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120 questions · 120 marks · 2 hours
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Correct answer: (E) None of the above
Turn (4/3)⁻⁸ over: it equals (3/4)⁸. The left side is then (3/4)⁻⁶ × (3/4)⁸ = (3/4)², so n = 2. There is no 2 among the options, so the answer is ‘None of the above’.
Correct answer: (A) 1/6
4⁻¹ + 8⁻¹ = 1/4 + 1/8 = 3/8. And (3/2)⁻² = (2/3)² = 4/9, so 1/(3/2)⁻² = 9/4. Then (3/8) ÷ (9/4) = (3/8) × (4/9) = 1/6.
Correct answer: (B) 8 : 6 : 10 : 9
Simplify each ratio: A : B = 1/2 : 3/8 = 4 : 3, B : C = 1/3 : 5/9 = 3 : 5 and C : D = 5/6 : 3/4 = 10 : 9. The first two give A : B : C = 4 : 3 : 5. To raise C from 5 to 10 multiply throughout by 2—8 : 6 : 10—and then D = 9. So A : B : C : D = 8 : 6 : 10 : 9.
Correct answer: (B) ₹3,400 and ₹2,200
The payment is shared in the ratio of the work done, and the rate of work is inversely proportional to the days: Suresh : Shashi = 1/11 : 1/17 = 17 : 11. Dividing 28 parts, Suresh gets 17 and Shashi 11—that is ₹3,400 and ₹2,200.
Correct answer: (A) 160
A is 25% of B and 40% of C, so 0·25B = 0·40C. That gives B = 1·6C, so B's weight is 160% of C's.
Correct answer: (E) None of the above
The volume of the sphere = (4/3)πr³ = (4/3)π(3)³ = 36π cm³, and the wire has the same volume, so πr² × length = 36π. Putting the length given and working out the radius gives a diameter of 0·2 cm, which matches none of the options.
Correct answer: (B) 10 cm and 4 cm
For circles touching internally the distance between the centres is R − r, so R − r = 6. From the sum of the areas, R² + r² = 116. Since (R − r)² = R² − 2Rr + r², 36 = 116 − 2Rr, so Rr = 40. Putting R = r + 6 gives r² + 6r − 40 = 0, so r = 4 and R = 10 cm.
Correct answer: (A) 50 km/hr and 40 km/hr
Take the slow train's speed as v, so the fast train's is v + 10. From 600/v − 600/(v + 10) = 3 we get 6000 = 3v² + 30v, that is v² + 10v − 2000 = 0, giving v = 40. So the speeds are 40 and 50 km/hr.
Correct answer: (B) 1/3
Add the three equations: 2(1/x + 1/y + 1/z) = 8 + 12 + 10 = 30, so 1/x + 1/y + 1/z = 15. Take the second equation (1/y + 1/z = 12) from it: 1/x = 3, that is x = 1/3.
Correct answer: (A) ₹3,972
A 50% rise in 5 years under simple interest means the rate is 50 ÷ 5 = 10% a year. At that rate the compound interest for 3 years = P[(1·1)³ − 1] = 0·331P, which on the given principal is ₹3,972.
Correct answer: (B) 380
Of the candidates 37½% were girls and the remaining 62½% boys. Those who passed were 75% of the boys and 62½% of the girls, so about 70·3% of the whole; the rest failed, and working it out gives 380 boys.
Correct answer: (B) −2/6, 2/6
−2/6 = −1/3, which is greater than −2/3, and 2/6 = 1/3, which is less than 1/2. So both numbers lie between −2/3 and 1/2.
Correct answer: (B) 25 years
Take the son's age as s, so the father's is 5s. After 15 years: 5s + 15 = 2(s + 15), that is 3s = 15 and s = 5. So the father is now 5 × 5 = 25 years old.
Correct answer: (C) 20%
Two lemons for ₹1 makes the cost ₹0·50 a lemon; five for ₹3 makes the selling price ₹0·60 a lemon. The profit is ₹0·10, so the profit per cent = (0·10 ÷ 0·50) × 100 = 20%.
Correct answer: (C) 75
By the set formula the percentage taking both = 50·8 + 64·2 − 100 = 15%. Fifteen per cent of the given total comes to 75 students.
Correct answer: (B) 1
Multiplying powers of the same base adds the indices: a(b − c) + b(c − a) + c(a − b) = ab − ac + bc − ab + ca − cb = 0. So the expression equals x⁰ = 1.
Correct answer: (B) At a fixed height
A geostationary satellite must go round once in 24 hours, together with the Earth, and that is possible only at one fixed height—about 36,000 km above the equator.
Correct answer: (C) Violet
In a prism the colour of the shortest wavelength bends the most. Violet has the shortest wavelength, so its deviation is the greatest.
Correct answer: (E) None of the above
Carrying an open umbrella, standing under a lone tall tree and standing in an open field are all dangerous in a storm, since each makes you the tallest thing about. The safe course is to stay inside a solid building or a closed vehicle, which is not among the options.
Correct answer: (C) Remains constant
In free fall the potential energy falls and just as much kinetic energy is gained. Without friction their sum, the total mechanical energy, stays constant—that is the law of conservation of energy.
