List of practice Questions

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.”
Image P shows an object as seen from the top. Which of the objects given below will appear as shown in image P when viewed from the top? Consider all the objects are made with opaque solids.
Several kettles are shown below. What is the total number of usable kettles that are designed to store and pour hot water?
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?
Find the electric flux through one face of a cube if a charge \(q\) is placed at its center.
Point out the antonym of the word ‘Vague'.
What is the product of the reaction between Benzene and \(CH_3Cl\) in the presence of anhydrous \(AlCl_3\)?
A particle moves with velocity ($v = 3t^2 + 2t$). Find acceleration at ($t = 2$) s. ____.
For a first-order reaction, the unit of rate constant is:
Choose the incorrect pair of stain and its type.
The purpose of opening a Demat Account with a Depository Participant (DP) is :
Calculate the ratio of de Broglie wavelengths of an electron \((\lambda_e)\) and a proton \((\lambda_p)\) moving with the same velocity.