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Quantitative Aptitude

31 Questions
GATE→2026→General Aptitude→Quantitative Aptitude
Q1
MCQ[1 Mark]
If a positive real xx satisfies the following equation log⁡2x+log⁡2x=48\log_{2}x + \log_{\sqrt{2}}x = 48, then the value of xx is (A) 2162^{16} (B) 4164^{16} (C) 2142^{14} (D) 4144^{14}
GATE→2026→General Aptitude→Quantitative Aptitude
Q2
MCQ[1 Mark]
The next figure (indicated by '?') in the sequence is...
Figure for Question 2
GATE→2026→General Aptitude→Quantitative Aptitude
Q3
MCQ[1 Mark]
Consider the following statements about four numbers: (S1) The average of the four numbers is 25 (S2) Each number is at most 40 (S3) Each number is at least 20\nChoose the option that is necessarily correct. (A) (S1) and (S2) together imply (S3) (B) (S2) and (S3) together imply (S1) (C) (S1) and (S3) together imply (S2) (D) (S1) implies (S3)
GATE→2026→General Aptitude→Quantitative Aptitude
Q4
MCQ[2 Marks]
Consider a string P of length ll laid out as a straight-line segment. String K is a semicircular arc with P as diameter. Both strings are shortened by length xx, such that shortened K forms a full circle with shortened P as its diameter. The value of x/lx/l is (A) π\pi (B) π−12π\frac{\pi-1}{2\pi} (C) π2(π−1)\frac{\pi}{2(\pi-1)} (D) ππ−1\frac{\pi}{\pi-1}
Figure for Question 4
GATE→2026→General Aptitude→Quantitative Aptitude
Q5
MCQ[2 Marks]
The Roman senator Meritorius, his brother, his son, and his daughter have varying oratory skill levels, seated in a 2x2 grid. Conditions given: (i) Daughter and brother in same column. (ii) Son is seated diagonally across the sibling of the worst orator. (iii) Best and worst orators in the same row. Who is the best orator? (A) Meritorius (B) Meritorius' brother (C) Meritorius' son (D) Meritorius' daughter
Figure for Question 5
GATE→2026→General Aptitude→Quantitative Aptitude
Q6
MCQ[2 Marks]
Which one of the patterns labelled P, Q, R, and S is used to generate the given figure? (A) P (B) Q (C) R (D) S
Figure for Question 6
GATE→2025→General Aptitude→Quantitative Aptitude
Q7
MCQ[1 Mark]
If Pex=Qe−xPe^{x} = Qe^{-x} for all real values of xx, which one of the following statements is true? (A) P=Q=0P = Q = 0 (B) P=Q=1P = Q = 1 (C) P=1;Q=−1P = 1; Q = -1 (D) PQ=0\frac{P}{Q} = 0
GATE→2025→General Aptitude→Quantitative Aptitude
Q8
MCQ[1 Mark]
The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube?
Figure for Question 8
GATE→2025→General Aptitude→Quantitative Aptitude
Q9
MCQ[1 Mark]
Let p1p_{1} and p2p_{2} denote two arbitrary prime numbers. Which one of the following statements is correct for all values of p1p_{1} and p2p_{2}? (A) p1+p2p_{1}+p_{2} is not a prime number. (B) p1p2p_{1}p_{2} is not a prime number. (C) p1+p2+1p_{1}+p_{2}+1 is a prime number. (D) p1p2+1p_{1}p_{2}+1 is a prime number.
