List of top Questions asked in JEE Main- 2014

If the point \((1,\ 4)\) lies inside the circle \(x^2+y^2-6x+10y+p=0\) and the circle does not touch or intersect the coordinate axes, then the set of all possible values of \(p\) is the interval

Let \(a\) and \(b\) be any two numbers satisfying \(\frac1{a^2}+\frac1{b^2}=\frac14\). Then, the foot of perpendicular from the origin on the variable line \(\frac xa+\frac yb=1\) lies on :

The number of terms in the expansion of \((1+x)^{101}(1-x+x^2)^{100}\) in powers of \(x\) is

If \(\operatorname{cosec}\theta=\frac{p+q}{p-q}\ (p\ne q,\ p\ne 0)\), then \(\left|\cot\left(\frac{\pi}{4}+\frac{\theta}{2}\right)\right|\) is equals to:

The number of values of \(\alpha\) in \([0,\ 2\pi]\) for which \(2\sin^3\alpha-7\sin^2\alpha+7\sin\alpha=2\), is :

Given three points \(P,Q,R\) with \(P(5,3)\) and \(R\) lies on the \(x\)-axis. If the equation of \(RQ\) is \(x-2y=2\) and \(PQ\) is parallel to the \(x\)-axis, then the centroid of \(\Delta PQR\) lies on the line

The sum of the digits in the unit's place of all the 4 - digit numbers formed by using the numbers 3, 4, 5 and 6, without repetition is :

If the sum \(\frac{3}{1^2}+\frac{5}{1^2+2^2}+\frac{7}{1^2+2^2+3^2}+\ldots\) up to 20 terms is equal to \(\frac{k}{21}\), then \(k\) is equal to

Let \(w\ (\mathrm{Im}\,w\ne 0)\) be a complex number. Then, the set of all complex numbers \(z\) satisfying the equation \(w-\overline{w}z=k(1-z)\), for some real number \(k\), is

If equations \(ax^2+bx+c=0\), \((a,\ b,\ c\in R,\ a\ne 0)\) and \(2x^2+3x+4=0\) have a common root, then \(a:b:c\) equals :

In the reaction,
\(\mathrm{CH_3COOH \xrightarrow{LiAlH_4} A \xrightarrow{PCl_5} B \xrightarrow{Alc.\ KOH} C}\),
the product C is :

Which one of the following bases is not present in DNA ?

Which one is classified as a condensation polymer ?

For which of the following molecule significant \(\mu \neq 0\) ?

Sodium phenoxide when heated with \(\mathrm{CO_2}\) under pressure at \(125^\circ\mathrm{C}\) yields a product which on acetylation produces C.

The major product C would be :

The major organic compound formed by the reaction of 1, 1, 1 - trichloroethane with silver powder is :

On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic compound formed is :

Which one of the following properties is not shown by NO ?

For the non-stoichiometric reaction \(\mathrm{2A + B \rightarrow C + D}\), the following kinetic data were obtained in three separate experiments, all at 298 K.

Initial Concentration (A)	Initial Concentration (B)	Initial rate of formation of C (mol L-1 s-1)
0.1 M	0.1 M	\(1.2\times 10^{-3}\)
0.1 M	0.2 M	\(1.2\times 10^{-3}\)
0.2 M	0.1 M	\(2.4\times 10^{-3}\)

The rate law for the formation of C is :

Consider separate solutions of 0.500 M \(\mathrm{C_2H_5OH(aq)}\), 0.100 M \(\mathrm{Mg_3(PO_4)_2(aq)}\), 0.250 M \(\mathrm{KBr(aq)}\) and 0.125 M \(\mathrm{Na_3PO_4(aq)}\) at 25\(^\circ\)C. Which statement is true about these solutions, assuming all salts to be strong electrolytes ?

The equation which is balanced and represents the correct product(s) is :

For the estimation of nitrogen, 1.4 g of an organic compound was digested by Kjeldahl method and the evolved ammonia was absorbed in 60 mL of \(\frac{M}{10}\) sulphuric acid. The unreacted acid required 20 mL of \(\frac{M}{10}\) sodium hydroxide for complete neutralization. The percentage of nitrogen in the compound is :

The forward biased diode connection is :

A student measured the length of a rod and wrote it as \(3.50\ \mathrm{cm}\). Which instrument did he use to measure it ?

Hydrogen (\({}_1\mathrm{H}^1\)), Deuterium (\({}_1\mathrm{H}^2\)), singly ionised Helium (\(({}_2\mathrm{He}^4)^+\)) and doubly ionised lithium (\(({}_3\mathrm{Li}^6)^{++}\)) all have one electron around the nucleus. Consider an electron transition from \(n=2\) to \(n=1\). If the wave lengths of emitted radiation are \(\lambda_1,\ \lambda_2,\ \lambda_3\) and \(\lambda_4\) respectively then approximately which one of the following is correct ?