List of practice Questions

If \(A\) is a \(3 \times 3\) matrix such that \( |A| = 5 \), find the value of \( |adj(A)| \).
A bag contains 4 red and 6 black balls. A ball is drawn at random, its colour is noted and it is returned to the bag. Moreover, 2 additional balls of the colour drawn are put in the bag and then a ball is drawn at random. What is the probability that the second ball is red?
An electron falls through a distance 1.5 cm in a uniform electric field of magnitude 2.0 \(\times\) 10\(^4\) N/C from rest. The time taken to cover this distance in second is \textunderscore\textunderscore\textunderscore\textunderscore\textunderscore.
(e = 1.6 \(\times\) 10\(^{-19}\) C, m\(_e\) = 9.11 \(\times\) 10\(^{-31}\) kg)
A company took a loan of ₹10,00,000 at 12% p.a. and offered ₹15,00,000 in 8% Debentures as collateral security. Calculate the finance cost for the year.
If \( S_n = 3n^2 + 5n \) represents the sum of \( n \) terms of an A.P., find the \(10^{th}\) term \( (a_{10}) \).
If \( \omega \) is an imaginary cube root of unity, find the value of \( (1 + \omega - \omega^2)^7 \).
Complete the series: \(285,\,253,\,221,\,189,\, ?\)
A compound is formed by two elements \(X\) and \(Y\). Atoms of \(Y\) make ccp and those of element \(X\) occupy all the octahedral voids. What is the formula of the compound?
Which linkage joins the monosaccharide units in sucrose?
Which of the following electrolytes is most effective in the coagulation of a negative sol like \(As_2S_3\)?
In a common emitter transistor amplifier, the audio signal voltage across the collector resistance of \(2\,k\Omega\) is \(2V\). If the current amplification factor (\(\beta\)) is \(100\) and the base resistance is \(1\,k\Omega\), find the input signal voltage.
A circular coil of radius \(R\) carries a current \(I\). The magnetic field at its centre is \(B\). At what distance from the centre on the axis of the coil will the magnetic field be \(B/8\)?
In an LCR series circuit, the resonance frequency is \( f \). If the capacitance is made 4 times, what will be the new resonance frequency?
Find the integrating factor (I.F.) for the differential equation \[ \frac{dy}{dx} + y\sec x = \tan x . \]
Point out the antonym of the word ‘Vague'.
If ‘ORANGE' is coded as ‘PSBOHF', how is ‘GRAPES' coded?
Which of the following noble gas compounds has a square planar geometry: \(XeF_2\), \(XeF_4\), or \(XeF_6\)?
Identify the monomer units used in the preparation of Nylon-6,6.
A coil has a self-inductance of \(2H\); find the induced EMF if the current changes from \(5A\) to \(2A\) in \(0.1\) seconds.
Find the electric flux through one face of a cube if a charge \(q\) is placed at its center.
Calculate the de Broglie wavelength of an electron accelerated through a potential difference of \(100V\).
Evaluate the integral \( \displaystyle \int \frac{1}{x\log x}\,dx \).
Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.
If \[ \lim_{x\to 0} \frac{e^{(a-1)x}+2\cos bx+(c-2)e^{-x}} {x\cos x-\log_e(1+x)} =2, \] then \(a^2+b^2+c^2\) is equal to
What is the function of diaphragm in human respiratory system ? Where is it present in human body ?