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The pattern is 'multiply by 2 and add 1': 3×2+1=7, 7×2+1=15, 15×2+1=31, 31×2+1=63. Applying the same rule to 63 gives 63×2+1=127. Verify each step against the given terms before fixing the answer.
Each letter is replaced by the letter immediately after it in the alphabet. Shifting C, E, P, T, A, M one place forward gives D, F, Q, U, B, N in the same order. Every position must be shifted individually without disturbing the sequence.
The only son of the man's mother is the man himself, since he has no brothers. The girl is therefore the daughter of the speaker. The word 'only' is decisive because it rules out the possibility that the son referred to is a brother.
Trace the displacement: 5 km north, then 3 km east, then 5 km south returns the person to the east-west line at 3 km east, and the final 2 km east adds to it. The north and south legs cancel, leaving a net displacement of 5 km due east.
The statement 'Some graduates are managers' converts validly to 'Some managers are graduates', so conclusion II is definite. The engineers need not be among those graduates who are managers, so conclusion I is only a possibility and cannot be declared valid.
At 3:40 the minute hand is at 40×6 = 240° and the hour hand is at 3×30 + 40×0.5 = 110° measured from 12. The difference is 240 − 110 = 130°, which is below 180° and hence the smaller angle.
B's rank from the left is 40 − 15 + 1 = 26. Since A is 12th from the left, the students strictly between them are 26 − 12 − 1 = 13. The final subtraction of 1 removes both A and B from the count.
A 4×4×4 cube has 12 edges, and the two corner cubes on each edge carry three painted faces. The remaining interior edge cubes, 4 − 2 = 2 per edge, have exactly two painted faces, giving 12 × 2 = 24.
The year 2024 is a leap year, so 1 January 2024 to 1 January 2025 spans 366 days, that is, 52 weeks plus 2 odd days. Two days after Monday is Wednesday, so 1 January 2025 was a Wednesday and the preceding day, 31 December 2024, was a Tuesday.
The number liking at least one game is 60 − 10 = 50. By inclusion-exclusion, 50 = 35 + 30 − x, where x is the overlap, so x = 65 − 50 = 15. The 10 students who like neither must be removed before applying the formula.
121 = 11², 144 = 12² and 169 = 13², so these three are consecutive perfect squares. The number 180 lies between 13² = 169 and 14² = 196 and is not a perfect square. Hence 180 is the odd one out.
Using A = 1 through Z = 26, P + E + N = 16 + 5 + 14 = 35 and B + O + O + K = 2 + 15 + 15 + 11 = 43, which matches the given codes. For CAP, C + A + P = 3 + 1 + 16 = 20. Therefore the required code is 20.
B is the mother of C and D because C is D's sister and both share B as mother. A is B's brother, so A is the brother of D's mother, which makes him D's maternal uncle. The relation does not depend on D's gender.
Number the seats 1 to 5 from left to right. P is at seat 1; Q is second to the right of P, so Q is at seat 3; R is immediately right of Q at seat 4; S is at seat 5; T occupies seat 2. The middle seat is seat 3, occupied by Q.
From 'All pens are books', the converse 'Some books are pens' follows under the usual existential assumption of these tests. The red books need not include any pen, so conclusion I is not forced. Hence only conclusion II follows.
At sunrise the Sun is in the east, so a vertical pole's shadow points west. If west is on the guard's right, the guard must be facing south, because when facing south the right hand points west. Thus the guard is facing south.
The differences between consecutive terms are 4, 6, 8, 10, increasing by 2 each time. The next difference should be 12, so the next term is 30 + 12 = 42. The terms also fit n(n+1) for n = 1, 2, 3, 4, 5, 6.
Cutting into 27 cubes gives a 3×3×3 arrangement. A small cube with exactly two painted faces lies on an edge but not at a corner; each of the 12 edges contributes one such middle cube. Therefore the count is 12.
At 4:00 the hour hand is 120° ahead of the minute hand. The minute hand gains 330° per hour, or 5.5° per minute, so the gap closes in 120 ÷ 5.5 = 21 9/11 minutes. The hands coincide at 4:21 9/11 minutes.
From 1 March 2024 to 1 March 2025 there are 365 days because 29 February 2024 falls before the starting date. An interval of 365 days has one odd day, so the weekday advances by one from Friday to Saturday. Hence 1 March 2025 was a Saturday.
Each term is obtained by doubling the previous term and adding 1: 5 × 2 + 1 = 11, 11 × 2 + 1 = 23, and 23 × 2 + 1 = 47. Therefore the next term is 47 × 2 + 1 = 95.
The word 'blue' appears in both coded phrases, and the only code word common to both is 'na'. Hence 'na' represents 'blue'.
Starting from north, a 90° clockwise turn gives east; a 180° anticlockwise turn from east gives west; a final 90° clockwise turn from west gives north. Thus he faces north.
N is the daughter of O, and M is N's brother, so O is also M's mother. Since O is the wife of P, P is the father of M.
