List of practice Questions

A metal wire of length 0.5 m and cross-sectional area 10^–4 m² has breaking stress 5 × 10⁸ Nm^–2. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be _____ ms^–1

When ethanol is heated with conc. H₂SO₄, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer’s reagent, is

Portland cement contains ‘X’ to enhance the setting time. What is ‘X’?

The velocity of a small ball of mass 0.3 g and density 8 g/cc when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g/cc, then the value of viscous force acting on the ball will be x × 10^–4 N. The value of x is _______. [use g = 10 m/s²]

A modulating signal 2sin (6.28 × 10⁶) t is added to the carrier signal 4sin(12.56 × 10⁹) t for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass filter. The bandwidth of the output signal of band pass filter will be ______MHz.

The Hinsberg reagent is

The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is 60 ms^–1. The area of cross-section of the wire is 2.0 mm² and its Young’s modulus is 1.2 × 10¹¹ Nm^–2. The extension of the wire over its natural length due to its tension will be x × 10^–5 m. The value of x is _____.

When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to

Let a line L pass through the point intersection of the lines \(bx + 10y – 8 = 0\) and \(2x - 3y = 0, \quad b \in \mathbb{R} - \left\{\frac{4}{3}\right\}\). If the line L also passes through the point \((1, 1)\) and touches the circle \(17(x^2 + y^2) = 16\), then the eccentricity of the ellipse \(\frac{x^2}{5} + \frac{y^2}{5} = 1\) is

The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes 5√x s. The value of x will be _____.

Two radioactive materials A and B have decay constants 25λ and 16λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be ‘e’ after a time \(\frac{1}{(aλ)}\). The value of a is _____.

If [t] denotes the greatest integer ≤ t, then the value of \(\int\limits_{0}^{1}\)[2x−|\(3x^2\)−5x+2|+1]dx is

A capacitor of capacitance 500 μF is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in the LC circuit will be ______A.

The number of points, where the function $f: \mathbb{R} \to \mathbb{R}$, $$ f(x) = |x - 1|\cos|x - 2|\sin|x - 1| + (x - 3)|x^2 - 5x + 4|, $$ is NOT differentiable, is 

The number of elements in the set S= {x∈R : 2cos⁡\((\frac{x_2+x}{6})\)=\(4^x+4^{-x}\)}

Let S = {1, 2, 3, …, 2022}. Then the probability that a randomly chosen number n from the set S such that HCF (n, 2022) = 1, is

If (2, 3, 9), (5, 2, 1), (1, λ, 8) and (λ, 2, 3) are coplanar, then the product of all possible values of λ is :

The statement (p∧q) ⇒ (p∧r) is equivalent to :

Given below are two statements.
Statement-I: Stannane is an example of a molecular hydride.
Statement-II: Stannane is a planar molecule
In the light of the above statement, choose the most appropriate answer from the options given below.

In liquation process used for tin (Sn), the metal

Let 
\(\begin{array}{l} f\left(x\right)=3^{\left(x^2-2\right)^3+4},x\in \mathbb{R}.\end{array}\)
Then which of the following statements are true? 
P : x = 0 is a point of local minima of f
Q : x = √2 is a point of inflection of f 
R : f ′ is increasing for x > √2

Let \(\vec{a} = 3\hat{i} + \hat{j}\) and \(\vec{b} = \hat{i} + 2\hat{j} + \hat{k}\).
Let \(\vec{c}\) be a vector satisfying \(\vec{a} \times (\vec{b} \times \vec{c}) = \vec{b} + \lambda \vec{c}\)
If \(\vec{b}\) and \(\vec{c}\) are non-parallel, then the value of \(λ\) is