List of practice Questions

Let \(π‘Ž_1=𝑏_1=1\)and \(π‘Ž_𝑛=π‘Ž_{π‘›βˆ’1}+(π‘›βˆ’1)\), \(𝑏_𝑛=𝑏_{π‘›βˆ’1}+π‘Ž_{π‘›βˆ’1}\), \(βˆ€π‘›β‰₯2\). If \(𝑆= \displaystyle\sum_{β€Šπ‘›=1}^{10}\frac {𝑏_𝑛}{2^𝑛}\) and \(𝑇= \displaystyle\sum_{𝑛=1}^{8}β€Š\frac {𝑛}{2^{π‘›βˆ’1}}\), then \(2^7(2π‘†βˆ’π‘‡)\)  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? β€œArvind coughed LOUDLY to attract attention.”

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

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

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

Which kind of adverb is the word in capitals? β€œThe 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:
Let \(R=\{(3,3),(6,6),(9,9),(12,12),(6,12),(3,9),(3,12),(3,6)\}\) be a relation on the set \(A=\{3,6,9,12\}\). The relation is
Let \(S=\{x\in \mathbb{R}\mid x\ge 0 \text{ and } 2|\sqrt{x}-3|+\sqrt{x}(\sqrt{x}-6)+6=0\}\), then \(S=\)
If \(A=(a_{ij})_{4\times 4}\) such that \[ a_{ij}= \begin{cases} 2 & \text{if } i=j\\ 0 & \text{if } i\neq j \end{cases} \] then \[ \left\{\dfrac{\det(\operatorname{adj}(\operatorname{adj}A))}{7}\right\} \] is (where \(\{\ \}\) represents fractional part function)
If \(x\neq 0,\; y\neq 0,\; z\neq 0\) and \[ \left| \begin{array}{ccc} 1+x & 1 & 1 \\ 1+y & 1+2y & 1 \\ 1+z & 1+z & 1+3z \end{array} \right|=0, \] then \(x^{-1}+y^{-1}+z^{-1}=\)
If \(A=\{(x,y)\mid x^2+y^2\le 4;\; x,y\in \mathbb{R}\}\) and \(B=\{(x,y)\mid x^2+y^2\ge 9;\; x,y\in \mathbb{R}\}\), then
Ketose sugar is
The water potential of pure water at atmospheric pressure is
Which of the following is non-reducing sugar?
The water readily available to plants for absorption by roots is