List of practice Questions

A park is shaped like a rhombus and has area 96 sq m. If 40 m of fencing is needed to enclose the park, the cost, in INR, of laying electric wires along its two diagonals, at the rate of ₹125 per m, is

Total capacity of the system of capacitors

The given matchstick figure shows 5 squares, how many minimum number of sticks are required to be moved to achieve 7 squares.

For $x \in R$, the number of real roots of the equation $3 x^{2}-4\left|x^{2}-1\right|+x-1=0$ is ______

A compound gives two fragments in a mass spectrometer. They are C₁₉H₇N⁺ and C₁₉H₅0⁺. To separate peaks due to these fragments the instrument should have a resolution of

a block of mass m slides on the wooden wedge which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is:
[ Given m= 8kg, M=16kg ]
[Assume all the surfaces shown in the figure to be frictionless]

Which of the following pairs has both the ions coloured in aqueous solution? [Atomic numbers of Sc = 21, Ti = 22, Ni = 28, Cu = 29, Mn = 25]

A cooking gas contains carbon and hydrogen only. A volume of 11.2 L of this gas is found to weigh 22 g at STP. Then the molecular formula of the gas is

The radius of a circular plate is 1.05 m. Its area (in $m^2$) up to correct significant figures is

What is the next number in the series given below?
$10, 11, 13, 17, 25, 32, 37, 47, ?$

A sentence is divided into four parts. Choose the part that is/are grammatically incorrect
When $\underline{\text{it became apparent }}$to Clive that not one of the remaining jurors $\underline{\text{were going}}$ to believe his $\underline{\text{client’s}}$ alibi, he began to reconsider the District Attorney’s $\underline{\text{offer}}$ of a plea bargain.

For any two positive rational numbers m and n, a binary operation * is defined by $m*n=\frac{m+n}{3}$, then $\frac{7}{2}*\frac{5}{2}$ is equal to

Let $f: R \rightarrow R$ be defined by $f(x)=\frac{x^{2}-3 x-6}{x^{2}+2 x+4}$. Then which of the following statements is(are) TRUE?

Consider a helium (He) atom that absorbs a photon of wavelength 330 nm. The change in the velocity (in cm s^-1) of the He atom after the photon absorption is_____.
(Assume: Momentum is conserved when the photon is absorbed.
Use: Planck constant = 6.6 × 10^-34 J s, Avogadro number = 6 × 1023 mol^-1, Molar mass of He = 4 g mol^-1)

Ratio of Ashok's age to Pradeep's age is 4 : 3. Ashok will be 26 years old after 6 years. How old is Pradeep now?

Investment of ₹ 4,000 at $R\%$ per annum compounded annually becomes 16,000 in 8 years. If 2,000 is invested at $R\%$ per annum compounded annually, then in how many years will the investment become 16,000?

Choose the correct option to complete the sentence:
This is a birthday gift___my brother.

Six books are placed from left to right on a shelf. History book is neither on extreme left nor on extreme right. English book is to the immediate left of Science book. Geography book has three books to its right side. Between Science and Sociology books, there are exactly two books. Remaining one book is of Arts. How many books are there to the right of History book?

A certain sum of money becomes 13,824 after 3 years and 32,768 after 6 years if the interest is compounded annually. What is the rate of interest per annum?

In three of the given options the first and second number follow the same property. Which is the odd one out?

Choose the correct option to complete the sentence:
My mother does not like to see _ untidy room.

The calculated spin only magnetic moments of $\left[ Cr \left( NH _{3}\right)_{6}\right]^{3+}$ and $\left[ CuF _{6}\right]^{3-}$ in BM, respectively, are
(Atomic number of $Cr$ and $Cu$ are $24$ and $29$ , respectively)