## Marks 1

$$\underbrace {{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,{\rm{a}}\,{\rm{ + }}\,.......\,{\rm{ + }}\,{\rm{a}}}_{{\rm{n}}\,{\rm{times}}} = {a^2}b$$ an...

A three-member committee has to be formed from a group of 9 people. How many such
distinct committees can be formed?

For non-negative integers, a, b, c, what would be the value of a + b + c if
$$$\log \,a\, + \,\log \,b\, + \,\log \,c\, = \,0?$$$

Tower A is 90 m tall and tower B is 140 m tall. They are 100 m apart. A horizontal
skywalk connects the floors at 70 m in both the towers. If a taut r...

Hema's age is 5 years more than twice Hari's age. Suresh's age is 13 years less than 10
times Hari's age. If Suresh is 3 times as old as Hema, how old...

The temperature T in a room varies as a function of the outside temperature T0 and the
number of persons in the room p, according to the relation $$T ...

## Marks 2

In manufacturing industries, loss is usually taken to be proportional to the square of the
deviation from a target. If the loss is Rs. 4900 for a devi...

A faulty wall clock is known to gain 15 minutes every 24 hours. It is synchronized to the
correct time at 9 AM on 11th July. What will be the correct ...

The annual average rainfall in a tropical city is 1000 mm. On a particular rainy day
(24-hour period), the cumulative rainfall experienced by the city...

Each of the letters in the figure below represents a unique integer from 1 to 9. The letters
are positioned in the figure such that each of (A+B+C), (...

Given that $${{\log \,P} \over {y - z}} = {{\log \,Q} \over {z - x}} = {{\log \,R} \over {x - y}} = 10$$ for $$x \ne y \ne z$$, what is the value of t...

The price of a wire made of a superalloy material is proportional to the square of its length.
The price of 10 m length of the wire is Rs. 1600. What ...

A fruit seller sold a basket of fruits at 12.5% loss. Had he sold it for Rs. 108 more, he
would have made a 10% gain. What is the loss in Rupees incur...

Which of the following function(s) is an accurate description of the graph for the range(s)
indicated?
$$\eqalign{
& (i)\,\,y = 2x + 4\,for\, -...

Consider a sequence of numbers $${a_1},{a_2},{a_3},....,{a_n}$$ where $${a_n} = {1 \over n} - {1 \over {n + 2}}$$, for each integer
n > 0. What is ...

Each of the letters arranged as below represents a unique integer from 1 to 9. The letters are
positioned in the figure such that (A $$ \times $$ B $$...