List of practice Questions

A building designed by the famous Indian architect Raj Rewal was demolished in the year 2017, after much controversy. \textit{Identify the building from the given options.}
Which of the following graphics represents the United Nations’ ‘Sustainable Development Goal 3 (SDG 3): Good Health and Well-being’?
United Nations’ ‘Sustainable Development Goal 3
A hemispherical vessel of radius 30 cm is full of mixture to prepare kulfis. Kulfi-moulds are right circular cones of 5 cm diameter at base, having a height of 10 cm. Maximum how many kulfis can be prepared by filling the moulds up to the brim?
You overheard a conversation between X and Y in a building. The conversations were as follows: \begin{quote} X: I am a part of a window and can be appreciated from outside.
Y: Well, I might be invisible, but I carry the building load.
X: While I ensure light inside the room, I am not affected by the weather.
Y: I am not exposed to the weather, and people take advantage of my strength, which you don’t have much. \end{quote} Identify X and Y from the options given below.
With respect to 'Green Buildings', consider the following statements and select the appropriate option.
Let \( \vec{a} = \hat{i} - \hat{j} \), \( \vec{b} = \hat{j} - \hat{k} \), and \( \vec{c} = \hat{k} - \hat{i} \), then the value of \( \vec{b} \cdot (\vec{a} + \vec{c}) \) is:
Let \( \mathbf{u}, \mathbf{v}, \mathbf{w} \) be vectors such that \( \mathbf{u} + \mathbf{v} + \mathbf{w} = \mathbf{0} \). If \( |\mathbf{u}| = 3 \), \( |\mathbf{v}| = 4 \), and \( |\mathbf{w}| = 5 \), then \( \mathbf{u} \cdot \mathbf{v} + \mathbf{w} \cdot \mathbf{u} \) is:
If a vector makes angles \( \frac{\pi}{3}, \frac{\pi}{4} \) and \( \gamma \) with \( \hat{i}, \hat{j} \), and \( \hat{k} \), respectively, where \( \gamma \in \left( \frac{\pi}{2}, \pi \right) \), then the angle \( \gamma \) is:
Evaluate \( \cos \left( \cot^{-1} \left( \frac{7}{24} \right) \right) \):
If \( 3 \sin \theta + 5 \cos \theta = 5 \), then the value of \( 5 \sin \theta - 3 \cos \theta \) is:
The value of \( \tan \left[ \tan^{-1} \left( \frac{3}{4} \right) + \tan^{-1} \left( \frac{2}{3} \right) \right] \) is:
If \( \alpha = \tan^2 x + \cot^2 x \), where \( x \in \left( 0, \frac{\pi}{2} \right) \), then \( \alpha \) lies in the interval:
The domain of the function \( f(x) = \frac{\sin^{-1} \left( x-3 \right)}{\sqrt{9 - x^2}} \) is:
If \( \sin \theta = \frac{b}{a} \), then \( \frac{\sqrt{a+b}} {\sqrt{a-b}} + \frac{\sqrt{a-b}} {\sqrt{a+b}} \) is equal to:
If \( \frac{\sec^2 15^\circ - 1}{\sec^2 15^\circ} \) equals:
Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
If the determinant of the matrix \( \begin{bmatrix} |x| & 1 & 2 \\ 4 & 1 & x \\ 1 & -1 & 3 \end{bmatrix} \) equals -10, then the values of \( x \) are:
The magnetic field at the centre of a circular coil having a single turn of the wire carrying current \( I \) is \( B \). The magnetic field at the centre of the same coil with 4 turns carrying the same current is:
A current carrying square loop is suspended in a uniform magnetic field acting in the plane of the loop. If \( \vec{F} \) is the force acting on one arm of the loop, then the net force acting on the remaining three arms of the loop is:
In an LCR circuit, at resonance, the value of the power factor is:
An electromagnetic wave is propagating in a medium with velocity \( \vec{v} = v \hat{i} \). The instantaneous oscillating magnetic field of this electromagnetic wave is along positive \( z \)-direction. Then the direction of the oscillating electric field is in the:
Focal length of a convex lens of refractive index 1.5 is 3 cm. When the lens is immersed in water of refractive index \( \frac{4}{3} \), its focal length will be:
A narrow single slit of width \( d \) is illuminated by white light. If the first minimum for violet light (\( \lambda = 4500 \, {Å} \)) falls at \( \theta = 30^\circ \), the width of the slit \( d \) in microns is (1 micron = \( 10^{-6} \) m):
Threshold frequency for photoelectric effect from a metallic surface corresponds to a wavelength of 6000 \({Å}\). The photoelectric work function for the metal is \( h = 6.6 \times 10^{-34} \, {Js} \):
Bohr atom model is invalid for: