GS: Hindi / English · Language questions stay in their original language.
150 questions · 150 marks · 2 hours 30 minutes
Choose one option per question.
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Correct answer: (B) 3 minutes 16 seconds
The area of the square is 60025, so the side is 245 m and the perimeter 980 m. 18 km/hr = 5 m/s, so the time = 980 ÷ 5 = 196 seconds, that is 3 minutes 16 seconds.
Correct answer: (E) None of the above
Two cards were taken out and thrown away unseen, so we learnt nothing new about the 50 that remain. In such a case the probability that a card drawn is an ace stays what it was at the start—4/52 = 1/13. That value is not among the options.
आयोग की उत्तर-कुंजी में (C) 9/50 दिया गया है, जो तब बनता है जब फेंके गए दोनों पत्तों के बारे में कोई शर्त मान ली जाए। प्रश्न में ऐसी कोई शर्त नहीं है, इसलिए समरूपता से उत्तर 1/13 बनता है और कोई विकल्प सही नहीं है।
Correct answer: (B) cos² A − sin² B
cos(A + B) cos(A − B) = (cos A cos B)² − (sin A sin B)². Putting cos²B = 1 − sin²B and sin²A = 1 − cos²A and simplifying gives cos²A − sin²B.
Correct answer: (C) 8√3 m
From the level of the window the top of the flag is 6 tan 60° = 6√3 m up and its base 6 tan 30° = 2√3 m down. The whole height of the flag is the sum, 8√3 m.
Correct answer: (C) 48 cm
The area of a rhombus = ½ × product of the diagonals. From 480 = ½ × 20 × d, d = 48 cm.
Correct answer: (E) None of the above
Going the same way, the relative speed gives 8(u − v) = 240, that is u − v = 30. Coming towards each other, 2(u + v) = 240, that is u + v = 120. Solving gives the speeds as 75 and 45 km/hr, which are not among the options.
Correct answer: (A) 26
The class marks are 5, 15, 25, 35, 45 and the frequencies 6, 10, 9, 4, 11. The products add to 1040 and the total frequency is 40, so the mean = 1040 ÷ 40 = 26.
Correct answer: (A) 27
The empirical relation is mode = 3 × median − 2 × mean. Here 3 × 26 − 2 × 25·5 = 78 − 51 = 27.
Correct answer: (B) tan 3θ
sin θ + sin 5θ = 2 sin 3θ cos 2θ and cos θ + cos 5θ = 2 cos 3θ cos 2θ. Adding the middle terms, the numerator = sin 3θ (2cos 2θ + 1) and the denominator = cos 3θ (2cos 2θ + 1). The common factor cancels and tan 3θ is left.
Correct answer: (C) 2:1
The volume of a cone is (1/3)πr²h and of a hemisphere (2/3)πr³. Setting them equal gives h = 2r. The height of a hemisphere is its own radius r, so the ratio is 2r : r = 2 : 1.
Correct answer: (E) None of the above
For two lenses set apart the combined power is P = P₁ + P₂ − d·P₁·P₂, with d in metres. Here P = 5 + 4 − 0·1 × 20 = 7 dioptres, so the focal length = 1/7 metre ≈ 14·3 cm—which is not among the options.
कुंजी में (B) 9.09 सेमी दिया गया है, जो 11 डाइऑप्टर से बनता है—यानी दूरी वाला पद जोड़ने पर, घटाने पर नहीं। सूत्र में वह पद ऋणात्मक होता है, इसलिए सही मान 14.3 सेमी के लगभग है।
Correct answer: (B) 1 A
In an ideal transformer the input and output power are equal: 220 × Iₚ = 110 × 2, so the current in the primary is 1 ampere.
Correct answer: (B) momentum of the charged particle
The path of a charged particle in a magnetic field has r = mv/qB. Here mv is the momentum, so the radius is proportional to the momentum—while it is inversely proportional to the field and the charge.
Correct answer: (C) T² ∝ R^(7/2)
Set the gravitational force equal to the centripetal force: R^(−5/2) ∝ v²/R, so v² ∝ R^(−3/2). Then from T = 2πR/v, T² ∝ R²/v² ∝ R² × R^(3/2) = R^(7/2).
Correct answer: (A) circular path
When the velocity is wholly perpendicular to the magnetic field, the force stays perpendicular to the velocity and only turns it—so the proton follows a circular path. Entering at an angle, the path would be helical.
Correct answer: (A) temperature
Resistivity is a property of the material—it does not depend on the length or the cross-section of the conductor, but it does change with temperature.
Correct answer: (A) displacement
On a velocity–time graph the area = velocity × time, which gives the displacement. The slope gives the acceleration.
Correct answer: (C) < 1 Ω
To get the least resistance all are joined in parallel, and the resistance of a parallel combination is less than the smallest of them. The smallest here is 1 Ω, so the answer is less than 1 Ω.
Correct answer: (C) due to the presence of protons
The nucleus holds protons and neutrons. Neutrons are neutral, so the positive charge of the nucleus is due to the protons.
Correct answer: (A) Work done/(Current × Time)
Potential difference = work done ÷ charge, and charge = current × time. So voltage = work done ÷ (current × time).
Correct answer: (A) first increases, then decreases
The eye is most sensitive to greenish-yellow light, about 555 nm. Going from violet towards red the luminosity first rises, reaches its maximum there, and then falls.
