Class 12 practice
Class 12 reasoning questions.
Reasoning questions for Class 12, at the level of students aged 15–17, each with its answer and a short explanation. Try each one before opening the answer.
A wooden cube has faces labeled with numbers 1 through 6. From one viewing angle, faces 1, 2, and 3 share a common vertex. From a second angle, faces 2, 3, and 5 share a vertex. From a third angle, faces 1, 3, and 6 share a vertex. Which number is on the face opposite to face 3?
Level 4 of 5Show the answer
Answer: 4
Faces 1, 2, 5, and 6 all share a vertex with face 3, making them adjacent to it. Because any cube face is adjacent to exactly four faces, the remaining face, 4, must be opposite.
Consider three true statements: All sitarists are vocalists. Some vocalists are mathematicians. No mathematician is a dancer. Which deduction follows with absolute logical certainty?
Level 4 of 5Show the answer
Answer: Some vocalists are not dancers.
Vocalists who are also mathematicians exist, as established by the second premise. Since no mathematician can be a dancer, those specific vocalists cannot be dancers. Hence, some vocalists are definitely not dancers.
In the addition alphametic AB + BA = CDC, each letter represents a distinct digit from 1 to 9. What is the value of the digit D?
Level 4 of 5Show the answer
Answer: 2
The maximum sum of two two-digit numbers is 198, so C is 1. The three-digit palindrome 1D1 is divisible by 11 only when D is 2.
In a group of 45 athletes, each person plays at least one sport among football, cricket, and badminton. Exactly 20 play football, 22 play cricket, and 24 play badminton. Exactly 3 athletes play all three sports. How many athletes play exactly two of these sports?
Level 4 of 5Show the answer
Answer: 15
Let x be the number playing exactly two sports. Total participations equal 45 + x + 2(3) = 66, simplifying to 51 + x = 66. Thus, x = 15.
In the addition problem AB + BA = CDC, each distinct letter represents a different single-digit positive integer from 1 to 9. The two-digit numbers AB and BA add up to the three-digit number CDC. What digit does D represent?
Level 4 of 5Show the answer
Answer: 2
The sum equals 11(A + B). Since the sum is a three-digit value under 198, C must be 1. For the palindrome 1D1 to divide by 11, the alternating digit sum (2 - D) requires D = 2.
Five runners—Aman, Bina, Charan, Diya, and Eklavya—finished a race in five distinct positions. Charan finished ahead of Aman. Diya finished behind Eklavya but ahead of Charan. Bina finished immediately behind Diya. Who finished in first place?
Level 4 of 5Show the answer
Answer: Eklavya
Eklavya finished ahead of Diya, who finished ahead of Bina, Charan, and Aman. Therefore, Eklavya is in first place, followed by Diya, Bina, Charan, and Aman.
A jeweller in Jaipur has nine identical gold coins, but one counterfeit coin is slightly lighter than the rest. Using only a two-pan balance scale, what is the minimum number of weighings guaranteed to identify the lighter coin?
Level 4 of 5Show the answer
Answer: 2
Divide the 9 coins into three groups of three. Weigh two groups to identify the lighter triplet. Then weigh two coins from that group to isolate the fake coin.
Four suspects—Aditi, Bikram, Chaya, and Danish—make the following statements about a missing medal: Aditi: "Bikram took the medal." Bikram: "Danish took the medal." Chaya: "I did not take the medal." Danish: "Bikram is lying." If exactly one suspect took the medal and exactly one statement is true, who took the medal?
Level 4 of 5Show the answer
Answer: Chaya
Bikram and Danish make contradictory statements, so exactly one of them must be telling the truth. Therefore, the single true statement is already accounted for, meaning Chaya's statement must be false. Hence, Chaya took the medal.
A box contains 12 red, 15 green, and 18 blue identical glass marbles. In a dark room, Meera blindly draws marbles one by one. What is the minimum number of marbles she must draw to guarantee having at least six marbles of each colour?
