List of practice Questions

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?

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)

Among 165 examinees in a certain school, the ratio of successful to unsuccessful students is 10: 1. If 5 more students were successful, then what would have been the ratio of successful to unsuccessful students?

Which option will come next in the following figure series?

For a prism of prism angle 𝜃 = 60°, the refractive indices of the left half and the right half are, respectively, 𝑛₁ and 𝑛₂ (𝑛₂ ≥ 𝑛₁) as shown in the figure. The angle of incidence 𝑖 is chosen such that the incident light rays will have minimum deviation if 𝑛₁  = 𝑛₂  = 𝑛 = 1.5. For the case of unequal refractive indices, 𝑛₁  = 𝑛 and 𝑛₂ = 𝑛 +∆𝑛 (where∆𝑛≪𝑛), the angle of emergence \(𝑒 =𝑖+∆𝑒\). Which of the following statement(s) is (are) correct?

Which figure replaces the question mark in the given figure series?

The distance between two stars of masses 3M_S and 6M_S is 9R. Here R is the mean distance between the centres of the Earth and the Sun, and M_S is the mass of the Sun. The two stars orbit around their common centre of mass in circular orbits with period nT, where T is the period of Earth’s revolution around the Sun. The value of n is ___.

In the circuit shown below, the switch $S$ is connected to position $P$ for a long time so that the charge on the capacitor becomes $q _{1}\, \mu C$ Then $S$ is switched to position $Q$ After a long time, the charge on the capacitor is $q _{2}\, \mu C$ 
The magnitude of $q_2$ is ____

In order to measure the internal resistance r₁ of a cell of emf E, a meter bridge of wire resistance R₀ = 50 Ω, a resistance \(\frac{R_0}{2}\), another cell of emf \(\frac{E}{2}\) (internal resistance r) and a galvanometer G are used in a circuit, as shown in the figure. If the null point is found at l = 72 cm, then the value of r ₁ = ____

In the circuit shown below, the switch $S$ is connected to position $P$ for a long time so that the charge on the capacitor becomes $q _{1}\, \mu C$ Then $S$ is switched to position $Q$ After a long time, the charge on the capacitor is $q _{2}\, \mu C$ The magnitude of $q_1$is ____

 

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \,m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $05\, s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 \,m / s ^{2}$. The value of $t$ is ____

A heavy nucleus $Q$ of half-life $20$ minutes undergoes alpha-decay with probability of $60 \%$ and beta-decay with probability of $40 \%$. Initially, the number of $Q$ nuclei is $1000 $. The number of alpha-decay of $Q$ in the first one hour is

An extended object is placed at point O, 10 cm in front of a convex lens L1 and a concave lens L2 is placed 10 cm behind it, as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are 20 cm. The refractive index of both the lenses is 1.5. The total magnification of this lens system is

An ideal gas undergoes a four step cycle as shown in the $P-V$ diagram below During this cycle, heat is absorbed by the gas in

The smallest division on the main scale of a Vernier calipers is $01 \,cm$ Ten divisions of the Vernier scale correspond to nine divisions of the main scale The figure below on the left shows the reading of this calipers with no gap between its two jaws The figure on the right shows the reading with a solid sphere held between the jaws The correct diameter of the sphere is