The speed of light in media ‘A’ and ‘B’ are 2.0 × 1010 cm/s and 1.5 × 1010 cm/s respectively. A ray of light enters from the medium B to A at an incident angle ‘θ’. If the ray suffers total internal reflection, then
Let f and g be twice differentiable even functions on (–2, 2) such that\(ƒ(\frac{1}{4})=0, ƒ(\frac{1}{2})=0, ƒ(1) =1\) and \(g(\frac{3}{4}) = 0 , g(1)=2\).Then, the minimum number of solutions of f(x)g′′(x) + f′(x)g′(x) = 0 in (–2, 2) is equal to_____.
A dilute solution of sulphuric acid is electrolysed using a current of 0.10 A for 2 hours to produce hydrogen and oxygen gas. The total volume of gases produced at STP is ____ cm3. (Nearest integer)
[Given : Faraday constant F = 96500 C mol–1 at STP, molar volume of an ideal gas is 22.7 L mol–1]
The major product (P) of the given reaction is (where, Me is –CH3)
Let \(\vec{a}\) be a vector which is perpendicular to the vector \(3\hat{i}+\frac{1}{2}\hat{j}+2\hat{k}. \)If \(\vec{a}×(2\hat{i}+\hat{k})=2\hat{i}−13\hat{j}−4\hat{k}\), then the projection of the vector on the vector\( 2\hat{i}+2\hat{j}+\hat{k}\) is:
Match List I with List II.
Choose the correct answer from the options given below:
If the plane P passes through the intersection of two mutually perpendicular planes 2x + ky – 5z = 1 and 3kx – ky + z = 5, k < 3 and intercepts a unit length on positive x-axis, then the intercept made by the plane P on the y-axis is
\(\begin{array}{l} \frac{2^3-1^3}{1\times7}+\frac{4^3-3^3+2^2-1^3}{2\times 11}+\frac{6^3-5^3+4^3-3^3+2^3-1^3}{3\times 15}+\cdots+\frac{30^3-29^3+28^3-27^3+\cdots+2^3-1^3}{15\times63}\end{array}\)
is equal to _______.
