List of practice Questions

A board game and two views of a unique dice are shown below. This unique dice has only three faces with numbers one, two, and three. Consider all the ladders as advantages that allow the player to jump from initial to final point. What is the minimum number of dice throws that is required to move from Point A to Point B using all given advantages on the board?

A coloured sheet is folded into an octahedron as shown on the left. Which of the options show(s) the \textbf{CORRECT rotated views of the octahedron?}

Which option(s) is/are \textbf{NOT a part of the image on the left?}

Four objects that are symmetrical along vertical planes are placed in four containers in the orientation shown below. Molten wax is poured in each of these containers up to the level indicated on the objects. Assuming that wax does not stick to the objects, which of the objects will leave its \textbf{exact negative impression on the set wax when they are vertically lifted?}

Shown below is an ice-cream cone completely filled with ice-cream. Assume the top portion (visible portion of ice-cream) is a perfect hemisphere. What is the total mass of the ice-cream in grams? The density of ice-cream is \(0.9\) grams/cubic centimeter. Consider the value of \( \pi = 3.14 \).

A square paper of side \(10\) cm is folded sequentially and a circular cut of radius \(1\) cm is made at the corners as shown below. After unfolding the sheet completely, what will be the total area of all the pieces which have been cut-out from the original square sheet? Assume the value of \( \pi = 3.14 \).

How many unique patterns are there in the image shown below?

How many spheres are rotating in the space shown below? \quad [This question contains an animated GIF image.]

Nine tiles containing parts of English letters in different text fonts are shown below. What is the maximum number of \textbf{COMPLETE letters that can be formed by rearranging the tiles in a \(3 \times 3\) grid?}

A plane passes through three vertices of a cube and divides the cube into two parts, a green part and a blue part, and they remain together, as shown below. Eight such cubes are assembled to create a larger cube, where the blue portion is on the inside as shown on the right. Calculate the volume of the blue part in the larger cube, if the edge of the original cube is \(1\) cm.

Five geometric blocks with their dimensions are given below. Calculate the length of the path as shown in the image below, between points A and B.

If \( f(3) = 18, f'(3) = 0 \) and \( f''(3) = 4 \), then the value of \[ \lim_{x \to 3} \ln \left( \frac{f(x+2)}{f(3)} \right)^{\frac{18}{(x-3)^3}} \] is equal to

Ph-CH=CH$_2 \xrightarrow[\text{(PhCOO)}_2]{\text{HBr}}$ Product.
Correct statement(s) regarding product :
(a) Ph-CH(Br)-CH$_3$ is minor product
(b) Benzene is also form a bi product
(c) Reaction follow free radical mechanism
(d) In absence of peroxide carbocation mechanism is followed

5.8 g of Aniline is converted into benzanilide with some reaction sequences. Calculate the mass of benzanilide formed, if percentage yield of reaction is 82%. \[ \text{Ph} - \text{COCl} + \text{PhNH}_2 \xrightarrow{\text{Py}} \text{Benzanilide} \]

A capacitor of capacitance 10 μF is connected with a battery of emf 6V. Now the battery is disconnected and another uncharged capacitor of capacitance 20 μF is connected to the capacitor. Find the charge on the 20 μF capacitor.

Find the percentage change in height risen by liquid if density of fluid, radius of capillary, and surface tension of liquid are decreased by 1%. Assume contact angle doesn’t change and capillary is of sufficient length.

Statement-1: Kinetic energy of system = \( \frac{1}{2} m_1 v_1^2 + \frac{1}{2} m_2 v_2^2 + \dots + \frac{1}{2} m_n v_n^2 \) Statement-2: Kinetic energy of system = Kinetic energy of center of mass + kinetic energy with respect to center of mass.

In hydrogen type atom, shortest wavelength in Lyman series is given as 91 nm. Then the longest wavelength in Paschen series of this atom shall be

If the string connecting \( m \) and the ground is cut, find the speed with which the \( 2m \) block hits the ground as shown. \( g = 10 \, \text{m/s}^2 \)

Choose the correct graph between time period \( T \) and length of pendulum \( l \).

For the given arrangement of charges, find the strength of electric field \( E \) and potential \( V \) at the geometrical center \( O \).

Which of the following is/are true for YDSE experiment?

Three identical liquid drops, each carrying the same charge, coalesce to form a single drop. The ratio of the potential of the large drop and the smaller drop is \( 3^{1/3} \). Then, \( N \) is:

An alkene on reductive ozonolysis gives methanal as one of the products. Its structure is: