List of top Questions asked in JEE Main

Let a hyperbola be \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) and ellipse be \(\frac{x^2}{9} + \frac{y^2}{8} = 1\). If length of latus rectum of hyperbola is equal to minor axis of ellipse and eccentricity of hyperbola is equal to semi-major axis of ellipse, then \(2ae\) is equal to (where 'e' is the eccentricity of hyperbola)

Let \(f(x+y) = f(x) f(y)\), \(f(0) \neq 0\). If \(x^2 g(x) = \int_0^x (t^2 f(t) + t g(t)) \, dt\), then \(g(2)\) is equal to

If system of equations \(x \cos \theta - 8y - 12z = 0\), \(x \cos 2\theta + y + 3z = 0\), \(x + y + 3z = 0\) has non-trivial solution, then find sum of values of \(\theta\) (where \(\theta \in [0, 2\pi]\)).

A bag contains 6 Red and 6 black balls. 6 pair of balls are selected one by one without replacement then the probability that each of the 6 pairs contains 1 red and 1 black ball.

The shortest distance between the lines \(\frac{x-3}{-1} = \frac{y-2}{4} = \frac{z-1}{2}\) and \(\frac{x-1}{2} = \frac{y-1}{1} = \frac{z-2}{5}\) is:

Consider the observations: 2, 4, \(\alpha\), \(\beta\), 6, 12, 14. If their mean is 8 and variance = 16, then the quadratic equation whose roots are \(3\alpha + 2\) and \(2\beta + 1\), is

Let \(\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}\), \(\vec{b} = 6\hat{i} + 3\hat{j} + 3\hat{k}\). If \(2\vec{a} + 3\vec{b}\) and \(\vec{a} - \vec{b}\) are two adjacent sides of a triangle then square of area of the triangle is

An ellipse has directrix \(x = 9\) & eccentricity \(= \frac{1}{3}\). If one of its focus is \((\alpha,0)\), \(\alpha<0\), then locus of the mid-point of the chord passing through \(P(\alpha,0)\) is

Let \(x = 9\) be a directrix of an ellipse centred at \((0, 0)\) and having eccentricity \(\frac{1}{3}\). If focus at \((\alpha, 0)\) (\(\alpha<0\)), then locus of the mid-point of the chord passing through the focus \((\alpha, 0)\) is

A lift of a 10 floor building contains 9 persons and group of 4 and 5 leave the lift on different floor and there is no stoppage of lift at 1st and 2nd floor, then find number of ways this can be done.

\(\int_{-1}^{1} \frac{x^3 + |x| + 1}{x^2 + |x| + 1} \, dx\) is equal to

Statement - I: \(\text{Ph-O-CH}_2\text{Ph} \xrightarrow[\text{HI}]{\Delta}\) Product is mixture of benzyl alcohol and iodobenzene.
Statement - II: \(\text{Ph-O-CH}_2\text{Ph}\), O-CH\(_2\) bond cleavage takes place during reaction with HI.

Let \((n^2 - 2n + 2)x^2 - 3x + (n^2 - 2n + 2)^2 = 0\) be a quadratic equation. If \(\alpha\) is the minimum value of product of roots and \(\beta\) is the maximum value of sum of roots, then the sum of first six terms of geometric progression whose first term is \(\alpha\) and common ratio is \(\left(\frac{\alpha}{\beta}\right)\), is

Give IUPAC name of the final product Z.

Which of the following test will give confirmation of functional group in (D)?

Compare the bond length X, Y and Z in the following compound
Where: (X) is the C=O bond, (Y) is the C-O bond between carbonyl group and oxygen, (Z) is the C-O bond between the oxygen and the methyl group.

Statement I: Mixture of Sugar and NaCl is separated by using ethanol because of difference in their solubility.
Statement II: Rose essence from rose petals is separated by steam distillation because of its higher volatility and insolubility in \( H_2O \).

Count the total number of electrons present in lone pair and \( \pi \) bond.

For the given coordination compounds:
(A) \([Ni(NH_3)_6]^{2+}\) is \(sp^3d^2\), octahedral and paramagnetic.
(B) \([Ni(CO)_4]\) is \(sp^3\), tetrahedral and paramagnetic.
(C) \([Ni(CN)_4]^{2-}\) is \(dsp^2\), square planar and diamagnetic.
(D) \([NiCl_4]^{2-}\) is \(sp^3\), tetrahedral and paramagnetic.
The correct set of coordination compounds against the mentioned properties is

How many of the following reaction(s) product formed can also be prepared by Gabriel phthalimide synthesis:

1 mol of alkane (X) for complete combustion required 8 mol of oxygen. When it is brominated in presence of sunlight it gives only one product. How many primary carbons are present in alkane (X)?

If excess of AgNO\(_3\) is added to 0.05M, 100ml of Tetraaquadichlorochromium(III) chloride complex aqueous solution, then the number of moles of AgCl precipitated is \( x \times 10^{-3} \) moles. Find ‘x’.

In a period, ionization energy of left most element is _ _ _ _ _ _ _ _ and \(|\Delta H_{eg}|\) value of right most element is _ _ _ _ _ _ _ _ . [Except noble gases]

0.2M, 500ml MnO\(_4^-\) solution is treated with 1.5M, 500ml KI solution in basic medium. The liberated \(I_2\) required ‘X’M, 300ml hypo solution. The value of ‘X’ is -