Numerical Ability · General Aptitude · GATE CSE

Two wizards try to create a spell using all the four elements, water, air, fire, and earth. For this, they decide to mix all these elements in all pos...

In an engineering college of 10,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core br...

For positive non-zero real variables $x$ and $y$, if $\ln \left( \frac{x + y}{2} \right) = \frac{1}{2} [ \ln (x) + \ln (y) ]$ then, the value of $\fra...

In the sequence 6, 9, 14, $x$, 30, 41, a possible value of $x$ is

Consider the following sample of numbers:9, 18, 11, 14, 15, 17, 10, 69, 11, 13The median of the sample is

The number of coins of ₹1, ₹5, and ₹10 denominations that a person has are in the ratio 5:3:13. Of the total amount, the percentage of money in ₹5 coi...

If two distinct non-zero real variables $x$ and $y$ are such that $(x + y)$ is proportional to $(x - y)$ then the value of $\frac{x}{y}$

For positive non-zero real variables $p$ and $q$, if$\log \left(p^2 + q^2\right) = \log p + \log q + 2 \log 3$,then, the value of $\frac{p^4 + q^4}{p^...

A series of natural numbers $$F_1,F_2,F_3,F_4,F_5,F_6,F_7,\,.....$$ obeys $$F_{n+1}=F_n+F_{n-1}$$ for all integers $$n\ge2$$. If $$F_6=37$$, and $$F_7...

A function y(x) is defined in the interval [0, 1] on the x-axis as $$y(x) = \left\{ \matrix{ 2\,if\,0 \le x Which one of the following is the area ...

Let r be a root of the equation x2 + 2x + 6 = 0. Then the value of the expression (r + 2) (r + 3) (r + 4) (r + 5) is

If $${\left( {x - {1 \over 2}} \right)^2} - {\left( {x - {3 \over 2}} \right)^2} = x + 2$$, then the value of x is :

If $$\theta$$ is the angle, in degrees, between the longest diagonal of the cube and any one of the edges of the cube, then cos $$\theta$$ = _______

The ratio of boys to girls in a class is 7 to 3. Among the options below, an acceptable value for the total number of students in the class is :...

Ten friends planned to share equally the cost of buying a gift for their teacher. When two of them decided not to contribute, each of the other friend...

Two cars start at the same time from the same location and go in the same direction. The speed of the first car is 50 Km/h and the speed of the second...

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

What would be the smallest natural number which when divided either by $$20$$ or by $$42$$ or by $$76$$ leaves a remainder of $$7$$ in each case?

The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?

In a quadratic function, the value of the product of the roots $$\left( {\alpha ,\beta } \right)$$ is $$4.$$ Find the value of $$${{{\alpha ^n} + {\b...

Among $$150$$ faculty members in an institute, $$55$$ are connected with each other through Facebook® and $$85$$ are connected through WhatsApp®. $$30...

Choose the correct expression for $$f(x)$$ given in the graph. ...

In a $$2 \times 4$$ rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid? ...

A cube is built using $$64$$ cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting...

Given set A = {2, 3, 4, 5} and Set B = {11, 12, 13, 14, 15}, two numbers are randomly selected, one from each set. What is probability that the sum of...

A person sold two different items at the same price. He made 10% profit in one item, and 10% loss in the other item. In selling these two items, the p...

The pie charts depict the shares of various power generation technologies in the total electricity generation of a country for the years 2007 and 2023...

A rectangular paper sheet of dimensions 54 cm × 4 cm is taken. The two longer edges of the sheet are joined together to create a cylindrical tub...

The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal diet of a person. Macronutrient energy contribu...

A rectangular paper of 20 cm × 8 cm is folded 3 times. Each fold is made along the line of symmetry, which is perpendicular to its long edge. Th...

The least number of squares to be added in the figure to make AB a line of symmetry is...

Consider two functions of time (t), $$f(t)=0.01\,t^2$$ $$g(t)=4\,t$$ where $$0 Now consider the following two statements : (i) For some $$t > 0,g(t) ...

$$f(x)$$ and $$g(y)$$ are functions of x and y, respectively, and $$f(x)=g(y)$$ for all real values of x and y. Which one of the following options is ...

A box contains five balls of same size and shape. Three of them are green coloured balls and two of them are orange coloured balls. Balls are drawn fr...

The number of student in three classes is in the ratio 3 : 13 : 6. If 18 students are added to each class, the ratio changes to 15 : 35 : 21.The total...

The number of units of a product sold in three different years and the respective net profits are presented in the figure above. The cost/unit in yea...

There are five bags each containing identical sets of ten distinct chocolates. One chocolate is picked from each bag.The probability that at least two...

We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm $$\times$$ 1 cm each. Sheet M is rolled to form an open cylinder by bringing the sh...

Items Cost Profit% Marked price P 5400 - 5860 Q - 25 10000 Details of prices of...

Two straight lines are drawn perpendicular to each other in X-Y plane. If $$\alpha $$ and $$\beta $$ are the acute angles the straight lines make with...

The figure below shows an annular ring with outer and inner radii as b and a, respectively. The annular space has been painted in the form of blue col...

The total revenue of a company during 2014-2018 is shown in the bar graph. If the total expenditure of the company in each year is 500 million rupees,...

In a college, there are three student clubs. Sixty students are only in the Drama club, 80 students are only in the Dance club, 30 students are only i...

In appreciation of the social improvements completed in a town, a wealthy philanthropist decided to gift Rs $$750$$ to each male senior citizen in the...

A six sided unbiased die with four green faces and two red faces is rolled seven times. Which of the following combinations is the most likely outcome...

In a party, $$60\% $$ of the invited guests are male and $$400\% $$ are female. If $$80\% $$ of the invited guests attended the party and if all the i...

If $$pqr \ne 0$$ and $${p^{ - x}} = {1 \over q},{q^{ - y}} = {1 \over r},\,{r^{ - z}} = {1 \over p},$$ what is the value of the product $$𝑥𝑦𝑧$$?

A shaving set company sells $$4$$ different types of razors, Elegance, Smooth, Soft and Executive. Elegance sells at Rs. $$48,$$ Smooth at Rs. $$63,$$...

If $$f\left( x \right) = 2{x^7} + 3x - 5,$$ which of the following is a factor of $$f(x)$$?

In a process, the number of cycles to failure decreases exponentially with an increase in load. At a load of $$80$$ units, it takes $$100$$ cycles for...

The probabilities that a student passes in Mathematics, Physics and Chemistry are m, p, and c respectively. Of these subjects, the student has 75% cha...

The number of students in a class who have answered correctly, wrongly, or not attempted each question in an exam, are listed in the table below. The ...

The pie chart below has the breakup of the number of students from different departments in an engineering college for the year 2012. The proportion o...