List of practice Questions

If $ y = \sqrt{\sin x + \sqrt{\sin x + \sqrt{\sin x + \cdots \infty}}} $, then the value of $ \frac{d^2y}{dx^2} $ at $ (\pi,1) $ is:

Water is flowing in a streamline manner in a horizontal pipe. If the pressure at a point where cross-sectional area is $ 10 $ cm$^2$ and velocity $ 1 $ m/s is $ 2000 $ Pa, then the pressure of water at another point where the cross-sectional area is $ 5 $ cm$^2$ is:

If $\alpha$ and $\beta$ are two double roots of the equation: $$ x^2 + 3(a + 3)x - 9a = 0 $$ for different values of $a$ (where $\alpha > \beta$), then the minimum value of the equation: $$ x^2 + \alpha x - \beta = 0 $$ is:

If $ P(A \cap B) + P(B \mid A \cap B) = $, then:

The bond angles $ b_1, b_2, b_3 $ in the above structure are respectively in $ ^\circ $:

A metallic wire of resistance 30 $ \Omega $ is bent in the form of an equilateral triangle. The resistance between any two vertices of the triangle is:

The mass of particle X is four times the mass of particle Y. The velocity of particle Y is four times the velocity of X. The ratio of de Broglie wavelengths of X and Y is:

Let $ f(x) = \begin{cases 1 + \frac{2x}{a}, & 0 \le x \le 1
ax, & 1<x \le 2 \end{cases} $. If $ \lim_{x \to 1} f(x) $ exists, then the sum of the cubes of the possible values of $ a $ is: }

A mass $ M $, attached to a horizontal spring executes simple harmonic motion with amplitude $ A_1 $. When mass $ M $ passes mean position, then a smaller mass $ m $ is attached to it, and both of them together execute simple harmonic motion with amplitude $ A_2 $. Then the value of $ \frac{A_1}{A_2} $ is:

In the given circuit, batteries are ideal and Galvanometer shows zero deflection, then the value of 'R' is:

Which of the following orders are correct regarding their covalent bond character?
i. KF $<$ KI
ii. SnCl2 $<$ SnCl4
iii. NaCl $<$ CuCl

When a transistor in CE configuration, the resistance connected at the collector circuit and base circuit are 10 $ \Omega $ and 8 $ \Omega $ respectively, if the AC current gain $ \beta_{{ac}} = 1.4 $, then the voltage amplification is

The correct statements about the adsorption of gas on solid adsorbent are:
Adsorption is always exothermic. Physisorption may transform into chemisorption at high temperature. Physisorption increases with increasing temperature but chemisorption decreases with increasing temperature. In physisorption enthalpy of adsorption is 100 kJ mol$^{-1}$.

What are X and Z in the following reaction sequence?