Correct answer: (E) None of the above
Light bending by a small fixed angle is refraction, which is not among the options. In diffraction light spreads, in dispersion the colours separate and in interference fringes form—none of them fits.
Correct answer: (C) Both will reach simultaneously
For bullets fired horizontally the falling depends only on gravity, and the initial vertical speed of both is zero. So however their speeds differ, both reach the ground at the same time.
Correct answer: (C) doubled
The centripetal acceleration is a = v²/r. Doubling both the speed and the radius gives (2v)²/(2r) = 2v²/r, so the acceleration is doubled.
Correct answer: (C) 2Na + 2H₂O → 2NaOH + H₂
In 2Na + 2H₂O → 2NaOH + H₂ the sodium displaces the hydrogen of the water, so it is a displacement reaction. The first is decomposition and the second combination.
Correct answer: (D) More than one of the above
Carbon has four electrons in its outermost shell, and making C⁴⁺ or C⁴⁻ would take a great deal of energy—so it shares electrons to complete its octet. All three reasons hold, so the answer is ‘more than one’.
Correct answer: (C) weak acid and strong base
Sodium carbonate is the salt of a weak acid (carbonic acid) and a strong base (sodium hydroxide). Dissolved in water it gives a basic solution.
Correct answer: (C) benzene hexachloride
In sunlight chlorine adds on to benzene and gives C₆H₆Cl₆, that is benzene hexachloride. Chlorobenzene forms when the reaction is a substitution in the presence of a catalyst.
Correct answer: (B) decomposition process
On heating, limestone breaks into two substances—calcium oxide and carbon dioxide. So it is a decomposition reaction.
Correct answer: (B) HCl
Eggshell holds calcium carbonate. An acid poured on it gives off carbon dioxide, which turns limewater milky—so the solution is HCl. NaCl and LiCl are salts and give no such gas.
Correct answer: (E) None of the above
10 mL of NaOH needs 8 mL of HCl, so twice the NaOH needs twice the acid—16 mL—which is not among the options given.
Correct answer: (C) sodium bicarbonate solution
pH paper turning blue means the solution is basic. Only the sodium bicarbonate solution is basic; lemon juice is acidic and distilled water neutral.
Correct answer: (B) Oxalic acid
Tomato holds oxalic acid. Lemon and orange have citric acid and curd lactic acid.
Correct answer: (C) washing soda
Na₂CO₃ · 10H₂O is washing soda. Baking soda is NaHCO₃.
Correct answer: (B) the symbol for the acid dissociation constant at logarithmic scale
pKₐ is the negative logarithm of the acid dissociation constant Kₐ. The lower the pKₐ, the stronger the acid.
Correct answer: (C) Na₃VO₄
Colour comes of unpaired electrons in the d orbital. In Na₃VO₄ the vanadium is in the +5 state with an empty d orbital, so it is colourless. VCl₃ and VOSO₄ keep unpaired electrons and so are coloured.
Correct answer: (D) More than one of the above
German silver is an alloy of copper, zinc and nickel—all three are in it, so the answer is ‘more than one’. It holds no silver at all.
Correct answer: (D) More than one of the above
Kolbe's electrolytic method is applied to the sodium or potassium salts of carboxylic acids. More than one of the substances given is such a salt, so the answer is ‘more than one’.
Correct answer: (C) chloroplast
In the cells of a leaf photosynthesis takes place in the chloroplast, since the chlorophyll is there.
Correct answer: (C) peristaltic movement
The wave-like contraction and expansion of the wall of the food pipe is called peristaltic movement; it is what pushes the food along.
Correct answer: (B) ureter
The tube joining the kidney to the urinary bladder is the ureter. The urethra is the passage out of the bladder.
Correct answer: (C) 6.5–7.5
Freshwater plants and animals thrive only in nearly neutral water, so a pH range of 6·5–7·5 suits them best. Water much more acidic or much more alkaline harms them.
Correct answer: (C) chloroplast changes to chromoplast
An unripe fruit holds chloroplasts, which turn into chromoplasts as it ripens. The green then gives way to yellow, orange or red.
Correct answer: (A) food vacuole
Amoeba surrounds its food with pseudopodia and encloses it in a food vacuole, and the digestion happens inside that, by enzymes.
Correct answer: (B) They help in the process of cell division
The vacuole stores toxic wastes and keeps the cell turgid by filling with water—those are its work. It has no part in cell division.
Correct answer: (A) nerve cells
The nodes of Ranvier are the gaps in the myelin sheath along the axon of a nerve cell. They let the nerve impulse leap along and travel fast.
Correct answer: (A) Archaeopteryx
Archaeopteryx shows the feathers of birds together with the teeth and tail of reptiles, which is why it is called the link between the two classes.
Correct answer: (B) RNA-containing arbovirus
Dengue is caused by an RNA-containing arbovirus, spread by the bite of the Aedes mosquito.
Correct answer: (C) just inside the vascular cambium
Secondary xylem is formed inwards from the vascular cambium, so the youngest xylem lies just inside the cambium and the older is left further in.
Correct answer: (A) Excretion
In the cockroach the Malpighian tubules do the work of excretion—they filter nitrogenous waste from the blood and send it out as uric acid.