GATE→2025→General Aptitude→Quantitative Aptitude
Q10
MCQ[2 Marks]
If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which one among the given options is the most appropriate code for BEACH ? (A) CEADP (B) IDBFC (C) JGIBC (D) IBCEC
GATE→2025→General Aptitude→Quantitative Aptitude
Q11
MCQ[2 Marks]
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 passes through the corner S of the square. What is the area (in cm2^2) of the rectangle PLMN? (A) 222\sqrt{2} (B) 2 (C) 8 (D) 4
Figure for Question 11
GATE→2025→General Aptitude→Quantitative Aptitude
Q12
MCQ[2 Marks]
The diagram below shows a river system consisting of 7 segments, marked P, Q, R, S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We need to connect these zones using the least number of bridges. Out of the following options, which one is correct? (A) Bridges on P, Q, and T (B) Bridges on P, Q, S, and T (C) Bridges on Q, R, T, and V (D) Bridges on P, Q, S, U, and V
Figure for Question 12
GATE→2024→General Aptitude→Quantitative Aptitude
Q13
MCQ[1 Mark]
If two distinct non-zero real variables xx and yy are such that (x+y)(x+y) is proportional to (x−y)(x-y) then the value of x+yx−y\frac{x+y}{x-y} or related ratio... [Note: options evaluate constant ratio properties]
GATE→2024→General Aptitude→Quantitative Aptitude
Q14
MCQ[1 Mark]
Consider the following sample of numbers: 9,18,11,14,15,17,10,69,11,139, 18, 11, 14, 15, 17, 10, 69, 11, 13\nThe median of the sample is (A) 13.5 (B) 14 (C) 11 (D) 18.7
GATE→2024→General Aptitude→Quantitative Aptitude
Q15
MCQ[1 Mark]
The number of coins of ₹1, 25 paise, and 10 paise denominations that a person has are in the ratio 5:3:135:3:13. Of the total amount, the percentage of money in 25 paise coins is (A) 21%21\% (B) 1427%14\frac{2}{7}\% (C) 10%10\% (D) 30%30\%
GATE→2024→General Aptitude→Quantitative Aptitude
Q16
MCQ[1 Mark]
For positive non-zero real variables pp and qq, if log⁡(p2+q2)=log⁡p+log⁡q+2log⁡3\log(p^2 + q^2) = \log p + \log q + 2\log 3, then the value of p4+q4p2q2\frac{p^4 + q^4}{p^2 q^2} is (A) 79 (B) 81 (C) 9 (D) 83
GATE→2024→General Aptitude→Quantitative Aptitude
Q17
MCQ[2 Marks]
A rectangular paper sheet of dimensions 54 cm×4 cm54\text{ cm} \times 4\text{ cm} is taken. The two longer edges are joined to create a cylindrical tube. A cube whose surface area is equal to the area of the sheet is also taken. Then, the ratio of the volume of the cylindrical tube to the volume of the cube is (A) 1/π1/\pi (B) 2/π2/\pi (C) 3/π3/\pi (D) 4/π4/\pi
GATE→2024→General Aptitude→Quantitative Aptitude
Q18
MCQ[2 Marks]
A rectangular paper of 20 cm×8 cm20\text{ cm} \times 8\text{ cm} is folded 3 times along lines of symmetry perpendicular to the long edge. The perimeter of the final folded sheet (in cm) is (A) 18 (B) 24 (C) 20 (D) 21
GATE→2024→General Aptitude→Quantitative Aptitude
Q19
MCQ[2 Marks]
The least number of squares to be added in the figure to make AB a line of symmetry is...
Figure for Question 19
GATE→2023→General Aptitude→Quantitative Aptitude
Q20
MCQ[1 Mark]
In the given figure, PQRS is a parallelogram with PS=7 cmPS = 7\text{ cm}, PT=4 cmPT = 4\text{ cm} and PV=5 cmPV = 5\text{ cm}. What is the length of RSRS in cm?
Figure for Question 20
GATE→2023→General Aptitude→Quantitative Aptitude
Q21
MCQ[1 Mark]
A line of symmetry is defined as a line that divides a figure into two parts in a way such that each part is a mirror image... minimum number of squares that must be coloured black, such that both PQ and MN form lines of symmetry? (A) 3 (B) 4 (C) 5 (D) 6
Figure for Question 21
GATE→2023→General Aptitude→Quantitative Aptitude
Q22
MCQ[2 Marks]
To construct a wall, sand and cement are mixed in the ratio of 3:13:1. The cost of sand and that of cement are in the ratio of 1:21:2. If the total cost of sand and cement to construct the wall is 10001000 rupees, what is the cost (in rupees) of cement used? (A) 400 (B) 600 (C) 800 (D) 200
GATE→2023→General Aptitude→Quantitative Aptitude
Q23
MCQ[2 Marks]
The coefficient of x4x^4 in the polynomial (x−1)3(x−2)3(x-1)^3(x-2)^3 is equal to (A) 33 (B) -3 (C) 30 (D) 21
GATE→2023→General Aptitude→Quantitative Aptitude
Q24
MCQ[2 Marks]
Which one of the following shapes can be used to tile (completely cover by repeating) a flat plane, extending to infinity in all directions, without leaving any empty spaces in between them? The copies of the shape used to tile are identical and are not allowed to overlap. (A) circle (B) regular octagon (C) regular pentagon (D) rhombus
GATE→2022→General Aptitude→Quantitative Aptitude
Q25
MCQ[1 Mark]
A sum of money is to be distributed among P, Q, R, and S in the proportion 5:2:4:35:2:4:3, respectively. If R gets 1000 more than S, what is the share of Q (in ?)? (A) 500 (B) 1000 (C) 1500 (D) 2000
GATE→2022→General Aptitude→Quantitative Aptitude
Q26
MCQ[1 Mark]
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 cmPQ=11\text{ cm}, QR=4 cmQR=4\text{ cm}, RS=6 cmRS=6\text{ cm} and SP=3 cmSP=3\text{ cm}. What is the shortest distance between PQ and SR (in cm)? (A) 1.80 (B) 2.40 (C) 4.20 (D) 5.76
GATE→2022→General Aptitude→Quantitative Aptitude
Q27
MCQ[1 Mark]
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 4×44\times4 grid using the unit squares as building blocks? (A) 15 (B) 20 (C) 21 (D) 26
Figure for Question 27
GATE→2022→General Aptitude→Quantitative Aptitude
Q28
MCQ[1 Mark]
An art gallery engages a security guard... boundary walls are opaque... Which one of the following correctly represents the set of ALL possible locations among P, Q, R and S where the security guard can be posted to watch over the entire inner space? (A) P and Q (B) Q (C) Q and S (D) R and S
Figure for Question 28
GATE→2022→General Aptitude→Quantitative Aptitude
Q29
MCQ[2 Marks]
Consider the following inequalities. (i) 2x−1>72x - 1 > 7 (ii) 2x−9<12x - 9 < 1\nWhich one of the following expressions below satisfies the above two inequalities? (A) x≤−4x \le -4 (B) −4<x≤4-4 < x \le 4 (C) 4<x<54 < x < 5 (D) x≥5x \ge 5
GATE→2022→General Aptitude→Quantitative Aptitude
Q30
MCQ[2 Marks]
Four points P(0,1)P(0,1), Q(0,−3)Q(0,-3), R(−2,−1)R(-2,-1), and S(2,−1)S(2,-1) represent the vertices of a quadrilateral. What is the area enclosed by the quadrilateral? (A) 4 (B) 424\sqrt{2} (C) 8 (D) 828\sqrt{2}
GATE→2022→General Aptitude→Quantitative Aptitude
Q31
MCQ[2 Marks]
Consider the following square with the four corners and the center marked as P, Q, R, S and T respectively. Operations X, Y, Z defined... sequences (1) XYZZ, (2) XY, (3) ZZZZ. Which statement is correct? (A) The sequence of operations (1) and (2) are equivalent (B) The sequence of operations (1) and (3) are equivalent (C) The sequence of operations (2) and (3) are equivalent (D) The sequence of operations (1), (2) and (3) are equivalent
Figure for Question 31

Data Interpretation

3 Questions
GATE→2026→General Aptitude→Data Interpretation
Q32
MCQ[2 Marks]
The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The observations are: - Q of S = 2×2 \times Q of T - Q of R = 3×3 \times Q of T - Q of Q = 4×4 \times Q of T\nPrices: P = 50, Q = 100, R = 60, S = 60, T = 40.\nWhat is the quantity of product P sold on that day? (A) 40 (B) 50 (C) 60 (D) 70
GATE→2025→General Aptitude→Data Interpretation
Q33
MCQ[2 Marks]
Which one of the following options is correct for the given data in the table? (A) X(i)=X(i−1)+I(i)X(i)=X(i-1)+I(i); Y(i)=Y(i−1)I(i)Y(i)=Y(i-1)I(i); i>0i>0 (B) X(i)=X(i−1)I(i)X(i)=X(i-1)I(i); Y(i)=Y(i−1)+I(i)Y(i)=Y(i-1)+I(i); i>0i>0 (C) X(i)=X(i−1)I(i)X(i)=X(i-1)I(i); Y(i)=Y(i−1)I(i)Y(i)=Y(i-1)I(i); i>0i>0 (D) X(i)=X(i−1)+I(i)X(i)=X(i-1)+I(i); Y(i)=Y(i−1)I(i−1)Y(i)=Y(i-1)I(i-1); i>0i>0
GATE→2024→General Aptitude→Data Interpretation
Q34
MCQ[2 Marks]
The pie chart presents the percentage contribution of different macronutrients to a typical 2,000 kcal2,000\text{ kcal} diet (Carbohydrates 35%, Proteins 20%, Unsaturated fat 20%, Saturated fat 20%, Trans fat 5%). Energy densities: Carb 4, Protein 4, Fat 9 kcal/g. Total fat consumed in grams is (A) 44.4 (B) 77.8 (C) 100 (D) 3,600
Figure for Question 34

Verbal Ability

16 Questions
GATE→2026→General Aptitude→Verbal Ability
Q35
MCQ[1 Mark]
'The team _______ more than 300 runs in 20 overs _______ rains. However, some players needed to improve their batting skills.' Choose the option with the correct sequence of words to fill the blanks. (A) score; despite (B) scoring; instead of (C) scored; despite (D) scoring; in spite of
GATE→2026→General Aptitude→Verbal Ability
Q36
MCQ[1 Mark]
'All the mangoes in the basket are good.' If the above statement is false, then which one of the following statements is necessarily true? (A) All the mangoes in the basket are not good. (B) No mango in the basket is good. (C) In the basket, some of the mangoes are good and some are not good. (D) There exists at least one mango in the basket that is not good.
GATE→2026→General Aptitude→Verbal Ability
Q37
MCQ[2 Marks]
'People are crowding around [blank 1] pit into which [blank 2] elephant has fallen. I have never seen an elephant looking more bewildered [blank 3] miserable. Here it is in a most undignified position, thrust into a pit and made to look up [blank 4] a vast, curiosity-stricken crowd.' Choose the option with the correct sequence of words to fill the blanks. (A) an; a; at; and (B) a; an; and; at (C) and; a; an; at (D) at; a; an; and
GATE→2025→General Aptitude→Verbal Ability
Q38
MCQ[1 Mark]
Despite his initial hesitation, Rehman's _______ to contribute to the success of the project never wavered. Select the most appropriate option to complete the above sentence. (A) ambivalence (B) satisfaction (C) resolve (D) revolve
GATE→2025→General Aptitude→Verbal Ability
Q39
MCQ[1 Mark]
Bird : Nest :: Bee : _______\nSelect the correct option to complete the analogy. (A) Kennel (B) Hammock (C) Hive (D) Lair
GATE→2025→General Aptitude→Verbal Ability
Q40
MCQ[2 Marks]
Based only on the conversation below, identify the logically correct inference: "Even if I had known that you were in the hospital, I would not have gone there to see you", Ramya told Josephine. (A) Ramya knew that Josephine was in the hospital. (B) Ramya did not know that Josephine was in the hospital. (C) Ramya and Josephine were once close friends; but now, they are not. (D) Josephine was in the hospital due to an injury to her leg.
GATE→2024→General Aptitude→Verbal Ability
Q41
MCQ[1 Mark]
If '→\rightarrow' denotes increasing order of intensity, then the meaning of the words [dry →\rightarrow arid →\rightarrow parched] is analogous to [diet →\rightarrow fast →\rightarrow \_]. Which one of the given options is appropriate to fill the blank? (A) starve (B) reject (C) feast (D) deny
GATE→2024→General Aptitude→Verbal Ability
Q42
MCQ[2 Marks]
In the given text, fill in the blanks with the correct prepositions/words: Steve was advised to keep his head (i) his shoulders... [Options match (C)]
GATE→2023→General Aptitude→Verbal Ability
Q43
MCQ[1 Mark]
"You are delaying the completion of the task. Send _______ contributions at the earliest." (A) you are (B) your (C) you're (D) yore
GATE→2023→General Aptitude→Verbal Ability
Q44
MCQ[1 Mark]
Blueprint : Design :: Guidelines : _________ (By word meaning) (A) Sight (B) Site (C) Cite (D) Plagiarise
GATE→2023→General Aptitude→Verbal Ability
Q45
MCQ[1 Mark]
In 2022, June Huh was awarded the Fields medal... Based only on the above information, which one of the following statements can be logically inferred with certainty? (A) Every Fields medalist has won a medal in an International Mathematics Olympiad. (B) Everyone who has dropped out of college has won the Fields medal. (C) All Fields medalists are part-time poets. (D) Some Fields medalists have dropped out of college.
GATE→2023→General Aptitude→Verbal Ability
Q46
MCQ[2 Marks]
Human beings are one among many creatures... If "Some human beings are not cruel creatures" is FALSE, which statements can be inferred? (i) All human beings are cruel creatures. (ii) Some human beings are cruel creatures. (iii) Some creatures that are cruel are human beings. (iv) No human beings are cruel creatures. (A) only (i) (B) only (iii) and (iv) (C) only (i) and (ii) (D) (i), (ii) and (iii)
GATE→2023→General Aptitude→Verbal Ability
Q47
MCQ[2 Marks]
The World Bank has declared that it does not plan to offer new financing to Sri Lanka... Based only on the above passage, which one of the following statements can be inferred with certainty? (A) According to the World Bank, the root cause of Sri Lanka's economic crisis is that it does not have enough foreign exchange. (B) The World Bank has stated that it will advise the Sri Lankan government about how to tackle the root causes of its economic crisis. (C) According to the World Bank, Sri Lanka does not yet have an adequate macroeconomic policy framework. (D) The World Bank has stated that it will provide Sri Lanka with additional funds for essentials such as food, fuel, and medicines.
GATE→2022→General Aptitude→Verbal Ability
Q48
MCQ[1 Mark]
Mr. X speaks _______ Japanese _______ Chinese. (A) neither/or (B) either/nor (C) neither / nor (D) also / but
GATE→2022→General Aptitude→Verbal Ability
Q49
MCQ[2 Marks]
Mosquitoes pose a threat to human health. Controlling mosquitoes using chemicals may have undesired consequences. In Florida, authorities have used genetically modified mosquitoes to control the overall mosquito population. It remains to be seen if this novel approach has unforeseen consequences.\nWhich one of the following is the correct logical inference based on the information in the above passage? (A) Using chemicals to kill mosquitoes is better than using genetically modified mosquitoes because genetic engineering is dangerous (B) Using genetically modified mosquitoes is better than using chemicals to kill mosquitoes because they do not have any side effects (C) Both using genetically modified mosquitoes and chemicals have undesired consequences and can be dangerous (D) Using chemicals to kill mosquitoes may have undesired consequences but it is not clear if using genetically modified mosquitoes has any negative consequence
GATE→2022→General Aptitude→Verbal Ability
Q50
MCQ[2 Marks]
In a class of five students P, Q, R, S and T, only one student is known to have copied in the exam. The disciplinary committee has investigated the situation and recorded the statements from the students as given below.\nStatement of P: R has copied in the exam.\nStatement of Q: S has copied in the exam.\nStatement of R: P did not copy in the exam.\nStatement of S: Only one of us is telling the truth.\nStatement of T: R is telling the truth.\nThe investigating team had authentic information that S never lies.\nBased on the information given above, the person who has copied in the exam is (A) R (B) P (C) Q (D) T