Numerical Ability · General Aptitude · GATE CE

A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the p...

If the sum of the first 20 consecutive positive odd numbers is divided by $20^2$, the result is

The ratio of the number of girls to boys in class VIII is the same as the ratio of the number of boys to girls in class IX. The total number of studen...

In a locality, the houses are numbered in the following way:The house-numbers on one side of a road are consecutive odd integers starting from 301, wh...

For positive integers $p$ and $q$, with $\frac{p}{q} \neq 1$, $\left(\frac{p}{q}\right)^\frac{p}{q}= p^{\left(\frac{p}{q}-1\right)}$. Then,

Which one of the given options is a possible value of x in the following sequence? 3, 7, 15, x, 63, 127, 255

On a given day, how many times will the second-hand and the minute-hand of a clock cross each other during the clock time 12:05:00 hours to 12:55:00 h...

In how many ways can cells in a 3 × 3 grid be shaded, such that each row and each column have exactly one shaded cell? An example of one valid shading...

There are 4 red, 5 green, and 6 blue balls inside a box. If 𝑁 number of balls are picked simultaneously, what is the smallest value of 𝑁 that guaran...

Consider a circle with its centre at the origin (O), as shown. Two operations are allowed on the circle. Operation 1: Scale independently along the x...

In the given figure, PQRSTV is a regular hexagon with each side of length 5 cm. A circle is drawn with its centre at V such that it passes through P. ...

An ant walks in a straight line on a plane leaving behind a trace of its movement. The initial position of the ant is at point P facing East. The ant ...

$$x:y:z = {1 \over 2}:{1 \over 3}:{1 \over 4}$$ What is the value of $${{x + z - y} \over y}$$ = ?

Both the numerator and the denominator of $${3 \over 4}$$ are increased by a positive $${15 \over 17}$$ integer, x, and those of _____ are decreased b...

Two straight lines pass through the origin (x0, y0) = (0, 0). One of them passes through the point (x1, y1) = (1, 3) and the other passes through the ...

If p : q = 1 : 2 q : r = 4 : 3 r : s = 4 : 5 and u is 50% more than s, what is the ratio p : u?

In the following diagram, the point R is the center of the circle. The lines PQ and ZV are tangential to the circle. The relation among the areas of t...

P invested Rs.5000 per month for 6 months of a year and Q invested Rs. x per month for 8 months of the year in a partnership business. The profit is s...

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

Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks ins...

The plot below shows the relationship between the mortality risk of cardiovascular disease and the number of steps a person walks per day. Based on th...

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view rem...

Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are defin...

The chart given below compares the Installed Capacity (MW) of four power generation technologies, T1, T2, T3, and T4, and their Electricity Generation...

In the $4 \times 4$ array shown below, each cell of the first three columns has either a cross (X) or a number, as per the given rule.Rule: The number...

Three husband-wife pairs are to be seated at a circular table that has six identical chairs. Seating arrangements are defined only by the relative pos...

If x satisfies the equation $\rm 4^{8^x}=256$, then x is equal to ______.

Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, ...

Which one of the options can be inferred about the mean, median, and mode for the given probability distribution (i.e. probability mass function), 𝑃(...

Let a = 30! , b = 50! , and c = 100! . Consider the following numbers: loga c, logc a, logb a, loga b Which one of the following inequalities is COR...

A square of side length 4 cm is given. The boundary of the shaded region is defined by one semi-circle on the top and two circular arcs at the bottom,...

In a partnership business the monthly investment by three friends for the first six months is in the ratio 3 : 4 : 5. After six months, they had to in...

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 $$...