List of practice Questions

Name the phenomenon that proves the transverse nature of light.

In which specific year did the People's Republic of China officially conclude multilateral negotiations and gain entry into the World Trade Organization (WTO)?

The term used for species in which the last individual has died or is not recorded is

A charged particle moves in a magnetic field \(B\) with velocity components both along and perpendicular to \(B\). What is its path?

Assertion (A): Urbanization leads to growth of secondary relationships.
Reason (R): Urban life is generally more formal and impersonal.

Given \(\int_1^a (2x + 1) \, dx = 5\), find the sum of all values of \(a\).

If \( \tan^{-1}x + \tan^{-1}y = \frac{\pi}{4} \), then what is the value of \(x + y + xy\)?

Which transition element among the following shows the highest number of oxidation states?

The worst case time complexity of finding an element using linear search is ______.

If the current in a coil changes from \(2A\) to \(4A\) in \(0.1\,s\), inducing an EMF of \(20V\), find the self-inductance.

Complete the series: \(3, 7, 15, 31, 63, \ldots\)

Which group contains the most electronegative elements in the periodic table?

Match commissions/societies with their year of establishment :

Find \(x\): \(4(x - 2) = 3(x + 5)\).

Find the missing number in the series: \(2,\,6,\,12,\,20,\,30,\,?\)

Which of the following noble gas compounds has a square planar geometry: \(XeF_2\), \(XeF_4\), or \(XeF_6\)?

Let \[ \alpha= \left(1-2\cos\frac{\pi}{11}\right) \left(1-2\cos\frac{3\pi}{11}\right) \left(1-2\cos\frac{9\pi}{11}\right) \left(1-2\cos\frac{27\pi}{11}\right) \left(1-2\cos\frac{81\pi}{11}\right) \] Then the value of \[ 5-\alpha^2 \] is ________.

Two cylinders, both fitted with frictionless pistons, are filled with mixtures of He and Ar gases. In the first cylinder, the masses of He and Ar are \(m_1\) and \(m_2\), respectively. In the second cylinder, the masses of He and Ar are \(m_2\) and \(m_1\), respectively. The molar mass of Ar is \(10\) times the molar mass of He. The external pressure applied by the piston on the first cylinder needs to be \(5\) times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming He and Ar behave like ideal gases, the value of \(\left(\dfrac{m_1}{m_2}\right)\) is ____.

A nuclear reactor starts producing a radioactive nuclide $X$ from $t = 0$, at a constant rate of $\alpha$ per second. Each decay of $X$ produces energy $E_0$, which is utilized to heat a liquid of mass $m$ and specific heat $s$. Assuming no heat loss from the liquid and taking $\lambda$ as the decay constant of $X$, the rate of increase in the temperature of the liquid is:

Let \(P\) be the plane such that it contains the straight line \[ \frac{x-1}{2}=\frac{y-3}{3}=\frac{z+2}{1} \] and is perpendicular to the plane \[ x+2y+3z=4 \] Let \(P_1\) be the plane which passes through the point \((4,2,2)\) and is parallel to \(P\). Then which of the following statements is (are) TRUE?

Statement I: The structure of Maltose is given below: Maltose is a non-reducing sugar.

Statement II: The structure of Lactose is given below: Lactose is a reducing sugar.

In the light of the above statements, choose the correct answer:

'The team ______ more than 300 runs in 20 overs ___________ rains. However, some players needed to improve their batting skills.'
Choose the option with the correct sequence of words to fill the blanks.

If a positive real \(x\) satisfies the following equation
\[ \log_2 x + \log_{\sqrt{2}} x = 48, \]
then the value of \(x\) is _________________