Numerical Ability · General Aptitude · GATE ECE
Marks 1
Five years ago, the ratio of Aman’s age to his father’s age was 1:4, and five years from now, the ratio will be 2:5. What was his father’s age when Aman was born?
For a real number $x > 1$ ,
$$ \frac{1}{\log_{2}x} + \frac{1}{\log_{3}x} + \frac{1}{\log_{4}x} = 1$$
The value of $x$ is
The greatest prime factor of $(3^{199} - 3^{196})$ is
What is the smallest number with distinct digits whose digits add up to 45?
In a class of 100 students,
(i) there are 30 students who neither like romantic movies nor comedy movies,
(ii) the number of students who like romantic movies is twice the number of students who like comedy movies, and
(iii) the number of students who like both romantic movies and comedy movies is 20.
How many students in the class like romantic movies?
How many rectangles are present in the given figure?
A sum of money is to be distributed among P, Q, R, and S in the proportion 5 : 2 : 4 : 3, respectively.
If R gets Rs. 1000 more than S, what is the share of Q (in Rs.) ?
A trapezium has vertices marked as P, Q, R and S (in that order anticlockwise). The side PQ is parallel to side SR.
Further, it is given that, PQ = 11 cm, QR = 4 cm, RS = 6 cm and SP = 3 cm. What is the shortest distance between PQ and SR (in cm) ?
The figure shows a grid formed by a collection of unit squares. The unshaded unit square in the grid represents a hole.
What is the maximum number of squares without a "hole in the interior" that can be formed within the 4 $$\times$$ 4 grid using the unit squares as building blocks?
Four points P(0, 1), Q(0, $$-$$3), R($$-$$2, $$-$$1), and S(2, $$-$$1) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral?
(i) At least one bench is a table
(ii) At least one shelf is a bench
(iii) At least one chair is a table
(iv) All benches are chairs
Which of the following statement is correct?
A, CD, GHI, ? , UVWXY
Marks 2
Four identical cylindrical chalk-sticks, each of radius $r = 0.5$ cm and length $l = 10$ cm, are bound tightly together using a duct tape as shown in the following figure.
The width of the duct tape is equal to the length of the chalk-stick. The area (in cm2) of the duct tape required to wrap the bundle of chalk-sticks once, is
The bar chart shows the data for the percentage of population falling into different categories based on Body Mass Index (BMI) in 2003 and 2023.
Based on the data provided, which one of the following options is INCORRECT?
Two identical sheets A and B, of dimensions 24 cm × 16 cm, can be folded into half using two distinct operations, FO1 or FO2.
In FO1, the axis of folding remains parallel to the initial long edge, and in FO2, the axis of folding remains parallel to the initial short edge.
If sheet A is folded twice using FO1, and sheet B is folded twice using FO2, the ratio of the perimeters of the final shapes of A and B is
Which one of the following options represents the given graph?
Out of 1000 individuals in a town, 100 unidentified individuals are covid positive. Due to lack of adequate covid-testing kits, the health authorities of the town devised a strategy to identify these covid-positive individuals. The strategy is to:
(i) Collect saliva samples from all 1000 individuals and randomly group them into sets of 5.
(ii) Mix the samples within each set and test the mixed sample for covid.
(iii) If the test done in (ii) gives a negative result, then declare all the 5 individuals to be covid negative.
(iv) If the test done in (ii) gives a positive result, then all the 5 individuals are separately tested for covid.
Given this strategy, no more than __________ testing kits will be required to identify all the 100 covid positive individuals irrespective of how they are grouped.
A 100 cm $$\times$$ 32 cm rectangular sheet is folded 5 times. Each time the sheet is folded, the long edge aligns with its opposite side. Eventually, the folded sheet is a rectangle of dimensions 100 cm $$\times$$ 1 cm.
The total number of creases visible when the sheet is unfolded is __________.
Consider the following inequalities.
(i) 2x $$-$$ 1 > 7
(ii) 2x $$-$$ 9 < 1
Which one of the following expressions below satisfies the above two inequalities?
Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively.
Let X, Y and Z represent the following operations :
X : rotation of the square by 180 degree with respect to the S-Q axis.
Y : rotation of the square by 180 degree with respect to the P-R axis.
Z : rotation of the square by 90 degree clockwise with respect to the axis perpendicular, going into the screen and passing through the point T.
Consider the following three distinct sequences of operation (which are applied in the left to right order).
(1) XYZZ
(2) XY
(3) ZZZZ
Which one of the following statements is correct as per the information provided above?
Corners are cut from an equilateral triangle to produce a regular convex hexagon as shown in the figure above.
The ratio of the area of the regular convex to the area of the original equilateral triangle is
The number of minutes spent by two students, X and Y, excercising every day in a given week are shown in the bar chart above.
The number of days in the given week in which one of the students spent a minimum of 10% more than the other student, on a given day, is
Given the floor plan, what is the current location of Q, R and T ? [O = office, WR = Wash room]
(i) 85% of cabs in the city are green and the remaining cabs are blue.
(ii) A witness identified the cab involved in the accident as blue.
(iii) It is known that a witness can correctly identify the cab colour only 80% of the time.
Which of the following options is closest to the probability that the accident was caused by a blue cab?
The path from P to Q is best described by
Which of the following is the steepest path leaving from P?
W,E,K,O
I,Q,W,A
F,N,T,X
N,V,B,D
One of the legacies of the Roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battlefield kept units obedient, intact and fighting, even when the odds and conditions were against them.
Which one of the following statements best sums up the meaning of the above passage?
The approximate percentage of the monthly budget NOT spent on savings is
The distances covered during four laps of the journey are listed in the table below
From the given data, we can conclude that the fuel consumed per kilometre was least during the lap
Which of the following statements best sums up the meaning of the above passage:
i. Hari’s age + Gita’s age > Irfan’s age + Saira’s age.
ii. The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest.
iii. There are not twins.
In what order were they born (Oldest first)?