sin2x,\ x\in\left(0,\frac{\pi}{2}\right) \). If \( y\left(\frac{\pi}{3}\right)=0 \), then \( y\left(\frac{\pi}{4}\right) \) is equal to :

The derivative of
\(\tan^{-1}\left(\dfrac{\sqrt{1+x^2} - 1}{x}\right)\)
with respect to
\(\tan^{-1}\left(\dfrac{2x\sqrt{1-x^2}}{1-2x^2}\right)\)
at \(x = \dfrac{1}{2}\) is :

If the system of linear equations
\( x+y+3z=0 \)
\( x+3y+k^2z=0 \)
\( 3x+y+3z=0 \)
has a non-zero solution \((x, y, z)\) for some \(k\in R\), then \( x+\left(\frac{y}{z}\right) \) is equal to :