Level 4 of 5Show the answer
Answer: 39
In the worst-case scenario, Meera draws all 18 blue marbles and all 15 green marbles before drawing 6 red marbles. Therefore, she must draw 18 + 15 + 6 = 39 marbles.
On an island, every resident is either a perpetual truth-teller or a perpetual liar. You meet two residents, Kabir and Tarun. Kabir says, 'At least one of us is a liar.' Which statement must be logically true?
Level 4 of 5Show the answer
Answer: Kabir is a truth-teller and Tarun is a liar.
If Kabir were a liar, his claim would be false, making both truth-tellers, which is contradictory. Thus, Kabir tells the truth, which means Tarun must be the liar.
Pointing to a portrait, Rohan says, "The man in this portrait is the son of the only brother of my maternal grandfather's only daughter." How is the man in the portrait related to Rohan?
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Answer: Cousin
Rohan's maternal grandfather's only daughter is Rohan's mother. Her only brother is Rohan's maternal uncle. The son of Rohan's maternal uncle is Rohan's cousin.
- True or false?
Kabir flips an unbiased coin four times consecutively and observes heads on every single toss. On his fifth flip, the theoretical probability of observing heads remains exactly one in two.
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Answer: True
Successive tosses of an unbiased coin represent independent events. Prior outcomes exert zero influence on subsequent probabilities, refuting the gambler's fallacy.
- True or false?
A truth table defines the conditional proposition 'If P, then Q'. Whenever proposition P is false, the compound proposition 'If P, then Q' evaluates as true, regardless of the truth value of Q.
Level 4 of 5Show the answer
Answer: True
In classical propositional logic, a conditional statement is vacuously true whenever the antecedent is false, because an implication fails only when true implies false.
- True or false?
In any group of seven students exchanging festive greetings, the number of students who greet an odd number of peers is always an even number.
Level 4 of 5Show the answer
Answer: True
By the Handshaking Lemma from graph theory, the sum of all individual greeting counts equals twice the total greetings, an even total. Thus, students with odd counts must occur in an even quantity.
- Fill in the blank.
Using a two-pan balance scale, the minimum number of weighings guaranteed to identify one heavier counterfeit coin among nine otherwise identical coins is ___.
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Answer: 2
Splitting nine coins into three sets of three identifies the heavier group in one weighing, and weighing two remaining coins isolates the counterfeit coin.
- Fill in the blank.
At 3:40, the smaller angle formed between the hour hand and the minute hand of a standard clock measures ___ degrees.
Level 4 of 5Show the answer
Answer: 130
The minute hand points at 240°. The hour hand is at 3 × 30° + 40 × 0.5° = 110°. The difference is 240° - 110° = 130°.
Identify the natural satellite that is the odd one out in this planetary group.
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Answer: Titan
Io, Europa, and Ganymede are Galilean moons orbiting Jupiter, whereas Titan orbits Saturn.
Which is the odd one out?
Level 4 of 5Show the answer
Answer: National Human Rights Commission
The other three are constitutional bodies directly created by explicit articles of the Constitution of India. The National Human Rights Commission is a statutory body established by an ordinary Act of Parliament.
A bag contains 8 red, 10 green, and 12 blue marbles. Vikram draws marbles blindly from the bag one by one, keeping each drawn marble. What is the minimum number of marbles he must draw to be certain of having at least 4 marbles of each colour?
Level 5 of 5Show the answer
Answer: 26
In the worst-case scenario, Vikram draws all 12 blue and all 10 green marbles first. He then needs 4 red marbles to fulfill the requirement: 12 + 10 + 4 = 26 marbles.
- Fill in the blank.
To guarantee obtaining at least one marble of each colour from 8 red, 14 blue, and 18 green marbles, the minimum number one must draw is ___.
Level 5 of 5Show the answer
Answer: 33
By the pigeonhole principle, the worst case involves drawing all 18 green and all 14 blue marbles before any red marble appears. Drawing one more marble (18 + 14 + 1 = 33) guarantees all three colours.
These questions come from Ado’s question bank and are written with AI help. They are never used in ranked play, so practising them here can’t change anyone’s rank.
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