Recent questions tagged cat2003-1

If the product of $n$ positive real numbers is unity, then their sum is necessarily a multiple of $n$equal to $n+\left(\frac{1}{n}\right)$never less than $n$a positive in...

There are $8436$ steel balls, each with a radius of $1$ centimeter, stacked in a pile, with $1$ ball on top, $3$ balls in second layer, $6$ in the third layer, $10$ in th...

In a triangle $\text{ABC, AB= 6, BC= 8}$ and $\text{AC=10}.$ A perpendicular dropped from $\text{B}$, meets the side $\text{AC}$ at $\text{D}.$ A circles of radius $\text...

A vertical tower $\text{OP}$ stands at the centre $\text{O}$ of a square $\text{ABCD}.$ Let $h$ and $b$ denote the lengths $\text{OP}$ and $\text{AB}$ respectively. Suppo...

In the diagram given below, $\measuredangle \text{ABD} = \measuredangle \text{CDB} = \measuredangle \text{PQD} = 90^{\circ}$. If $\text{AB : CD} = 3:1,$ the ratio of $\t...

How many three digit positive integers, with digits $x, y$ and $z$ in the hundred's, ten's and unit's place respectively, exist such that $x < y, z < y$ and $x \neq 0?$$2...

In the figure below, $\text{ABCDEF}$ is a rectangular hexagon and $\measuredangle \text{AOF} = 90^{\circ}$ is parallel to $\text{ED}.$ What is the ratio of the area of th...

Three horses are grazing within a semi-circular field. In the diagram given below, AB is the diameter of the semi-circular field with center at O. Horses are tied up at P...

Let $a, b, c, d$ be the four integers such that $a +b+c+d =4m+1$ where m is a positive integer. Given $m,$ which one of the following is necessarily true?The minimum poss...

There are two concentric circles such that the area of the outer circle is four times of the area of inner circle. Let A, B and C be the three distinct points on the peri...

Let $p$ and $q$ be the roots of the quadratic equation $x^2 - (a-2) x-a -1 =0.$ What is the minimum possible value of $p^2 + q^2?$$0$$3$$4$$5$

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is $90^{\circ}$ or concanve ...

Choose $1$ if the question can be answered by one of the statements alone but not by the other.Choose $2$ if the question can be answered by using either statement alone....

A positive whole number $\text{M}$ less than $100$ is represented in base $2$ notation, in base $3$ notation, and base $5$ notation. It is found that in all three cases t...

How many even integers $n,$ where $100 \leq n \leq 200$, are divisible neither by $7$ nor by $9?$$40$$37$$39$$38$

The function $f(x) = |x-2| + |2.5-x| + |3.6-x|$, where $x$ is a real number, attains a minimum at$x=2.3$$x=2.5$$x=2.7$None of these

Let $g(x) = \max(5-x, \: x+2)$. The smallest possible value of $g(x)$ is$4.0$$4.5$$1.5$None of these

$27$ persons attend a party. Which one of the following statements can never be true?There is a person in the party who is acquainted with all the $26$ members.Each perso...

A leather factory produces two kinds of bags, standard and deluxe. The profit margin is Rs. $20$ on a standard bag and Rs. $30$ on a deluxe bag. Every bag must be process...

Which one of the following conditions must $p, q,$ and $r$ satisfy so that the following system of linear simultaneous equations has at least one solution, such that $p+...

When the curves, $y=\log_{10} x$ and $y=x^{-1}$ are drawn in the $x-y$ plane, how many times do they intersect for values $x \geq 1?$NeverOnceTwiceMore than twice

New Age Consultants have three consultants Gyani, Medha and Buddhi. The sum of the number of projects handled by Gyani and Buddhi individually is equal to the number of p...

Answer the question on the basis of the information given below:Five friends meet every morning at Sree Sagar restaurant for an idli-vada breakfast. Each consumes a diffe...

Answer the question on the basis of the information given below:Five women decided to go for shopping in MG road, Bangalore. They arrived at the designated meeting place ...

Answer the question on the basis of the information given below:Some children were taking free throws at the basket ball court in the school during lunch break. Below are...

Choose 1 if the question can be answered by one of the statements alone but not by other.Choose 2 if the question can be answered by using either statement alone.Choose 3...

Choose 1 if the question can be answered by one of the statements alone but not by other.Choose 2 if the question can be answered by using either statement alone.Choose 3...

Choose 1 if the question can be answered by one of the statements alone but not by other.Choose 2 if the question can be answered by using either statement alone.Choose 3...

Choose 1 if the question can be answered by one of the statements alone but not by other.Choose 2 if the question can be answered by using either statement alone.Choose 3...

Answer the questions on the basis of the information given below:Seven varsity basketball players (A, B, C, D, E, F and G) are to be honoured at a special luncheon. The p...

Answer the question based in the information given below:Rang Barsey Paint Company (RBPC) is in the business of manufacturing paints. RBPC buys RED, YELLOW, WHITE, ORANGE...