List of top Questions asked in JEE Main

The area (in square units) of the part of the circle \(x^2 + y^2 = 169\) which is below the line \( 5x - y = 13 \) is\[\frac{\pi \alpha}{2 \beta} - \frac{65}{2} + \frac{\alpha}{\beta} \sin^{-1} \left( \frac{12}{13} \right)\]where \( \alpha \) and \( \beta \) are coprime numbers. Then \( \alpha + \beta \) is equal to
A line with direction ratios \( 2, 1, 2 \) meets the lines \(x = y + 2 = z\) and \(x + 2 = 2y = 2z\) respectively at the points \( P \) and \( Q \). If the length of the perpendicular from the point \( (1, 2, 12) \) to the line \( PQ \) is \( l \), then \( l^2 \) is
For the following data table

\(x_i\)

\(f_i\)  

0 - 42
4 - 84
8 - 127
12 - 168
16 - 206

Find the value of 20M (where M is median of the data)

Let \((\alpha, \beta, y)\) be the foot of perpendicular form the point \((1,2,3)\) on the line \(\bigg(\frac{x + 3}{5}\) = \(\frac{y - 1}{2}\) = \(\frac{z + 4}{3}\) \(\bigg)\)then \(19 (\alpha + \beta + y)\)
If \(z = x + iy, \quad xy \neq 0\) satisfies the equation \(z^2 + iz = 0\), then \(|z^2|\); equal to
 
\(\frac{dy}{dx}\) = \(\frac{(1-x-y^2)}{y}\) and \(x(1)=1\) , then \(5x(2)\) is equal to____.
There are 20 lines numbered as 1,2,3,..., 20. And the odd numbered lines intersect at a point and all the even numbered lines are parallel. Find the maximum number of point of intersections
Let \(a_1,a_2,a_3\), ..., an, be in A. P. and \(S_n\) denotes the sum of first \(n\) terms of this A. P. is \(S_{10}\) =\(390, \frac{a_{10}}{a_{50}} =\frac{15}{7}\), then \(S_{15} -S_5 =\) _________.
If the length of the minor axis of an ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is.
Given set = {1, 2, 3, ..., 50} one number is selected randomly from the set. Find the probability that number is multiple of 4 or 6 or 7.
The value of \(∫_{\frac \pi6}^{\frac \pi3}\sqrt {1-sin2x\ dx}\) is
Area bounded by \(0 ≤ y ≤ \text {min}(x^2+ 2, 2x + 2)\), \(x∈[0, 3]\), then \(12A\) is
A = {1, 2, 3, 4} minimum number of elements added to make an equivalence relation on set A containing (1, 3) & (1, 2) in it.
If ln a, ln b, ln c are in AP and ln a – ln 2b, ln 2b – ln 3c, ln 3c – ln a are in AP then a : b : c is
If \(r = |z|,\ θ = arg(z)\) and \( z = 2 – 2\ tan (\frac {5\pi}{8})\) then find \((r, θ)\).
In which interval the function \(f(x) = \frac {x}{(x^2-6x-16)}\) is increasing?
\((α, β)\) lie on the parabola \(y^2 = 4x\) and \((α, β)\) also lie on chord with midpoint \((1,\frac 54)\) of another parabola \(x^2 = 8y\), then value of \(|(8 – β)(α – 28)|\) is
If first term of non-constant GP be \(\frac 18\) and every term is AM of next two, then \( \displaystyle\sum_{r=1}^{20} T_r- \displaystyle\sum_{r=1}^{18} T_r\) is
The mean of 5 observations is \(\frac {24}{5}\) and variance is \(\frac {194}{25}\) . If the mean of first four observations is \(\frac 72\) , then the variance of first four observations is
The number of ways to distribute 8 identical books into 4 distinct bookshelf is (where any bookshelf can be empty)
If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.
The remainder when \(64^{{32}^{32}}\) is divided by 9 is.
Let \(f:→R→(0,∞)\) be increasing function such that \(Lt_{x→∞}\frac {f(7x)}{f(x)}=1\), then \(Lt_{x→∞}[\frac {f(5x)}{f(x)}-1]\) is equal to
\(z_1^3+z_2^3=20+15i\) then \(|z_1^4+z_2^4|\) is equal to
A coin is biased so that a head is twice as likely as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is