List of practice Questions

Several kettles are shown below. What is the total number of usable kettles that are designed to store and pour hot water?

Given below are 8 triangular pieces of a puzzle made from the shape P. What is the three-digit number formed when these pieces are arranged correctly?
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Given below is a drawing on a sheet of paper. Make a cut along the solid arcs and fold the resulting semicircular rings at 90 degrees along the dotted lines. What is the number of raised semicircular rings after following these steps?

A mobile screen has a dimension of 10 cm x 4 cm (height x width). A mobile user is viewing a picture in portrait mode and it occupies the entire screen. The user rotates the screen to landscape mode. After rotation, the height of the picture is now the width of the screen and its width gets reduced proportionally, leaving equal blank spaces on both sides of the picture. What is the area (in square centimeters) of the blank space on the left-hand side of the picture?

What number will replace the question mark?

In the image shown below, PQ = QR = QS = 2 units. Also, QT = TS = QU = UR. The points T and U are the centre points of the semicircles. What is the total area of shaded portions in square units?

What is the number that you get when you divide the difference between the number of triangles and number of circles by the number of rectangles for the image shown below?

Shown below is the front and top views of two cubes. The red and blue cubes are made up of metal and wax respectively. Red cube is heated and is hot enough to melt wax in the blue cube. As shown in the front and top views, the red cube is moved along the path PQRS creating sharp edges and flat surfaces on the blue cube. What is the total number of surfaces the blue cube will have after the red cube reaches the point S?

One of the pots does not belong to the group of pots shown below. What is the number written on that pot?
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What is the number of different patterns on the capsules shown?

How many times does the most used black coloured shape appear in the composition shown below?

The number of values of \(x\) satisfying \[ \tan^{-1}(4x)+\tan^{-1}(6x)=\frac{\pi}{6}, \quad x\in\left[-\frac{1}{2\sqrt{6}},\,\frac{1}{2\sqrt{6}}\right] \] is

The value of \[ \int_{\frac{\pi}{2}}^{\pi} \frac{dx}{[x]+4} \] where \([\,\cdot\,]\) denotes the greatest integer function, is

Let \( A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \) and \( B = \begin{bmatrix} 29 & 49 \\1 & 2 \end{bmatrix} \). If \( (A^5 + B)\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} 0 \\ 0 \end{bmatrix} \), then find \( (x, y) \).

Some species are given: \[ \mathrm{Ni^{2+},\ Fe^{2+},\ Co^{2+},\ V^{3+}\ \text{and}\ Ti^{2+}} \] How many species have magnetic moment (spin-only) less than \(3\) BM?

Given below are two statements: Statement-I: The correct order for radius is \[ \mathrm{Al > Mg> Mg^{2+} > Al^{3+}} \] Statement-II: Atomic size always depends on electronegativity. In the light of the above statements, choose the correct option.

An ideal solenoid is kept with its axis vertical. A current \( I_0 \) is flowing in the solenoid. A charge \( q \) is thrown vertically downward inside the solenoid. The acceleration of the charged particle is:

Two mechanical waves travel on strings of equal length \(L\) and equal tension \(T\). The linear mass densities of the strings are in the ratio \(\dfrac{\mu_1}{\mu_2} = \dfrac{1}{2}\). Find the ratio of time taken for a wave pulse to travel from one end to the other in both strings. (Neglect gravity).

If five men can build a house in 27 days, how long will it take nine men to build the same house, assuming they all work at the same rate?

Ravi has a briefcase with dimensions of two by 1 ½ by 1 ½ feet. He wishes to place several notebooks, each eight by nine by one inch, into the briefcase. What is the largest number of notebooks the briefcase will hold?

In which country did Bauhaus -- the first formal design school -- was established?

When "Rule of thirds" is applied to a picture/image, then in how many parts the picture/image will be divided?