List of top Questions asked in JEE Main- 2014

Let \(A(2,3,5)\), \(B(-1,3,2)\) and \(C(\lambda,5,\mu)\) be the vertices of a \(\triangle ABC\). If the median through A is equally inclined to the coordinate axes, then:

The angle of elevation of the top of a vertical tower from a point P on the horizontal ground was observed to be \(\alpha\). After moving a distance 2 metres from P towards the foot of the tower, the angle of elevation changes to \(\beta\). Then the height (in metres) of the tower is:

Let for \(i = 1,2,3\), \(p_i(x)\) be a polynomial of degree 2 in x, \(p_i'(x)\) and \(p_i''(x)\) be the first and second order derivatives of \(p_i(x)\) respectively. Let, \(A(x) = \begin{bmatrix}p_1(x)&p_1'(x)&p_1''(x)\\p_2(x)&p_2'(x)&p_2''(x)\\p_3(x)&p_3'(x)&p_3''(x)\end{bmatrix}\) and \(B(x) = [A(x)]^{T}A(x)\). Then determinant of B(x):

Two ships A and B are sailing straight away from a fixed point O along routes such that \(\angle AOB\) is always \(120^\circ\). At a certain instance, \(OA = 8\) km, \(OB = 6\) km and the ship A is sailing at the rate of 20 km/hr while the ship B sailing at the rate of 30 km/hr. Then the distance between A and B is changing at the rate (in km/hr):

If \(\lim_{x \to 2} \frac{\tan\left((x-2)\left\{x^2 + (k-2)x - 2k\right\}\right)}{x^2 - 4x + 4} = 5\), then \(k\) is equal to:

A stair-case of length \(l\) rests against a vertical wall and a floor of a room. Let P be a point on the stair-case, nearer to its end on the wall, that divides its length in the ratio \(1 : 2\). If the staircase begins to slide on the floor, then the locus of P is:

The base of an equilateral triangle is along the line given by \(3x + 4y = 9\). If a vertex of the triangle is \((1, 2)\), then the length of a side of the triangle is:

The proposition \(\sim(p \vee \sim q) \vee \sim(p \vee q)\) is logically equivalent to:

The set of all real values of \(\lambda\) for which exactly two common tangents can be drawn to the circles \(x^2 + y^2 - 4x - 4y + 6 = 0\) and \(x^2 + y^2 - 10x - 10y + \lambda = 0\) is the interval:

The sum of the first 20 terms common between the series \(3 + 7 + 11 + 15 + \ldots\) and \(1 + 6 + 11 + 16 + \ldots\) is:

If \(z_1, z_2\) and \(z_3, z_4\) are 2 pairs of complex conjugate numbers, then \(\arg\left(\frac{z_1}{z_4}\right) + \arg\left(\frac{z_2}{z_3}\right)\) equals:

If \(2\cos\theta + \sin\theta = 1\) \(\left(\theta \ne \frac{\pi}{2}\right)\), then \(7\cos\theta + 6\sin\theta\) is equal to:

In a geometric progression, if the ratio of the sum of first 5 terms to the sum of their reciprocals is 49, and the sum of the first and the third term is 35. Then the first term of this geometric progression is:

If \(\alpha\) and \(\beta\) are roots of the equation, \(x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0\) for some \(k\), and \(\alpha^2 + \beta^2 = 66\), then \(\alpha^3 + \beta^3\) is equal to:

The major product of the reaction is

Which one of the following reactions will not result in the formation of carbon-carbon bond ?

Structure of some important polymers are given. Which one represents Buna-S ?

Which one of the following class of compounds is obtained by polymerization of acetylene ?

In a nucleophilic substitution reaction : \(\mathrm{R-Br + Cl^-} \xrightarrow{\mathrm{DMF}} \mathrm{R-Cl + Br^-}\), which one of the following undergoes complete inversion of configuration ?

In the hydroboration - oxidation reaction of propene with diborane, \(\mathrm{H_2O_2}\) and NaOH, the organic compound formed is:

Which is the major product formed when acetone is heated with iodine and potassium hydroxide?

Allyl phenyl ether can be prepared by heating :

An octahedral complex of \(\mathrm{Co^{3+}}\) is diamagnetic. The hybridisation involved in the formation of the complex is :

The gas evolved on heating \(\mathrm{CaF_2}\) and \(\mathrm{SiO_2}\) with concentrated \(\mathrm{H_2SO_4}\), on hydrolysis gives a white gelatinous precipitate. The precipitate is:

The form of iron obtained from blast furnace is :