List of practice Questions

It XY = 5:7, XZ 3:8 and W:Y4:9 then what is X: W?

The product of two numbers is 91 and their arithmetic mean is 10, then the two numbers are

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 ______

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

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?

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 ____