GATE CSE
General Aptitude
Numerical Ability
Previous Years Questions

## Marks 1

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
In a recently conducted national entrance test, boys constituted 65% of those who appeared for the test. Girls constituted the remaining candidates an...
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 corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T and U, but not necessarily in the same order....
A plot of land must be divided between four families. They want their individual plots to be similar in shape, not necessarily equal in area. The land...
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 :
There are multiple routes to reach from node 1 to node 2, as shown in the network. The cost of travel on an edge between two nodes is given in rupees...
Ten freiends 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 frien...
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...
The area of a square is $$𝑑.$$ What is the area of the circle which has the diagonal of the square as its diameter?
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 is the missing number in the following sequence? $$2,\,12,\,60,\,240,\,720,\,1440,\,\_\_\_,\,0$$\$
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?
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...
Based on the given statements, select the most appropriate option to solve the given question. If two floors in a certain building are 9 feet apart, h...

## Marks 2

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 ...
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...
If P = 3, R = 27, T = 243, then Q + S = ______.
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...
Three of the five students allocated to a hostel put in special requests to the warden. Given the floor plan of the vacant rooms, select the allocatio...
In the given diagram, teachers are represented in the triangle, researchers in the circle and administrators in the rectngle. Out of the total number ...
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...
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 $$𝑥𝑦𝑧$$?
In the figure below, $$∠𝐷𝐸𝐶 + ∠𝐵𝐹𝐶$$ is equal to ____________ . ...
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...
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 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...
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 given statement is followed by some courses of action. Assuming the statement to be true, decide the correct option. Statement: There has been a s...
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