List of practice Questions

$PQ$ is a chord of length $4\ \text{cm}$ of a circle of radius $2.5\ \text{cm}$. The tangents at $P$ and $Q$ intersect at a point $T$. Find the length of $TP$.
 

Find the angle between the pair of lines:
\( \vec{r} = 3\hat{i} + \hat{j} - 2\hat{k} + \lambda(\hat{i} - \hat{j} - 2\hat{k}) \) and
\( \vec{r} = 2\hat{i} - \hat{j} - 56\hat{k} + \mu(3\hat{i} - 5\hat{j} - 4\hat{k}) \).
Why is ethyl alcohol not dried by anhydrous CaCl2?
The terms of Micro Economics and Macro Economics were coined by Norwegian Economist .................
If DE : BC = 3 : 5, then find A(\(\triangle\)ADE) : A(\(\square\)DBCE).

Courage : Bravery :: Yearning : 
Select the most appropriate option to complete the analogy.

Which one of the following options gives the correct temperature condition and the mixture of the gaseous components that were used by S.L. Miller in 1953 to prove abiogenesis of life?
A charge \( q \) enters with speed \( v \) in the direction of magnetic field \( B \). The force on the charge in magnetic field will be:
Consider a volume V enclosed by a closed surface S having unit surface normal \(\hat{n}\). For \(\mathbf{r} = x\hat{i} + y\hat{j} + z\hat{k}\), the value of the surface integral \(\frac{1}{9} \oint_{S} \mathbf{r} \cdot \hat{n} \,dS\) is
The angle between polarization plane and direction of propagation of electromagnetic waves is :
Which of the following is obtained by Wolff Kishner reduction?
The co-ordination number of Cu in [Cu(CN)$_4$]$^{3-$ ion is:}

In the given figure, \( PQ \) and \( PR \) are tangents to the circle such that \( PQ = 7 \, \text{cm} \) and \( \angle RPQ = 60^\circ \).

The length of chord QR is: 
 

The wavelength of a photon emitted during a transition from \( n = 3 \) to \( n = 2 \) state in the H atom is .............. nm. (answer in integer).
From the word ARRANGEMENT, how many distinct 9-letter words can be formed?
The sum of the following infinite series is: \[ 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \dots \]
Resistance of an ideal p-n junction diode in reverse bias is:
Indian Civilization and Culture

Mantri Mandir -- Where is it located?

Prove that \(\int_{\pi/6}^{\pi/3} \frac{dx}{1+\sqrt{\tan x}} = \frac{\pi}{12}\).
The domain and range of a real valued function \( f(x) = \cos (x-3) \) are respectively.
The safety device used to arrest forward runaway tubs in rope haulage is
Identify ‘A’ and ‘B’ in the following reaction and rewrite the complete reaction : \[ \text{CH}_3\text{-CH=CH}_2 \xrightarrow[\text{Peroxide}]{\text{HBr}} \text{A} \xrightarrow[\text{-KBr}]{\text{alcoholic KCN}} \text{B} \]
If \( A = \begin{bmatrix} 0 & -\tan{\frac{\alpha}{2}} \\[4pt] \tan{\frac{\alpha}{2}} & 0 \end{bmatrix} \), then prove that \[ (I + A) = (I - A)\begin{bmatrix} \cos{\alpha} & -\sin{\alpha} \\[4pt] \sin{\alpha} & \cos{\alpha} \end{bmatrix}. \]
Combine any one of the following as directed (synthesis):
(i) This mango is sweet. That mango is sweet. Only one mango of them is sweet. (Compound Sentence)