## Marks 1

What is the smallest number with distinct digits whose digits add up to 45?

In a class of 100 students,
(i) there are 30 students who neither like romantic movies nor comedy movies,
(ii) the number of students who like romanti...

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

A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs. 1000 more than S, what is the sh...

A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11...

The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of...

Consider the following inequalities.
(i) 2x $$-$$ 1 > 7
(ii) 2x $$-$$ 9
Which one of the following expressions below satisfies the above two inequali...

Four points P(0, 1), Q(0, $$-$$3), R($$-$$2, $$-$$1), and S(2, $$-$$1) represent the vertices of a quadrilateral. What is the area enclosed by the qua...

Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following op...

p and q are positive integers and $${p \over q} + {q \over p} = 3$$, then $${{{p^2}} \over {{q^2}}} + {{{q^2}} \over {{p^2}}}$$ =

The current population of a city is 11,02,500. If it has been increasing at the rate of 5% per annum, what was its population 2 yeas ago?

Five different books (P, Q, R, S, T) are to be arranged on a shelf. The books R and S are to be arranged
first and second respectively from right side...

It would take one machine 4 hours to complete a production order and another machine 2 hours to
complete the same order. If both machine work simultan...

If the number 715 ■ 423 is divisible by 3 (■ denotes the missing digit in the thousandths place), then the
smallest whole number in the place of ■ is ...

A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top
of the post casts her shadow. The length of ...

What is the value of $$1 + {1 \over 4} + {1 \over {16}} + {1 \over {64}} + {1 \over {256}} + ......$$?

A rule states that in order to drink beer one must be over 18 years old. In a bar, there are 4
people. P is 16 years old, Q is 25 years old, R is drin...

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics.
Registration records indicate course enrolment as follows: Che...

Fatima starts from point P, goes North for 3 km, and then East for 4 km to reach point Q. She
then turns to face point P and goes 15 km in that direct...

In the summer, water consumption is known to decrease overall by 25%. A water Board
official states that in the summer household consumption decreases...

40% of deaths on city roads may be attributed to drunken driving. The number of degrees
needed to represent this as a slice of a pie chart is

Some tables are shelves. Some shelves are chairs. All chairs are benches. Which of the
following conclusions can be deduced from the preceding sentenc...

The number that least fits this set: (324, 441, 97 and 64) is ________.

It takes 10 s and 15 s, respectively, for two trains traveling at different constant speeds to completely pass
a telegraph post. The length of the fir...

Given (9 inches)1/2 = (0.25 yards)1/2, which one of the following statements is TRUE?

S, M, E and F are working in shifts in a team to finish a project. M works with twice the
efficiency of others but for half as many days as E worked. ...

In a huge pile of apples and oranges, both ripe and unripe mixed together, 15% are unripe
fruits. Of the unripe fruits, 45% are apples. Of the ripe on...

Michael lives 10 km away from where I live. Ahmed lives 5 km away and Susan lives 7 km
away from where I live. Arun is farther away than Ahmed but clo...

If x>y>1, which of the following must be true?
$$$\begin{array}{l}\mathrm i.\;\ln\left(\mathrm x\right)>\ln\left(\mathrm y\right)\;\;\;\;\;\;...

Find the missing sequence in the letter series below:
A, CD, GHI, ? , UVWXY

Ram and Ramesh appeared in an interview for two vacancies in the same department. The
probability of Ram’s selection is 1/6 and that of Ramesh is 1/8....

If $$\log_x\left(\frac57\right)=\frac{-1}3$$, then the value of x is

Operators $$\square$$,◊,$$\rightarrow$$ are defined by : a $$\square$$ b = $$\frac{a-b}{a+b}$$; a ◊ b = $$\frac{a+b}{a-b}$$; a $$\rightarrow$$ b = ab....

In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was
41ºC and of Tuesday to Thursday was 43ºC. If the temperature on T...

If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =

There are two candidates P and Q in an election. During the campaign, 40% of
the voters promised to vote for P, and rest for Q. However, on the day of...

25 persons are in a room. 15 of them play hockey, 17 of them play football and 10
of them play both hockey and football. Then the number of persons pl...

## Marks 2

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

Out of 100 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities ...

A 100 cm $$\times$$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually,...

Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.The ratio of the area of the regular co...

Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut tr...

The number of minutes spent by two students, X and Y, excercising every day in a given week are shown in the bar chart above.The number of days in the...

Two design consultants, P and Q, started working from 8 AM for a client. The client budgeted a total of
USD 3000 for the consultants. P stopped workin...

The bar graph in Panel (a) shows the proportion of male and female illiterates in 2001 and 2011. The
proportions of males and females in 2001 and 2011...

Five people P, Q, R, S and T work in a bank. P and Q don’t like each other but have to share an office till
T gets a promotion and moves to the big of...

Two alloys A and B contain gold and copper in the ratios of 2 : 3 and 3 : 7 by mass, respectively. Equal
masses of alloys A and B are melted to make a...

Leila aspires to buy a car worth Rs. 10,00,000 after 5 years. What is the minimum amount
in Rupees that she should deposit now in a bank which offers ...

A cab was involved in a hit and run accident at night. You are given the following data about the cabs in
the city and the accident.
(i) 85% of cabs i...

Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y married and have two children
P and Q, Z is grandfather of the daughter ‘S’ o...

The number of 3 digit numbers such that the digit 1 is never to the immediate right of 2 is

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to
build the same bridge. How many men will be needed to...

A contour line joins locations having the same height above the mean sea level. The following is a contour
plot of a geographical region. Contour line...

S, T, U, V, W, X, Y and Z are seated around a circular table. T's neighbors are Y and V. Z is seated third
to the left of T and second to the right of...

There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we
choose so that every subgroup has at least one India...

Trucks (10 m long) and cars (5 m long) go on a single lane bridge. There must be a gap of at least 20 m
after each truck and a gap of at least 15 m af...

A contour line joins locations having the same height above the mean sea level. The following is a contour
plot of a geographical region. Contour line...

For submitting tax returns, all resident males with annual income below Rs 10 lakh should fill
up Form P and all resident females with income below Rs...

Find the odd one from the following group:
W,E,K,O I,Q,W,A F,N,T,X N,V,B,D

A train that is 280 meters long, traveling at a uniform speed, crosses a platform in 60 seconds
and passes a man standing on the platform in 20 second...

The exports and imports (in crores of Rs.) of a country from 2000 to 2007 are given in the
following bar chart. If the trade deficit is defined as exc...

You are given three coins: one has heads on both faces, the second has tails on both faces,
and the third has a head on one face and a tail on the oth...

The set of values of p for which the roots of the equation 3x2 + 2x + p(p - 1) = 0 are of
opposite sign is

Find the sum to n terms of the series 10 + 84 + 734 +.........

A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the
third quarter. The average speed of the car in km per ...

What is the chance that a leap year, selected at random, will contain 53 Sundays?

Raju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number o...

A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a
condition that whoever arrives first will not wait for the o...

The data given in the following table summarizes the monthly budget of an average household.
The approximate percentage of the monthly budget NOT spe...

There are eight bags of rice looking alike, seven of which have equal weight and one is slightly
heavier. The weighing balance is of unlimited capacit...

One of the legacies of the Roman legions was discipline. In the legions, military law prevailed
and discipline was brutal. Discipline on the battlefie...

Three friends, R, S and T shared toffee from a bowl. R took 1/3rd of the toffees,
but returned four to the bowl. S took 1/4rd of what was left but ret...

Given that f(y) = |y| / y, and q is any non-zero real number, the value of
| f(q) - f(-q) | is

The sum of n terms of the series 4 + 44 + 444 +.... is

The horse has played a little known but very important role in the field of
medicine. Horses were injected with toxins of diseases until their blood b...

The fuel consumed by a motorcycle during a journey while traveling at various
speeds is indicated in the graph below.
The distances covered during f...

Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters). All
were born on 1st January. The age difference between any two...

If 137+276=435 how much is 731+672?

5 skilled workers can build a wall in 20 days; 8 semi-skilled workers can build a wall
in 25 days; 10 unskilled workers can build a wall in 30 days. I...

Given digits 2,2,3,3,3,4,4,4,4 how many distinct 4 digit numbers greater than
3000 can be formed?

Modern warfare has changed from large scale clashes of armies to suppression of
civilian populations. Chemical agents that do their work silently appe...