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:
Let a circle C : (x – h)2 + (y – k)2 = r2, k > 0, touch the x-axis at (1, 0). If the line x + y = 0 intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of h + k + r is equal to ____.
Let
\(a→=α\^{i}+3\^{j}−\^{k}, \overrightarrow{b}=3\^{i}−β\^{j}+4\^{k} and \overrightarrow{c}=\^{i}+2\^{j}−2\^{k }\)
where α,β∈R, be three vectors. If the projection of
\(\overrightarrow{a} on \overrightarrow{c} is \frac{10}{3} and \overrightarrow{b}×\overrightarrow{c}=−6\^{i}+10\^{j}+7\^{k}, \)
then the value of α+β is equal to
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_____.
Match List I with List II.
Choose the correct answer from the options given below:
