GATE General Aptitude: Quantitative Aptitude: Algebra, Geometry and Mensuration – Previous Year Questions
125 GATE previous year questions on Quantitative Aptitude: Algebra, Geometry and Mensuration (General Aptitude, Aptitude) with answers and explanations, from every paper.
- GATE 2026 XH5 (Psychology) Q10 – As shown in the figure, circle C 1 with center O 1 and radius r 1 touches the square VWXY at points P and Q while circle C 2 with center O 2 and…
- GATE 2026 XH2 (English) Q10 – As shown in the figure, circle C 1 with center O 1 and radius r 1 touches the square VWXY at points P and Q while circle C 2 with center O 2 and…
- GATE 2025 XH5 (Psychology) Q3 – The 12 musical notes are given as C, C\#, D, D\#, E, F, F\#, G, G\#, A, A\#, and B. Frequency of each note is [12]2 times the frequency of the…
- GATE 2025 XH5 (Psychology) Q4 – The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration n’ is: Note:…
- GATE 2025 XH5 (Psychology) Q5 – Which one of the following plots represents f(x) = - x x, where x is a non-zero real number? Note: The figures shown are representative.
- GATE 2025 XH5 (Psychology) Q7 – A stick of length one meter is broken at two locations at distances of b 1 and b 2 from the origin (0), as shown in the figure. Note that 0 < b 1 < b…
- GATE 2025 XH2 (English) Q3 – The 12 musical notes are given as C, C\#, D, D\#, E, F, F\#, G, G\#, A, A\#, and B. Frequency of each note is [12]2 times the frequency of the…
- GATE 2025 XH2 (English) Q4 – The following figures show three curves generated using an iterative algorithm. The total length of the curve generated after ‘Iteration n’ is: Note:…
- GATE 2025 XH2 (English) Q5 – Which one of the following plots represents f(x) = - x x, where x is a non-zero real number? Note: The figures shown are representative.
- GATE 2025 XH2 (English) Q7 – A stick of length one meter is broken at two locations at distances of b 1 and b 2 from the origin (0), as shown in the figure. Note that 0 < b 1 < b…
- GATE 2024 XH5 (Psychology) Q2 – 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,…
- GATE 2024 XH5 (Psychology) Q3 – For positive integers p and q, with pq 1, (pq)p/q = p(pq - 1). Then,
- GATE 2024 XH5 (Psychology) Q7 – Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are…
- GATE 2024 XH5 (Psychology) Q10 – During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the…
- GATE 2024 XH2 (English) Q2 – 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,…
- GATE 2024 XH2 (English) Q3 – For positive integers p and q, with pq 1, (pq)p/q = p(pq - 1). Then,
- GATE 2024 XH2 (English) Q7 – Three distinct sets of indistinguishable twins are to be seated at a circular table that has 8 identical chairs. Unique seating arrangements are…
- GATE 2024 XH2 (English) Q10 – During a half-moon phase, the Earth-Moon-Sun form a right triangle. If the Moon-Earth-Sun angle at this half-moon phase is measured to be 89.85°, the…
- GATE 2023 XH5 (Psychology) Q3 – Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll…
- GATE 2023 XH5 (Psychology) Q7 – Which one of the following options represents the given graph?
- GATE 2023 XH5 (Psychology) Q10 – A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the…
- GATE 2023 XH2 (English) Q3 – Given a fair six-faced dice where the faces are labelled ‘1’, ‘2’, ‘3’, ‘4’, ‘5’, and ‘6’, what is the probability of getting a ‘1’ on the first roll…
- GATE 2023 XH2 (English) Q7 – Which one of the following options represents the given graph?
- GATE 2023 XH2 (English) Q10 – A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the…
- GATE 2022 XH5 (Psychology) Q2 – A sphere of radius r cm is packed in a box of cubical shape. What should be the minimum volume (in cm3) of the box that can enclose the sphere?
- GATE 2022 XH5 (Psychology) Q7 – A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes.…
- GATE 2022 XH5 (Psychology) Q8 – Consider the following inequalities. (i) 3p - q < 4 (ii) 3q - p < 12 Which one of the following expressions below satisfies the above two…
- GATE 2022 XH2 (English) Q2 – A sphere of radius r cm is packed in a box of cubical shape. What should be the minimum volume (in cm3) of the box that can enclose the sphere?
- GATE 2022 XH2 (English) Q7 – A game consists of spinning an arrow around a stationary disk as shown below. When the arrow comes to rest, there are eight equally likely outcomes.…
- GATE 2022 XH2 (English) Q8 – Consider the following inequalities. (i) 3p - q < 4 (ii) 3q - p < 12 Which one of the following expressions below satisfies the above two…
- GATE 2022 ME (ME1) Q7 – A rhombus is formed by joining the midpoints of the sides of a unit square. What is the diameter of the largest circle that can be inscribed within…
- GATE 2022 ME (ME1) Q8 – An equilateral triangle, a square and a circle have equal areas. What is the ratio of the perimeters of the equilateral triangle to square to circle?
- GATE 2022 CH Q2 – A sphere of radius r cm is packed in a box of cubical shape. What should be the minimum volume (in cm3) of the box that can enclose the sphere?
- GATE 2022 CH Q8 – Consider the following inequalities. (i) 3p - q < 4 (ii) 3q - p < 12 Which one of the following expressions below satisfies the above two…
- GATE 2023 CH Q3 – In the given figure, PQRS is a parallelogram with PS = 7 cm, PT = 4 cm and PV = 5 cm. What is the length of RS in cm? (The diagram is representative.)
- GATE 2023 CH Q9 – The coefficient of x4 in the polynomial (x - 1)3(x - 2)3 is equal to .
- GATE 2024 CH Q2 – 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,…
- GATE 2024 CH Q3 – For positive integers p and q, with pq 1, (pq)p/q = p(p/q - 1). Then,
- GATE 2023 CE (CE1) Q3 – 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.…
- GATE 2023 CE (CE1) Q9 – Let a = 30!, b = 50!, and c = 100!. Consider the following numbers: a c, c a, b a, a b Which one of the following inequalities is CORRECT?
- GATE 2023 CE (CE1) Q10 – 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,…
- GATE 2024 CE (CE2) Q3 – 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…
- GATE 2024 CE (CE2) Q5 – 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…
- GATE 2024 CE (CE2) Q7 – Seven identical cylindrical chalk-sticks are fitted tightly in a cylindrical container. The figure below shows the arrangement of the chalk-sticks…
- GATE 2024 CE (CE1) Q2 – 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,…
- GATE 2024 CE (CE1) Q3 – For positive integers p and q, with pq 1, (pq)p/q = p(p/q - 1). Then,
- GATE 2025 CE (CE2) Q5 – A bag contains Violet (V), Yellow (Y), Red (R), and Green (G) balls. On counting them, the following results are obtained: (i) The sum of Yellow balls…
- GATE 2025 CE (CE2) Q10 – Three villages P, Q, and R are located in such a way that the distance PQ = 13 km, QR = 14 km, and RP = 15 km. A straight road joins Q and R. It is…
- GATE 2023 ME Q7 – Consider the following inequalities p2 - 4q < 4 3p + 2q < 6 where p and q are positive integers. The value of (p + q) is .
- GATE 2024 DA Q4 – The sum of the following infinite series is 2 + 12 + 13 + 14 + 18 + 19 + 116 + 127 +
- GATE 2025 CH Q3 – The sum of the following infinite series is: 11! + 12! + 13! + 14! + 15! +
- GATE 2025 CH Q9 – A circle with center at (x, y) = (0.5, 0) and radius = 0.5 intersects with another circle with center at (x, y) = (1, 1) and radius = 1 at two points.…
- GATE 2026 CH Q10 – As shown in the figure, circle C 1 with center O 1 and radius r 1 touches the square VWXY at points P and Q while circle C 2 with center O 2 and…
- GATE 2025 DA Q5 – A rectangle has a length L and a width W, where L > W. If the width, W, is increased by 10%, which one of the following statements is correct for all…
- GATE 2025 DA Q8 – A regular dodecagon (12-sided regular polygon) is inscribed in a circle of radius r cm as shown in the figure. The side of the dodecagon is d cm. All…
- GATE 2025 DA Q9 – If a real variable x satisfies 3x2 = 27 9x, then the value of 2x2(2x)2 is:
- GATE 2026 DA Q4 – Consider two distinct positive real numbers m, n, with m > n. Let x = n 10(m) and y = m 10(n). The relation between x and y is .
