List of practice Questions

A bag contains 4 red balls, 6 yellow balls and 5 blue balls. In how many ways we can select 8 balls such that we get at least two balls of each colour?

The value of the sum of r / (4 + r⁴) for r = 1 to 10 is:

Escape velocity on Earth is ve = √(2gR). A planet of half the radius of Earth has the same density as Earth. The escape speed on that planet is ve / N. Find the value of N.

Styrene undergoes the following sequence of reactions Molar mass of product (P) is:

Identify correct statement(s):
(i) $ \text{Ar–Cl} $ and $ \text{R–Cl} $ show similar chemical properties.
(ii) Rate of $ S_N^1 $ $ C_6H_5CH_2–Cl<C_6H_5–CH–C_6H_5 $
(iii) Alcohol is more polar than water, so alcoholic KOH shows elimination reaction.
(iv) Vinyl alcohol is an alkene, whereas allyl alcohol is an alkyne.
(v) Alcohol with SOC$_2$ gives alkyl halide, but phenol does not give.

If $Z$ be a complex number such that $|Z + 2| = |Z - 2|$ and $\text{arg} \left( \frac{Z - 3}{Z + 1} \right) = \frac{\pi}{4}$, then the value of $|Z|^2$ is

Let the lines $L_1 : \vec r = \hat i + 2\hat j + 3\hat k + \lambda(2\hat i + 3\hat j + 4\hat k)$, $\lambda \in \mathbb{R}$ and $L_2 : \vec r = (4\hat i + \hat j) + \mu(5\hat i + + 2\hat j + \hat k)$, $\mu \in \mathbb{R}$ intersect at the point $R$. Let $P$ and $Q$ be the points lying on lines $L_1$ and $L_2$, respectively, such that $|PR|=\sqrt{29}$ and $|PQ|=\sqrt{\frac{47}{3}}$. If the point $P$ lies in the first octant, then $27(QR)^2$ is equal to}

"X" is an oxoanion of the lightest element of group 7 (in the periodic table). The metal is in +6 oxidation state in "X". The color of the potassium salt of X is

As shown in the figure, the ratio of $T_1$ and $T_2$ is