List of practice Questions

Three friends P, Q and R go for morning walks around a ground. They start out together from the gate in the same direction, but walk at different speeds. R walks half as fast as P. Q walks 1.5 times faster than R. P takes 1 minute to take one round around the ground. If they all stop when R has finished 4 rounds, which of the options must be true?

Which four pieces of a jigsaw puzzle can be combined to form a square?

Which option(s) can be folded to form the cube shown?

A digital clock reads hours and minutes. The sum of the digits it displays at 12:00 is 3 (1+2+0+0). At 12:01 it is 4 (1+2+0+1) and so on. What is the sum of all the digits it displays from 12:00 to 12:59?

A rhombus is inscribed in a rectangle which in turn is inscribed in a circle as shown in the figure below. P is the centre of all three shapes, PQ=QR=5 units. What is the perimeter of the rhombus?

A smaller square of 5 cm is placed inside a bigger square such that all 4 corners of the smaller square are touching the sides of the bigger square. If the smallest distance between the corners of the two squares is 3 cm, what is the area of the bigger square in sq. cm that falls outside smaller one?

Consider the following quote from J C Kumarappa’s Economy of Permanence:
“Man comes nearest to his God, the creator, when he utilizes his brain power to
marshal mechanical forces to serve his purposes. To do so in a way that will bring
blessings and not destruction, he has to follow closely nature’s way to get the best out
of it. We cannot get the co-operation of nature purely on our own terms. Any attempt
to do so will bring violent destruction in its wake.”
Which of the options is/are implied by the quote?

If colour and size differences are not to be counted as unique, how many types of leaves occur only once?

Three circles of radius 10 cm are drawn inside an equilateral triangle as shown below. The area of the red coloured region (in sq. cm., up to two decimal places) in the figure is ____.

When young Moosa started selling dosas on a street corner to support his daughter Lisa’s education, his age was six times that of Lisa’s. He started selling dosas for ₹2 each and he increased its price by ₹1 every year. Lisa grew up to be a successful lawyer and on Moosa’s 60th birthday she gifted him with a small shop near their house, the board of which is seen in the image. In which year Lisa will celebrate her 60th birthday?

Which of the options is/are rotation(s) of the given figure?

A Street has 13 houses in a row as shown in the figure. Some residents in the first house tested positive for COVID-19. The virus spreads in two ways: it can spread to the next house, or jump directly to the third house. Residents of house number 2 can get infection in only one way, the house number 3 in two ways, the house number 4 in 3 ways, the house number 5 in 5 ways and so on. If the virus only progresses from Left to Right direction, in how many ways can the residents of the house number 13 get infected?

Four views of a convex solid are shown. How many surfaces does the solid have?

How many triangles are there in the figure shown?

If each word is written in a single font and normal and bold versions of the same font are not to be counted separately, how many fonts are used in the given set of words?

If you start from the circle and end at the triangle, what is the minimum number of straight lines required to pass through all the dots without retracing any route? You are allowed to pass through a dot more than once.

In the container given below of dimensions (40 cm X 20 cm X 20 cm), four objects are dipped in water. Objects P and Q are made of some light material while objects R and S are made of iron and copper, respectively. The object P is a cube of edge 4 cm with 1/10^th floating above water; object Q displaces 50 cc of water while floating. The volumes of objects R and S are 295.4 cc and 397 cc, respectively. If all the objects are removed from the container, what would be the new water level inside the container measured from the bottom?

The corners of the green and red triangles coincide with the centres of the circles. All the circles have equal diameters and adjacent circles touch each other. If the area of the green triangle is 3.14, what is the area of the red triangle?

The figure shows views of the same solid. Count the number of surfaces.

There are apples and oranges in a basket that can carry a maximum of 50 fruits. Some fruits are rotten and some are good. The number of rotten apples is twice the number of good apples. The number of good oranges is twice the number of rotten oranges. The number of oranges is thrice the number of apples. If there are more than 40 fruits in the basket, what is the total number of apples and oranges?

A cricket team has 10 blue pairs of gloves and 10 white pairs of gloves in a cricket kit. If a batter reaches into the kit and pulls out one glove at a time without looking at it, what is the least number of gloves she must pull out to make sure that she has a pair of gloves of the same colour?

Chinnu was excited about the New Year when she bought a new calendar to keep on her study table. While playing, her baby sister poked a hole through the entire calendar from January through December as seen in the image. If every page had the same 5 week table structure for each month, and if all the consecutive months were printed back to back, which date in the month of April has a hole in it?

Four identical pieces of wood of length 50 cm x 8 cm x 2 cm are arranged as shown in the figure. Another larger square is generated by rotating all the wooden panels along the outer edges and extending the outermost edges till they touch each other. What is the area of this larger square thus constructed?

Let D and E be points on sides AB and AC, respectively, of a triangle ABC, such that AD : BD = 2 : 1 and AE : CE = 2 : 3. If the area of the triangle ADE is 8 sq cm, then the area of the triangle ABC, in sq cm, is

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