With C at the centre, A occupies the seat immediately left of C. E is at the extreme right, so B and D fill the two remaining seats. Since B is not adjacent to C, B must be at the extreme left and D immediately right of C. Reading left to right gives B, A, C, D, E, so second to the left of E is C.
The tablets mentioned in the second statement are a subset of computers, so some tablets are definitely computers. The laptops are entirely inside computers, but that does not guarantee any overlap with tablets.
At 7:20, the minute hand is at 120° from 12. The hour hand is at 7 × 30° + 20 × 0.5° = 220°. The difference is 100°, which is already the smaller angle.
The total is found by adding the rank from the top and the rank from the bottom, then subtracting 1 because Ravi is counted twice. Thus 9 + 18 − 1 = 26.
Replace the symbols first: the expression becomes 18 ÷ 3 − 2 × 4 + 6. By BODMAS, 18 ÷ 3 = 6 and 2 × 4 = 8, so 6 − 8 + 6 = 4.
P and S occupy opposite seats. Q takes one seat adjacent to P, so T must take the other adjacent seat because T is also adjacent to P. R is opposite Q, leaving U in the only remaining seat, which is opposite T.
A doctor normally works in a hospital, just as a teacher normally works in a school. The relationship is profession to usual workplace, not profession to client or tool.
In each term the first letter moves forward through the alphabet A, B, C, D, E, while the second moves backward Z, Y, X, W, V. Therefore the next pair is EV.
Each letter of DRDO is shifted one place forward to get ESEP: D becomes E, R becomes S, D becomes E, and O becomes P. Applying the same rule to STA gives TUB.
Q's son is P's father, so Q is P's grandparent. The relation asked is P to Q: P is Q's grandchild. P's gender is not specified, so 'grandchild' is the exact relation.
The engineers who are scientists cannot be managers because no scientist is a manager. Thus at least some engineers are not managers, so conclusion I follows. Conclusion II wrongly extends this to every engineer, including those who are not scientists.
The northward 5 km and southward 5 km cancel because the second right turn makes the final leg point south. The only remaining displacement is the 3 km east from the first right turn.
Each term follows n cubed plus 2 for n = 1, 2, 3, 4: 1 + 2 = 3, 8 + 2 = 10, 27 + 2 = 29, and 64 + 2 = 66. For n = 5, 125 + 2 = 127.
E is taller than C, C is taller than A, A is taller than B, and B is taller than D. The descending order is E, C, A, B, D, so C is second tallest.
Fix Q and place P two seats away on Q's right. R must occupy the neighbour seat that leaves S a position not adjacent to P; this places R immediately on P's left side. The remaining seats are then forced for S and T.
Each fold doubles the number of layers: two folds make four layers. Since the hole is away from every fold line, unfolding produces four distinct holes.
Article 53 vests the executive power of the Union in the President, who is the constitutional head of the Indian State. The Prime Minister heads the Council of Ministers, which aids and advises the President under Article 74, but the President remains the formal constitutional head.
The Tropic of Cancer crosses eight Indian states: Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura and Mizoram. It does not pass through any other Indian state, which is why eight is the standard answer.
The ampere is the SI base unit of electric current and is defined using the fixed numerical value of the elementary charge. Volt measures potential difference, ohm measures resistance, and watt measures power, so none of those units measures current.
The 42nd Constitutional Amendment Act, 1976, added Part IVA and Article 51A, introducing ten Fundamental Duties for citizens. The 44th Amendment later reversed several other changes made by the 42nd Amendment but did not remove the Fundamental Duties.
Allan Octavian Hume, a retired British civil servant, played the principal role in founding the Indian National Congress in 1885. Womesh Chandra Bonnerjee was its first president, while Dadabhai Naoroji and Surendranath Banerjee were prominent early leaders rather than its founder.
The Godavari is the longest river of peninsular India and is called Dakshin Ganga because of its length, large basin and cultural importance. It rises in the Western Ghats in Maharashtra and drains into the Bay of Bengal.
The Reserve Bank of India Act, 1934, and the RBI's Monetary Policy Department give the central bank the mandate to formulate and implement monetary policy. SEBI regulates securities markets, IRDAI regulates insurance, and NITI Aayog is a policy think tank.
Scurvy results from a deficiency of vitamin C (ascorbic acid), which is needed for collagen synthesis. Symptoms include bleeding gums, poor wound healing and fatigue, while vitamin A deficiency causes night blindness and vitamin D deficiency causes rickets.
The Defence Research and Development Organisation was formed in 1958 by merging the technical development establishments of the Indian Army with the Directorate of Technical Development and Production. It functions under the Ministry of Defence and is headquartered in New Delhi.
Article 324 establishes the Election Commission and vests in it the superintendence, direction and control of elections to Parliament, state legislatures and the offices of President and Vice-President. Article 315 deals with Public Service Commissions, Article 312 with All India Services, and Article 356 with President's Rule.