List of top Questions asked in JEE Main

If the domain of the function \(f(x)\) = \(\frac{\sqrt{x^2-25}}{(4-x^2)}+ \log(x^2+2x-15)\) is \((-∞, α) ∪ (β, ∞)\), then \(α^2+β^2\) is equal to \(b\)

The number of solution of the equation \(4sin^2 x-4cos^3 x+9-4cos x = 0\), \(x ∈ [-2\pi, 2\pi]\)

If the mirror image of the point \(P(3,4,9)\) in the Line 
\(\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}\) is \((α,β,γ)\) then find \(14(a+ẞ+y)\) is:

Let \(α\) and \(β\) the roots of equation \(px^2 + qx - r = 0\), where \(P≠ 0\). If \(p,q,r\) be the consecutive term of non constant G.P and \(\frac{1}{α} + \frac{1}{β} = \frac{3}{4}\) then the value of \((α - β)^2\) is:

Let m and n be the coefficient of \(7^{th}\) and \(13^{th}\) term in expansion of \(\bigg(\frac{1}{3x^{\frac{1}{3}}} +\frac{1}{2x^{\frac{2}{5}}}\bigg)^{18}\), then \(\bigg(\frac{m}{n}\bigg)^{\frac{1}{3}}\) is:

Let vertex \(A(2, 3, 1), B(3, 2, -1), C(-2, 1, 3)\). If \(AD\) is angle bisector of angle \(A\), then projection of \(\overrightarrow{AD}\) on \(\overrightarrow{AC}\) is equal to:

Find out charge (in C) required for electrolysis of \(1\) mole of \(H_2O\) to produce \(O_2\) on one of the electrodes. \((F = 96500 \;C)\)

Ethylene glycol of \(x\) \(kg\) is mixed with \(18.6\) \(kg\) of solvent, \(24 °C\) depression in freezing point takes place. Calculate value of \(x\). (Given: \(K_1\) = \(1.6 °C/molal\) M.W. of ethylene glycol = \(62\) \(g/mol\))

Consider the following two statements 
Statement I: In \(p\) and \(d\) block both metals and non - metals are present 
Statement II: Electronegativity and ionisation enthalpy of metals is greater than non - metals

Consider the following two statements Statement I: \(SiO_2\) and GeO₂\(GeO_2\) are acidic, \(SnO\) and \(PbO\) are amphoteric Statement II: Allotropes of carbon are formed due to catenation and \(dπ - ρπ\) bond

Consider the following two statements Statement I: \(π\) \(2p\) bonding molecular orbital has low electron density above & below internuclear axis Statement II: \(π\times2p\) antibonding molecular orbital has only one nodal plane

\(3, a, b, c\) are in Ap and \(3, a-1, b+1, c+9\) are in GP. Then AM of \(a, b, c\) is

Find the ratio of the charge on \(4\) \(µF\) to that on \(2\) \(µF\) in steady state.

A ball of mass \(120\) \(g\) moving with initial velocity \(25 \;m/s\) is stopped by an external force \(F\) in \(0.15\) \(sec\). Find value of \(F\) in newton :

Find the number of significant digits in the value 10.05

If the power of a light source is P and frequency of photons emitted is f. Find number photons emitted in time t.

The dimensions of angular impulse is equal to :

Which is homoleptic complex?

Statement I: \([Ni(H_2O)_6]^{2+}\) is green in colour.
Statement II: \([Ni(ON)_4]^{2-}\) is colourless.

In case of isoelectronic species the size of \(F^-\), \(Na\) and \(Na^+\) is affected by:

Two integers \( x \) and \( y \) are chosen with replacement from the set \( \{0, 1, 2, 3, \ldots, 10\} \). Then the probability that \( |x - y| > 5 \) is:

Let \( \vec{a} = a_1 \hat{i} + a_2 \hat{j} + a_3 \hat{k} \) and \( \vec{b} = b_1 \hat{i} + b_2 \hat{j} + b_3 \hat{k} \) be two vectors such that \( |\vec{a}| = 1 \), \( \vec{a} \times \vec{b} = 2 \), and \( |\vec{b}| = 4 \). If \( \vec{c} = 2(\vec{a} \times \vec{b}) - 3\vec{b} \), then the angle between \( \vec{b} \) and \( \vec{c} \) is equal to:

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:

A big drop is formed by coalescing 1000 small droplets of water. What will be the change in surface energy What will be the ratio between the total surface energy of the droplets and the surface energy of the big drop?

Let \( S_n \) denote the sum of the first \( n \) terms of an arithmetic progression. If \( S_{20} = 790 \) and \( S_{10} = 145 \), then \( S_{15} - S_5 \) is: