List of practice Questions

Explain with reasons: 
(i) Sulphuric acid is not used in the reaction of alcohol and KI. 
(ii) Haloalkanes form alkyl cyanide as chief product on reaction with KCN, while isocyanide as chief product on reaction with AgCN. 
(iii) Although chlorine is an electron withdrawing group, even then it is ortho- and para-directing in aromatic electrophilic substitution reactions.

A random variable X and its probability distribution is given below. The value of P(X<5) is _______. (rounded off to one decimal place)
X012345
P(X)0K2K3K4K5K
The total number of subset of a finite set A has 56 more elements then the total number of subset of another finite set B. What is the number of elements in set A
In a biprism experiment, the fringes are observed in the focal plane of the eye-piece at a distance of 1.2 m from the slit. The distance between the central bright band and the 20th bright band is 0.4 cm. When a convex lens is placed between the biprism and the eye-piece, 90 cm from the eye-piece, the distance between the two virtual magnified images is found to be 0.9 cm. Determine the wavelength of light used.
वारिधर का पर्यायवाची शब्द?
The temperature of a gas is -50° C. To what temperature the gas should be heated so that the rms speed is increased by 3 times?
Different views of the cross section of a fish toy are shown here. The points P and Q are connected in such way that the fish tail waves. The grey colour gear and the green colour part are joined together. The rod is free to move depending on how it is connected to the green part. Which of
the option(s) will work to wave the tail?
Fishes
Which of the following case may be considered as the first reported case of PIL in India?
What was the forecast made by the chief astrologer regarding the Tiger King?
Let \(𝑎_1=𝑏_1=1\)and \(𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)\), \(𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}\), \(∀𝑛≥2\). If \(𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}\) and \(𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}\), then \(2^7(2𝑆−𝑇)\)  is equal to ____ .
Let \(\sum_{n=0}^{\infty }\frac{n^{3}((2n)!+(2n-1)(n!))}{(n!)((2n)!)}=ae+\frac{b}{e}+c\), where $a, b, c \in Z$ and $e=\displaystyle\sum_{n=0}^{\infty} \frac{1}{n !}$ Then $a^2-b+c$ is equal to _______
A dislocation loop PQRSTU is on the (111) plane of a cubic single crystal with Burgers vector \( \vec{b} = \frac{a}{6}[\bar{1}\bar{2}1] \). The dislocation segments \(\vec{PU}\) and \(\vec{PQ}\) are parallel to \([0\bar{1}1]\) and \([1\bar{1}0]\) directions, respectively. The correct statement(s) is/are
Let sets A and B have 5 elements each. Let mean of the elements in sets A and B be 5 and 8 respectively and the variance of the elements in sets A and B be 12 and 20 respectively. A new set C of 10 elements is formed by subtracting 3 from each element of A and adding 2 to each element of B. Then the sum of the mean and variance of the elements of C is:

Which letter will come at the place of question mark (?) 

$Ka _1, Ka _2$ and $Ka _3$ are the respective ionization constants for the following reactions (a), (b) and (c)
(a) $H _2 C _2 O _4 \rightleftharpoons H ^{+}+ HC _2 O _4^{-}$
(b) $HC _2 O _4^{-} \rightleftharpoons H ^{+}+ HC _2 O _4^{2-}$
(c) $H _2 C _2 O _4 \rightleftharpoons 2 H ^{+}+ C _2 O _4^{2-}$
The relationship between $K _{ a _1}, K _{ a _2}$ and $K _{ a _3}$ is given as
The range of the function $f(x)=\sqrt{3-x}+\sqrt{2+x}$ is:
Let \( S = \{ M = [a_{ij}], a_{ij} \in \{0, 1, 2\}, 1 \leq i, j \leq 2 \} \) be a sample space and \( A = \{ M \in S : M \text{ is invertible} \} \) be an event. Then \( P(A) \) is equal to:
Object distance, \(u = (50.1 \pm 0.5)\,\text{cm}\) and image distance \(v = (20.1 \pm 0.2)\,\text{cm}\). The focal length is:

Which kind of adverb is the word in capitals? “Arvind coughed LOUDLY to attract attention.”

Which kind of adverb is the word in capitals? “The airline passengers were COMPLETELY exhausted after their long flight.”

Which kind of adverb is the word in capitals? “When he knocked on the door, he was asked to come INSIDE.

Which kind of adverb is the word in capitals? “When he knocked on the door, he was asked to come INSIDE.”

Which kind of adverb is the word in capitals? “The watchman FREQUENTLY makes a round of the office building.”

If \(X = \{\,8^n - 7n - 1 \mid n \in \mathbb{N}\,\}\) and \(Y = \{\,49(n-1) \mid n \in \mathbb{N}\,\}\), then
If \[ \left| \begin{array}{ccc} x^{n} & x^{n+2} & x^{n+3} \\ y^{n} & y^{n+2} & y^{n+3} \\ z^{n} & z^{n+2} & z^{n+3} \end{array} \right| =(x-y)(y-z)(z-x)\left(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}\right) \] then \(n\) is equal to: