List of practice Questions

The area of the region satisfying the inequalities \(|x|-y≤1,y≥0\) and \(y≤1\) is

A person spent Rs 50000 to purchase a desktop computer and a laptop computer. He sold the desktop at 20% profit and the laptop at 10% loss. If overall he made a 2% profit then the purchase price, in rupees, of the desktop is

How many distinct positive integer-valued solutions exist to the equation \((x^2-7x+11)^{(x^2-13x+42)}=1\)?

If \(y\) is a negative number such that \(2^{y^2log_35 }\)= \(5^{log_23}\), then \(y\) equals

The number of real-valued solutions of the equation \(2^x+2^{-x}=2-(x-2)^2\) is

Two persons are walking beside a railway track at respective speeds of 2 and 4 km per hour in the same direction. A train came from behind them and crossed them in 90 and 100 seconds, respectively. The time, in seconds, taken by the train to cross an electric post is nearest to

If \(log_45=(log_4y)(log_6\sqrt5)\),then \(y\) equals

On a rectangular metal sheet of area 135 sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two-thirds of the painted area then the perimeter of the rectangle in inches is

An alloy is prepared by mixing three metals A, B and C in the proportion 3: 4: 7 by volume. Weights of the same volume of the metals A, B and C are in the ratio 5: 2: 6. In 130 kg of the alloy, the weight, in kg, of the metal C is

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

Which of the given options matches the patterns (1, 2, 3, 4) with tiles (P, Q, R, S) correctly?

Which option will replace the question mark?

A square is cut into 4 pieces. One of the pieces is shown on the left and the remaining three are in the options. Which of the options is NOT a part of the square?

How many distinct motifs appear in the figure on the right? Flips and rotations are to be counted separately, for example the motifs P and Q are distinct.

Three options are made out of the same set of pieces WITHOUT flipping. Which of the options is NOT possible?

Shown below is a paint splatter on a wall surface. A paint squeegee is pulled over it. Which of the options correctly represents the part of the pattern formed?

Which of the options will replace the question mark?

Shown below is a T-shaped image on a transparent sheet of paper. Which of the options is/are made by overlapping and/or rotating multiple copies of the transparent sheet?

There are different types of pineapples in the given figure. How many pineapples appear only once?

Each of the options shows a pair of two different pieces. Which of the options CAN NOT be cut out of the given figure?

Figures 2 and 3 can be derived from figure 1 by overlapping some of the given options one at a time. If flipping and rotations are allowed, which option(s) will allow you to derive figure 2 and 3?

Assume that the English alphabet was redesigned, and the new alphabet had alternating upper case and lower case letters. The alphabet starts with uppercase A, and
1. all upper case letters were rotated clockwise by 90 degrees
2. all lower case letters were rotated anti-clock wise by 90 degrees
Using the new alphabet, the word “HELP” would be written as:

Seven identical playing dice are unfolded in an identical manner. Six of the unfolded dice are laid out on a flat surface and are arranged to touch each other without overlapping. The figure shows a portion of the arrangement. Which face(s) from the seventh unfolded dice CAN NOT replace X if overlap must be avoided?

A sphere, a cylinder and a cone, with equal heights are resting on a surface along a straight line. If the source of light is fixed and the light rays are parallel, which of the options show(s) the shadows correctly?