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On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

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When 5V potential difference is applied across a wire of length 0.1 m, the drift speed of electrons is $2.5×10_{−4}ms_{−1}$. If the electron density in the wire is $8×10_{28}m_{−3}$, the resistivity of the material is close to :

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is :

Let A and B be two events such that $p(A∪B)=61 ,p(A∩B)=41 $ and $p(A)=41 $, where $A$stands for thecomplement of the event A. Then the events A and B are

Given : A circle, $2x_{2}+2y_{2}=5$and a parabola, $y_{2}=45 x$.Statement - I : An equation of a common tangent to these curves is $y=x+5 $Statement - II : If the line, $y=mx+m5 (m=0)$is their common tangent, then m satisfies $m_{4}−3m_{2}+2=0.$

Experimentally it was found that a metal oxide has formula $M_{0.98}O.$ Metal M, is present as $M_{2+}andM_{3+}$ in its oxide. Fraction of the metal which exists as $M_{3+}$ would be:

The equation of the plane containing the line $2x−5y+z=3;x+y+4z=5$, and parallel to the plane, $x+3y+6z=1$, is :

Two charges, each equal to q, are kept at x = ?a and x = a on the x-axis. A particle of mass m and charge $q_{0}=2q $ is placed at the origin. If charge q0 is given a small displacement (y a) along the y-axis, the net force acting on the particle is proportional to:

If z is a complex number of unit modulus and argument q, then $arg(1+z1+z )$equal