Questions by momin

A plane passing through the point (3, 1, 1) contains two lines whose direction ratios are 1, –2, 2 and 2, 3, –1 respectively. If this plane also passes through the point ($\alpha$, –3, 5), then $\alpha$ is equal to (1) 5 (2) 10 (3) –5 (4) –10

Which of the following is a tautology ? (1) $(\sim p)\land(p\lor q)\to q$ (2) $(q\to p)\ \lor\sim(p\to q)$ (3) $(\sim q)\lor(p\land q)\to q$ (4) $(p\to q)\land(q\to p)$

Let f(x) be a quadratic polynomial such that f(–1) + f(2) = 0. If one of the roots of f(x) = 0 is 3, then its other root lies in : (1) (1, 3) (2) (–1, 0) (3) (–3, –1) (4) (0, 1)

The area (in sq. units) of an equilateral triangle inscribed in the parabola y2 = 8x, with one of its vertices on the vertex of this parabola is : (1) 64$\sqrt3$ (2) 192$\sqrt3$ (3) 128$\sqrt3$ (4) 256$\sqrt3$

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located around a circular path. Each pair of nearest stations is connected by a straight track only. Further, each pair of nearest station is connected by blue line, whereas all ...

If $y=\sum\limits_{k=1}^6 k\cos^{-1}\left\{{3\over5}\cos kx-{4\over5}\sin kx\right\}$ then $dy\over dx$ at x = 0 is Numerical Value Type

Let the position vectors of points 'A' and 'B' be $\hat{i}+\hat{j}+\hat{k}$ and $2\hat{i}+\hat{j}+3\hat{k}$ , respectively. A point 'P' divides the line segment AB internally in the ratio $\lambda$ : 1 ($\lambda$ > 0). If O is the origin and $\...

Let [t] denote the greatest integer less than or equal to t. Then the value of $\int\limits_1^2|2x-[3x]|\ dx$ is Numerical Value Type

For a positive integer n, $\left(1+{1\over x}\right)^n$ is expanded in increasing powers of x. If three consecutive coefficients in this expansion are in the ratio, 2 : 5 : 12 , then n is equal to _______ Numerical Value Type

If the variance of the terms in an increasing A.P. b1, b2, b3, ........ , b11 is 90, then the common difference of this A.P. is Numerical Value Type

What is the depth at which the value of acceleration due to gravity becomes $1\over n$ times the value that at the surface of earth? (radius of earth = R) (1) $R\over n$ (2) $R\over n^2$ (3) $R(n-1)\over n$ (4) $Rn\over (n-1)$

A wire of length L metre carrying a current of l ampere is bent in the form of circle. Its magnetic moment is (1) I L2/4π A m2 (2) I L2/4 A m2 (3) I πL2/4 A m2 (4) 2I L2/π A m2

The total energy of an electron in the nth stationary orbit of the hydrogen atom can be obtained by (1) $E_n=-13.6×n^2$ eV (2) $E_n={13.6\over n^2}$ eV (3) $E_n=-{13.6\over n^2}$ eV (4) $E_n=-{1.36\over n^2}$ eV

The angle of 1′ (minute of arc) in radian is nearly equal to (1) 1.75 × 10–2 rad (2) 2.91 × 10–4 rad (3) 4.85 × 10–4 rad (4) 4.80 × 10–6 rad

The de Broglie wavelength of an electron moving with kinetic energy of 144 eV is nearly (1) 102 × 10–2 nm (2) 102 × 10–3 nm (3) 102 × 10–4 nm (4) 102 × 10–5 nm

Three identical spheres, each of mass M, are placed at the corners of a right angle triangle with mutually perpendicular sides equal to 2 m (see figure). Taking the point of intersection of the two mutually perpendicular sides as the origin, find the ...

A light bulb and an inductor coil are connected to an ac source through a key as shown in the figure below. The key is closed and after sometime an iron rod is inserted into the interior of the inductor. The glow of the light bulb (1) increases (2) ...

Three stars A, B, C have surface temperatures TA, TB, TC respectively. Star A appears bluish, star B appears reddish and star C yellowish. Hence, (1) TA > TC > TB (2) TA > TB > TC (3) TB > TC > TA (4) TC > TB > TA

A liquid does not wet the solid surface if angle of contact is (1) zero (2) equal to 45° (3) equal to 60° (4) greater than 90°

The electric field at a point on the equatorial plane at a distance r from the centre of a dipole having dipole moment $\vec{p}$ is given by, (r >> separation of two charges forming the dipole, $\epsilon_0$ - permittivity of free space) (1) $\vec{E}=-{\vec{...

The efficiency of a Carnot engine depends upon (1) the temperature of the source only (2) the temperature of the sink only (3) the temperatures of the source and sink (4) the volume of the cylinder of the engine

The P-V diagram for an ideal gas in a piston cylinder assembly undergoing a thermodynamic process is shown in the figure. The process is (1) isothermal (2) adiabatic (3) isochoric (4) isobaric

A barometer is constructed using a liquid (density = 760 kg/m3). What would be the height of the liquid column, when a mercury barometer reads 76 cm? (density of mercury = 13600 kg/m3) (1) 0.76 m (2) 1.36 m (3) 13.6 m (4) 136 m

The magnetic field in a plane electromagnetic wave is given by, By = 2 × 10–7 sin(π × 103x + 3π × 1011t)T Calculate the wavelength. (1) π × 10–3 m (2) π × 103 m (3) 2 × 10–3 m (4) 2 × 103 m

The length of the string of a musical instrument is 90 cm and has a fundamental frequency of 120 Hz. Where should it be pressed to produce fundamental frequency of 180 Hz? (1) 80 cm (2) 75 cm (3) 60 cm (4) 45 cm