List of practice Questions

Out of 6 boys and 4 girls, a committee of 5 members is to be formed. In how many ways can this be done, if at least 2 girls are included?

Choose the correct pair from the following:

For what value of $ n $, the curve \[ \left( \frac{x}{a} \right)^n + \left( \frac{y}{b} \right)^n = 2 \text{ touches the straight line } \frac{x}{a} + \frac{y}{b} = 2 \text{ at the point } (a, b)? \]

The genetic nature of TMV (Tobacco Mosaic Virus) as RNA was confirmed by:

If $ f(x) $ and $ g(x) $ are two functions such that $ f(x) + g(x) = e^x $ and $ f(x) - g(x) = e^{-x} $, then:

Assertion (A): Nitrosomonas is a Chemoautotrophic bacteria.
Reason (R): Chemoautotrophs derive energy from sunlight and carbon from CO$_2$.

In plants, growth rate is expressed in Arithmetic and Geometric growth equations. Which equation is correct?

The range of the function $ f(x) = 7 - x\cdot P_{x-3} $ is:

Ratio of ATP:NADH:FADH2 produced in Krebs' cycle per one acetyl Co-A molecule by substrate level phosphorylation is:

Let the function $ f(x) $ be defined as follows: $$ f(x) = \begin{cases} (1 + | \sin x |)^{\frac{a}{|\sin x|}}, & -\frac{\pi}{6}<x<0 \\b, & x = 0 \\ \frac{\tan 2x}{\tan 3x}, & 0<x<\frac{\pi}{6} \end{cases} $$ Then the values of $ a $ and $ b $ are:

The value(s) of $ c \in (1, 2) $, where the conclusion of Lagrange’s M.V.T. is satisfied for the function $ f(x) = x^2 + 3x + 2 $ in $[1,2]$, is/are:

Let $ \phi_1(x) = e^{\sin x, \phi_2(x)} = e^{\phi_1(x)}, \ldots, \phi_{n+1}(x) = e^{\phi_n(x)}, \forall n \geq 1$. Then for any fixed $ n $, the expression $ \frac{d}{dx} \left\{ \phi_n(x) \right\} $ is:

Identify A, B, and C in the given Hatch and Slack pathway diagram: