List of top Questions asked in JEE Main

The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is \(\omega\). An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is (h << R, where R is the radius of the earth)
Two different wires having lengths \(L_1\) and \(L_2\), and respective temperature coefficient of linear expansion \(\alpha_1\) and \(\alpha_2\), are joined end-to-end. Then the effective temperature coefficient of linear expansion is :
The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is :
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 __________.
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 _______.
The coefficient of \(x^4\) in the expansion of \((1 + x + x^2 + x^3)^6\) in powers of \(x\), is ______.
A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2o, its figure of merit is close to :
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 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 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 :
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 \((1, 0)\)?
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 ___________.
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 \(a + x = b + y = c + z + 1\), 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 :
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 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 :
If the length of the chord of the circle, \( x^2+y^2=r^2 \) (\(r>0\)) along the line, \( y-2x=3 \) is r, then \(r^2\) is equal to :
If \(x=1\) is a critical point of the function \( f(x)=(3x^2+ax-2-a)e^x \), then :
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 :
\( \lim_{x\to0}\frac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1\right)/x}-1\right)}{\sqrt{1+x^2+x^4}-1} \)
The area (in sq. units) of the region \( A=\{(x,y):(x-1)[x]\le y\le2\sqrt{x},\ 0\le x\le2\} \), where [t] denotes the greatest integer function, is :
There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is :
If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eighth terms is 243, then the sum of the first 50 terms of this G.P. is :