- GATE 2026 DA Q10 – In the given figure, P, Q, and R are three points on a circle of radius 10 cm with O as its center, PQ = RQ, and PQR = 45°. The figure is…
- GATE 2024 ME Q4 – The real variables x, y, z, and the real constants p, q, r satisfy xpq - r2 = yqr - p2 = zrp - q2 Given that the denominators are non-zero, the value…
- GATE 2025 CE (CE1) Q3 – The sum of the following infinite series is: 11! + 12! + 13! + 14! + 15! +
- GATE 2025 CE (CE1) Q9 – A circle with center at (x, y) = (0.5, 0) and radius = 0.5 intersects with another circle with center at (x, y) = (1, 1) and radius = 1 at two points.…
- GATE 2026 CE (CE2) Q2 – If a positive real x satisfies the following equation 2 x + 2 x = 48, then the value of x is
- GATE 2026 CE (CE2) Q8 – Consider a string P of length l that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its…
- GATE 2026 CE (CE1) Q3 – At how many points will the curves y = x2 and y = -x2 - 2x - 1 intersect in the real (x, y) plane?
- GATE 2026 CE (CE1) Q7 – In the given figure, PQ is the diameter of a circle with center O. Two points R and S are chosen on the circle such that ROS = 80°. When PR and QS are…
- GATE 2025 ME Q4 – The ceiling function of a real number x, denoted by ce(x), is defined as the smallest integer that is greater than or equal to x. Similarly, the floor…
- GATE 2026 ME Q2 – If a positive real x satisfies the following equation 2 x + 2 x = 48, then the value of x is .
- GATE 2026 ME Q8 – Consider a string P of length l that is laid out as a straight-line segment. Another string K is laid out as a semicircular arc with string P as its…
- GATE 2017 EE Q8 – The expression (x + y) - x - y 2 is equal to
- GATE 2017 CS Q8 – The expression (x + y) - x - y 2 is equal to
- GATE 2015 EC Q5 – If x(5/7) = -1/3, then the value of x is
- GATE 2016 EC Q9 – If q-a = 1r and r-b = 1s and s-c = 1q, the value of abc is .
- GATE 2016 EE Q5 – In a quadratic function, the value of the product of the roots (, ) is 4. Find the value of n + n-n + -n
- GATE 2016 EE Q10 – Choose the correct expression for f(x) given in the graph. [Graph: a straight line rises from (-3, -2) to a peak at (1, 2), then falls in a straight…
- GATE 2016 CS Q9 – If f(x) = 2x7 + 3x - 5, which of the following is a factor of f(x)?
- GATE 2016 CS Q10 – 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…
- GATE 2018 CS Q3 – The area of a square is d. What is the area of the circle which has the diagonal of the square as its diameter?
- GATE 2018 CS Q7 – If pqr0 and p-x=1q, q-y=1r, r-z=1p, what is the value of the product xyz?
- GATE 2018 CS Q9 – In the figure below, DEC+ BFC is equal to . (The four options are given in terms of the angles marked in the figure.)
- GATE 2018 EE Q3 – The three roots of the equation f(x)=0 are x=\-2,0,3\. What are the three values of x for which f(x-3)=0?
- GATE 2019 EE Q9 – Given two sets X=\1,2,3\ and Y=\2,3,4\, we construct a set Z of all possible fractions where the numerators belong to set X and the denominators…
- GATE 2018 EC Q5 – A 1.5 m tall person is standing at a distance of 3 m from a lamp post. The light from the lamp at the top of the post casts her shadow. The length of…
- GATE 2020 EE Q9 – Given a semicircle with O as the centre, as shown in the figure, the ratio AC+CBAB is , where AC, CB and AB are chords.
- GATE 2021 EE Q3 – For a regular polygon having 10 sides, the interior angle between the sides of the polygon, in degrees, is:
- GATE 2021 EE Q7 – In the figure shown above, each inside square is formed by joining the midpoints of the sides of the next larger square. The area of the smallest…
- GATE 2020 EC Q5 – A superadditive function f() satisfies the following property f(x 1+x 2) f(x 1)+f(x 2) Which of the following functions is a superadditive function…
- GATE 2020 EC Q7 – It is quarter past three in your watch. The angle between the hour hand and the minute hand is .
- GATE 2020 EC Q8 – A circle with centre O is shown in the figure. A rectangle PQRS of maximum possible area is inscribed in the circle. If the radius of the circle is a,…
- GATE 2020 EC Q9 – a,b,c are real numbers. The quadratic equation ax2-bx+c=0 has equal roots, which is , then
- GATE 2021 EC Q2 – p and q are positive integers and pq+ qp=3, then p2q2+q2p2=
- GATE 2021 EC Q8 – Consider a square sheet of side 1 unit. In the first step, it is cut along the main diagonal to get two triangles. In the next step, one of the cut…
- GATE 2021 EC Q10 – 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…
- GATE 2022 EC Q3 – 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…
- GATE 2022 EC Q7 – Consider the following inequalities. (i) 2x-1>7 (ii) 2x-9<1 Which one of the following expressions below satisfies the above two inequalities?
- GATE 2022 EC Q8 – 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?
- GATE 2023 EE Q7 – Which one of the following options represents the given graph?
- GATE 2023 EE Q10 – A square with sides of length 6 cm is given. The boundary of the shaded region is defined by two semi-circles whose diameters are the sides of the…
- GATE 2024 EE Q5 – If, for non-zero real variables x, y, and real parameter a>1, x:y=(a+1):(a-1), then, the ratio (x2-y2):(x2+y2) is
- GATE 2024 EE Q7 – In the following figure, CD = 5 cm, BE = 10 cm, AE = 12 cm, ∠DAB = ∠DCB, and ∠DAE = ∠DBC = 90° Points AFCD create a rhombus. The length of BF (in cm)…
- GATE 2024 EE Q10 – A surveyor has to measure the horizontal distance from her position to a distant reference point C. Using her position as the center, a 200 m…
- GATE 2025 EE Q3 – The relationship between two variables x and y is given by x+py+q=0 and is shown in the figure. Find the values of p and q. Note: The figure shown is…
- GATE 2025 EE Q10 – In the triangle PQR, the lengths of PT and TR are in the ratio of 3:2. ST is parallel to QR. Two semicircles are drawn with PS and PQ as diameters, as…
- GATE 2026 EE Q3 – At how many points will the curves y=x2 and y=-x2-2x-1 intersect in the real (x,y) plane?
- GATE 2026 EE Q7 – In the given figure, PQ is the diameter of a circle with center O. Two points R and S are chosen on the circle such that ROS=80. When PR and QS are…
- GATE 2023 EC Q7 – Which one of the following options represents the given graph?
- GATE 2024 EC Q7 – 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…
- GATE 2025 EC Q5 – Which one of the following plots represents f(x)=- x x, where x is a non-zero real number? Note: The figures shown are representative.
- GATE 2025 EC Q7 – A stick of length one meter is broken at two locations at distances of b 1 and b 2 from the origin (0), as shown in the figure. Note that 0<b 1<b 2<1.…
- GATE 2026 EC Q4 – Real numbers y, p, and n (all greater than 1) satisfy ( p1/n y)( y1/n p) = 16, where the logarithms are taken to the bases p1/n and y1/n. The value of…
- GATE 2026 EC Q9 – The city of Atlantis was crafted by the God of the seas, Poseidon. It was made of alternating concentric circular rings of land (shaded) and water…
- GATE 2025 CS (CS2) Q3 – If Pex = Qe-x for all real values of x, which one of the following statements is true?
- GATE 2025 CS (CS2) Q9 – In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The corner L of the rectangle is on the side QR. Side MN of the rectangle…
- GATE 2025 CS (CS1) Q7 – In the diagram, the lines QR and ST are parallel to each other. The shortest distance between these two lines is half the shortest distance between…
- GATE 2024 CS (CS2) Q4 – For positive non-zero real variables x and y, if (x+y2)=12[(x)+(y)], then, the value of xy+yx is
- GATE 2024 CS (CS1) Q2 – If two distinct non-zero real variables x and y are such that (x+y) is proportional to (x-y) then the value of xy
- GATE 2024 CS (CS1) Q5 – For positive non-zero real variables p and q, if (p2+q2)= p+ q+2 3, then the value of p4+q4p2q2 is
- GATE 2024 CS (CS1) Q7 – 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 tube. A…
- GATE 2023 CS Q7 – Consider two functions of time (t), f(t) = 0.01\,t2 and g(t) = 4\,t where 0 < t < . Now consider the following two statements: (i) For some t > 0,…
- GATE 2023 CS Q9 – 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…
- GATE 2022 CS Q2 – A function y(x) is defined in the interval [0,1] on the x-axis as y(x)=cases2 & 0 x<13\\ 3 & 13 x<34\\ 1 & 34 x 1cases Which one of the following is…
- GATE 2022 CS Q3 – 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
- GATE 2021 CS Q2 – A polygon is convex if, for every pair of points, P and Q belonging to the polygon, the line segment PQ lies completely inside or on the polygon.…
- GATE 2021 CS Q6 – We have 2 rectangular sheets of paper, M and N, of dimensions 6 cm x 1 cm each. Sheet M is rolled to form an open cylinder by bringing the short edges…
- GATE 2020 CS Q8 – 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…
- GATE 2020 CS Q9 – Two straight lines are drawn perpendicular to each other in X-Y plane. If and are the acute angles the straight lines make with the X-axis, then + is…