Correct answer: (B) Cornea
In eye donation it is the donor's cornea that is transplanted, not the whole eye. Blindness caused by a clouded cornea is cured in this way.
Correct answer: (B) Cobalamin
The chemical name of vitamin B₁₂ is cobalamin, which holds the metal cobalt. Thiamin is B₁ and niacin B₃.
Correct answer: (B) Turmeric
Turmeric is a natural acid-base indicator—its yellow turns red on meeting a base. Vinegar is itself an acid and baking soda a base.
Correct answer: (A) Organic matter
When the soil is too basic, organic matter such as rotted manure or compost is added; as it decays it releases acids and brings the pH down. Quicklime would only make it more basic.
Correct answer: (C) −459.4 °F
Absolute zero is −273·15 °C. Using F = (9/5)C + 32: (9/5)(−273·15) + 32 ≈ −459·4 °F.
Correct answer: (D) More than one of the above
Light waves are electromagnetic, and their vibration is at right angles to the direction of travel, so they are transverse as well. Both statements holding, the answer is ‘more than one’.
Correct answer: (B) Less than 7
A salt of a strong acid and a weak base, such as ammonium chloride, gives an acidic solution on hydrolysis, so its pH is below 7.
Correct answer: (B) 1024 MB
In computing the units go up in multiples of 1024: 1 KB = 1024 bytes, 1 MB = 1024 KB and 1 GB = 1024 MB.
Correct answer: (A) Neutralization
An acid and a base together give a salt and water—that is a neutralisation reaction. Here NaOH + HCl → NaCl + H₂O.
Correct answer: (B) Glucose
In cellular respiration glucose is the first thing used for energy; it is broken down to make ATP. Fatty acids and amino acids come later.
Correct answer: (D) More than one of the above
The pituitary is called the master gland, since besides secreting the growth hormone it controls the other endocrine glands—from the development of the sex organs to metabolism. So more than one of the functions is right.
Correct answer: (E) None of the above
Blood pressure is controlled by the medulla oblongata, a part of the hindbrain. None of the options gives that alone, so the answer is ‘None of the above’.
Correct answer: (B) Britain
India announced a Net Zero Innovation Virtual Centre in collaboration with Britain, for shared research on clean energy.
Correct answer: (B) 1272
The new Parliament building seats 888 in the Lok Sabha chamber and 384 in the Rajya Sabha chamber; for a joint sitting the Lok Sabha chamber can hold 1,272 members in all.
Correct answer: (C) DigiClaim Platform
For settling the insurance claims of farmers the government launched the ‘DigiClaim’ platform, through which the money goes straight into the farmer's account.
Correct answer: (A) Amit Kshatriya
Amit Kshatriya, of Indian origin, was appointed head of NASA's ‘Moon to Mars’ programme.
Correct answer: (B) 50
By the Bihar Prohibition and Excise (Amendment) Act, 2022, a vehicle caught carrying liquor may be released on paying the prescribed penalty, the limit of which is set at 50.
Correct answer: (B) China
The C919 passenger plane was built by China, to compete with Airbus and Boeing.
Correct answer: (A) Weightlifting
Kriti Raj Singh is a sportswoman of weightlifting.
Correct answer: (A) Siwan
In the Industrial Development Ranking 2022 of the Bihar Industries Department, Siwan district stood first.
Correct answer: (B) Writ
For the enforcement of the Fundamental Rights a court issues a writ—habeas corpus, mandamus, prohibition, certiorari or quo warranto. A decree is passed in a civil suit and an ordinance issued by the executive.
Correct answer: (D) More than one of the above
There is more than one dam on the Mahanadi and its tributaries—Hirakud is the best known, and Dudhawa and Ghumarapadar are on the same system. So more than one option is correct.
Correct answer: (B) Jerusalem
The Al-Aqsa Mosque stands in the old city of Jerusalem and is counted the third holiest site of Islam.
Correct answer: (D) More than one of the above
Belgium, Canada and Denmark were all founder members of NATO in 1949, so more than one option is correct.
Correct answer: (B) G-20
‘One Earth, One Family, One Future’ was the motto of India's G-20 presidency, taken from the Sanskrit ‘Vasudhaiva Kutumbakam’.
Correct answer: (D) More than one of the above
The Quad is a strategic forum of India, the United States, Japan and Australia; its beginning is traced to the cooperation that followed the tsunami of 2004, and its purpose is to keep a free order in the Indo-Pacific. More than one statement is correct.
Correct answer: (C) Takshashila
Kautilya, or Chanakya, was a teacher of political science and economics at the university of Takshashila, where he taught Chandragupta Maurya.
Correct answer: (A) It was an uprising by the Zamindars.
The Bihar revolt of 1781 was a rising of the zamindars, against the raised revenue and the Company's interference.
Correct answer: (D) More than one of the above
The frigid zones are the belts from 66½° N to the North Pole and from 66½° S to the South Pole. Both of those lie in the frigid zone, so more than one option is correct.
Correct answer: (A) Kumaon Himalayas
The Himalaya between the Satluj and the Kali is called the Kumaon Himalaya. From the Kali to the Teesta is the Nepal Himalaya and from the Teesta to the Dihang the Assam Himalaya.