## Marks 1

Given a fair six-faced dice where the faces are labelled '1', '2', '3', '4', '5', and '6', what is the probability of getting a '1' on the first roll ...

How many triangles are present in the given figure?
...

Which of the following options represents the given graph?
...

the digit in the unit's place of the product $$3^{999}\times7^{1000}$$ is __________.

A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the squ...

In a 500 m race, P and Q have speeds in the ratio of 3 : 4. Q starts the race when P has already covered 140 m. What is the distance between P and Q (...

Three bells P, Q and R are rung periodically in a school. P is rung every 20 minutes; Q is rung every 30 minutes and R is rung every 50 minutes. If al...

The figure below shows the front and rear view of a disc, which is shaded with identical patterns. The disc is flipped once with respect to any one of...

There are two identical dice with a single letter on each of the faces. The following six letters : Q, R, S, T, U and V, one on each of the faces. Any...

The price of an item is 10% cheaper in an online store S compared to the price at another online store M. Store S charges Rs.150 for delivery. There a...

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order.
Consider the follo...

An ant is at the bottom-left corner of a grid (point P) as shown below in the figure. It aims to move to the top-right corner of the grid. The ant mov...

The missing number in the given sequence 343, 1331, _______, 4913 is

It takes two hours for a person X to mow the lawn. Y can mow the same lawn in four hours. How long (in
minutes) will it take X and Y, if they work tog...

Functions F(a, b) and G(a, b) are defined as follows:
F(a, b) = (a - b)2 and G(a, b) = |a - b| , where |x| represents the absolute value of x.
What wo...

The three roots of the equation f(x) = 0 are x = {-2, 0, 3}. What are the three values of x
for which f(x -3) = 0?

For what values of k given below is $${{{{\left( {k + 2} \right)}^2}} \over {k - 3}}$$ an integer?

## Marks 2

Given two sets X = {1, 2, 3} and Y = {2, 3, 4}, we construct a set Z of all possible fractions where the numerators
belong to set X and the denominato...

The ratio of the number of boys and girls who participated in an examination is 4 : 3. The total percentage of
candidates who passed the examination i...

How many integers are there between 100 and 1000 all of whose digits are even?

An e-mail password must contain three characters. The password has to contain one
numeral from 0 to 9, one upper case and one lower case character fro...

P, Q, R and S crossed a lake in a boat that can hold a maximum of two persons, with only
one set of oars. The following additional facts are available...

A class of twelve children has two more boys than girls. A group of three children are
randomly picked from this class to accompany the teacher on a f...

A designer uses marbles of four different colours for his designs. The cost of each marble
is the same, irrespective of the colour. The table below sh...