List of practice Questions

Satyagraha was
Who improved the steam engine?
The ideologies of nationalism and liberalism were a product of
The French Revolution pioneered and popularised the following principles:
For the first order thermal decomposition reaction, following data was obtained : Calculate rate constant.
[Given : log 3 = 0.48]
Glycosidic linkage.
Invert sugar.

Define the term:  Anomers. 
 

Nucleophilic addition of ammonia and its derivatives does not occur with carbonyl group in strongly acidic medium.
Alpha (\(\alpha\)) hydrogens of aldehydes and ketones are acidic in nature.

Give reason of the following
Carboxylic acids have higher boiling point than alcohols of comparable molecular masses. 
 

Write the reaction involved in Friedel-Crafts acylation of anisole.
Write the reaction involved in Kolbe’s reaction.
A lift is going up to the \(10^{\text{th}}\) floor. Number of ways in which \(3\) people can exit the lift at {three different floors, if the lift will not stop at I$^{\text{st}}$, II$^{\text{nd}}$ and III$^{\text{rd}}$ floors, is: }
Let \(\triangle ABC\) such that \(A(0,0)\) and vertices \(B\) and \(C\) lie on the parabola \[ y^2=8x. \] If \(\left(\frac{7}{3},\frac{4}{3}\right)\) is the centroid of \(\triangle ABC\), then \((BC)^2\) is equal to:
Let \(m\) and \(n\) be non–negative integers such that for \[ x\in\left(-\frac{\pi}{2},\frac{\pi}{2}\right),\qquad \tan x+\sin x=m,\quad \tan x-\sin x=n. \] Then the possible ordered pair \((m,n)\) is:
Let \(A=[a_{ij}]\), \(\det(A)\neq 0\), and \(B=[b_{ij}]\) be two \(3\times 3\) matrices. If \[ b_{ij}=3^{\,i-j}\,a_{ij}\quad \text{for all } i,j=1,2,3, \] then:
If \[ a_n=(2n^2-n+2)(n!) , \] then \[ \sum_{n=1}^{20} a_n \] is equal to:
Let \(\alpha\) and \(\beta\) be the roots of the equation \[ 2x^2-5x-1=0. \] For \(n\in\mathbb{N}\), let \[ P_n=\alpha^n+\beta^n. \] Then the value of \[ \frac{2P_{11}\,(2P_{10}-5P_9)}{P_8\,(5P_{10}+P_9)} \] is equal to:
Let \(X\) have a binomial distribution \(B(6,p)\). If the sum of the mean and the variance of \(X\) is \(\dfrac{21}{8}\), then \[ \frac{P(2\le X<4)}{P(4<X<6)} \] is equal to:
Let \( \overrightarrow{AB} = 2\hat{i} + 4\hat{j} - 5\hat{k} \) and \( \overrightarrow{AD} = \hat{i} + 2\hat{j} + \lambda \hat{k} \), \( \lambda \in \mathbb{R} \). Let the projection of the vector \( \vec{v} = \hat{i} + \hat{j} + \hat{k} \) on the diagonal \( \overrightarrow{AC} \) of the parallelogram \( ABCD \) be of length one unit. If \( \alpha, \beta \), where \( \alpha>\beta \), be the roots of the equation \( \lambda^2 x^2 - 6\lambda x + 5 = 0 \), then \( 2\alpha - \beta \) is equal to
The common difference of the A.P.: \( a_1, a_2, \ldots, a_m \) is 13 more than the common difference of the A.P.: \( b_1, b_2, \ldots, b_n \). If \( b_{31} = -277 \), \( b_{43} = -385 \) and \( a_{78} = 327 \), then \( a_1 \) is equal to:
Let \( f(x) = \begin{cases} \frac{ax^2 + 2ax + 3}{4x^2 + 4x - 3}, & x \neq -\frac{3}{2}, \frac{1}{2} \\ b, & x = -\frac{3}{2}, \frac{1}{2} \end{cases} \) be continuous at \( x = -\frac{3}{2} \). If \( f(x) = \frac{7}{5} \), then \( x \) is equal to :
Let the domain of \( f(x) = \log_3 \log_3 \log_7 (9x - x^2 - 13) \) be (m, n). Let the hyperbola \( \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \) have eccentricity \( \frac{n}{3} \) and latus rectum \( \frac{8m}{3} \). Then \( b^2 - a^2 \) is equal to :
Let $z$ be the complex number satisfying $|z - 5| \le 3$ and having maximum positive principal argument. Then $34 \left| \frac{5z - 12}{5iz + 16} \right|^2$ is equal to :