List of practice Questions

Given below are two statements:
Statement I: C–Cl bond is stronger in $\mathrm{CH_2 = CH{-}Cl}$ than in $\mathrm{CH_3{-}CH_2{-}Cl}$.
Statement II: The given optically active molecule, on hydrolysis, gives a solution that can rotate the plane polarized light.
In the light of the above statements, choose the correct answer from the options given below:
Given below are two statements :
Statement I : Presence of large number of unpaired electrons in transition metal atoms results in higher enthalpies of their atomisation.
Statement II : $d_{xy} = d_{xz} = d_{yz} < d_{x^2 - y^2} = d_{z^2}$ and $d_{x^2 - y^2} = d_{z^2} = d_{xy} <d_{xz} = d_{yz}$ are the d-orbital splittings in $[Fe(H_2O)_6]^{3+}$ and $[Ni(Cl)_4]^{2-}$ complex ions respectively.
In the light of the above statements, choose the correct answer from the options given below :
If two lines drawn from a point $P(2,3)$ intersect the line $x+y=6$ at a distance $\sqrt{\dfrac{2}{3}}$, then the angle between the lines is
Correct order of acidic strength: (I) Phenol, (II) p-Cresol, (III) m-Nitrophenol, (IV) p-Nitrophenol
$K_2Cr_2O_7 + KI \xrightarrow{H^+} I_2 + Cr^{3+}$
Statement-I : Size of $O^{2-}$ is smaller than $F^-$.
Statement-II: Second ionization energy of $\text{Na}$ is greater than second ionization energy of $\text{Mg}$.
A capacitor of \(10\,\mu F\) is charged to \(50\,V\). Calculate the energy stored in the capacitor.
The sum of the first \(10\) terms of an A.P. is \(150\). If the first term is \(10\), what is the common difference?
Find the distance between the planes \(2x + 3y + 4z = 4\) and \(4x + 6y + 8z = 12\).
In a Young's Double Slit Experiment, if the distance between the slits is halved and the distance to the screen is doubled, what happens to the fringe width?
Five geometric blocks with their dimensions are given below. Calculate the length of the path as shown in the image below, between points A and B.
Ravi has a briefcase with dimensions of two by 1 ½ by 1 ½ feet. He wishes to place several notebooks, each eight by nine by one inch, into the briefcase. What is the largest number of notebooks the briefcase will hold?
Choose the correct synonym for “Diligent.”
Find the distance of the point \( (1,-2,3) \) from the \(yz\)-plane.
Which one of the following matrices can be obtained by performing elementary row transformations on the \(3\times3\) identity matrix?
The equation \(x^2 - Ky^2 - 4x + 6y - 5 = 0\) represents a pair of straight lines. Find the point of intersection.
If \(A, B, C\) are vertices of a triangle with position vectors \(\vec{a}, \vec{b}, \vec{c}\) respectively, then find the position vector of the point \(D\) where the angle bisector from vertex \(A\) meets \(BC\).
In an LCR series circuit, the resonance frequency is \( f \). If the capacitance is made 4 times, what will be the new resonance frequency?
A proton \((q = 1.6 \times 10^{-19}\,C)\) enters a magnetic field of \(2\,T\) with a velocity of \(3 \times 10^6\,\text{m/s}\) perpendicular to the field. Find the magnetic force acting on the proton.
If ‘ORANGE' is coded as ‘PSBOHF', how is ‘GRAPES' coded?
Complete the series: \(285,\,253,\,221,\,189,\, ?\)
Evaluate the integral \[ \int_{0}^{\pi/2} \frac{\sin x}{\sin x + \cos x}\,dx. \]
If \( z = \frac{3i}{2} \), what is the value of \( \arg(z) \)?
Which of the following electrolytes is most effective in the coagulation of a negative sol like \(As_2S_3\)?
Fact 1: A town is hosting a 3-day music festival, which will feature a rock band show by local artists for the very first time.
Fact 2: 2000 tickets have been sold for the show.
Fact 3: The ticket sale will end next Monday.
Fact 4: The organizing committee has been working for the past 10 weeks to organize this event.
If the above statements are facts, which of the statements below must also be facts?
I. A few hundred seats will remain empty during the festival.
II. The family members of the rock band performers will be present at the festival.
III. Since the preparation started 10 weeks ago, all tickets will be sold by Monday.
The increasing use of artificial intelligence in various industries has led to concerns about job displacement and economic inequality. AI-powered automation can perform tasks more efficiently and accurately than humans, potentially leading to job losses in many sectors.
Courses of Action:
I. Governments should invest in education and training programs to equip the workforce with the skills needed to thrive in an AI-driven economy.
II. Companies should be mandated to provide retraining and reskilling opportunities to employees whose jobs are affected by automation.
III. A universal basic income should be implemented to provide financial security to those who lose their jobs due to automation.
Which of the following is the most appropriate course of action?