Staff Selection Commission Combined Graduate Level Exam
Question : What will be the value of $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$?
Option 1: $\frac{1}{\sqrt{2}}$
Option 2: $\sqrt{3}$
Option 3: $1$
Option 4: $\frac{1}{\sqrt{3}}$
Correct Answer: $1$
Solution : Given: $\frac{\sin 30^{\circ} \sin 40^{\circ} \sin 50^{\circ} \sin 60^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\sin (90^{\circ}-60^{\circ}) \sin (90^{\circ}-50^{\circ}) \sin (90^{\circ}-40^{\circ}) \sin (90^{\circ}-30^{\circ})}{\cos 30^{\circ} \cos 40^{\circ} \cos 50^{\circ} \cos 60^{\circ}}$ = $\frac{\cos 60^{\circ} \cos 50^{\circ} \cos 40^{\circ} \cos 30^{\circ}}{\cos 30^{\circ} \cos 40^{\circ} \cos
Question : A is twice as fast as B and B is thrice as fast as C. The journey covered by C in $1\frac{1}{2}$ hour will be covered by A in:
Option 1: 15 minutes
Option 2: 30 minutes
Option 3: 1 hour
Option 4: 10 minutes
Correct Answer: 15 minutes
Solution : Given: A is twice as fast as B and B is thrice as fast as C. The journey is covered by C in $1\frac{1}{2}$ hour. Let the speed of C be $x$ metre/min. So, the speed of B will be $3x$ metre/min. And the
Question : Which of the following chemicals is used as a preservative to slow browning and discolouration in foods and beverages during preparation, storage, and distribution?
Option 1: Nitrous oxide
Option 2: Phosgene
Option 3: Sulphites
Option 4: Chlorine
Correct Answer: Sulphites
Solution : The correct answer is Sulphites.
Sulphites is a sulphur-containing compound that has been used for centuries to prevent discolouration and slow browning during the storage and distribution of many foods. When some fruits are cut, the exposure of the flesh to oxygen results in
Question : A, B and C together can complete a work in 12 days. A and B alone can do the same work in 36 days. In how many days can C alone complete the same work?
Option 1: 48
Option 2: 25
Option 3: 12
Option 4: 36
Correct Answer: 36
Solution : Given: A and B alone can do the same work in 36 days. Let the total work = LCM of (12, 36, 36) = 36 units Efficiency of A $=\frac{36}{36} = 1$ unit per day Efficiency of B $=\frac{36}{36} = 1$ unit per day Efficiency
Question : Direction: Select the missing number from the given responses.
Option 1: 14
Option 2: 16
Option 3: 21
Option 4: 22
Correct Answer: 16
Solution : Given:
The middle number in a row is the product of the first number and the square root of the third number.
In row 1, the square root of 4 = 2 and 14 = 7
Question : G is the centroid of the equilateral triangle ABC. If AB = 10 cm, then the length of AG (in cm) is:
Option 1: $\frac{5 \sqrt3}{3}$
Option 2: $\frac{10 \sqrt3}{3}$
Option 3: $5 \sqrt3$
Option 4: $10\sqrt 3$
Correct Answer: $\frac{10 \sqrt3}{3}$
Solution : AB = 10cm Since AD is the perpendicular bisector of BC, ⇒ BD = 5cm and $\angle$ADB = 90° ⇒ AD = $\sqrt{\text{AB}^{2}-\text{BD}^{2}}$ = $\sqrt{10^{2}-5^{2}}$ = $\sqrt{75}$ = $5\sqrt{3}$ cm Since G is the centroid, AG : GD = 2 : 1 ⇒ AG
Question : If $(\sin \theta+\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=k+\tan ^2 \theta+\cot ^2 \theta$, then the value of $k$ is equal to:
Option 1: 7
Option 2: 2
Option 3: 5
Option 4: 9
Correct Answer: 7
Solution : Given: $(\sin \theta+\operatorname{cosec} \theta)^2+(\cos \theta+\sec \theta)^2=k+\tan ^2 \theta+\cot ^2 \theta$ ⇒ $\sin^{2}θ + 2\sinθ\operatorname{cosec}θ + \operatorname{cosec}^{2}θ +\cos^{2}θ + 2\cos θ \secθ + \sec^{2}θ=k+\tan ^2 \theta+\cot ^2 \theta$ ⇒ $k = \sin^{2}θ + \operatorname{cosec}^{2}θ + \cos^{2}θ+\sec^{2}θ + 2(1+1) - \tan ^2 \theta-\cot ^2 \theta$ ⇒ $k
Question : The following table shows the production of different types of two-wheelers from 1993 to 1998. Number of two-wheelers (in 1000s)
What is the percentage increase in the total production of all types of two-wheelers in 1998 in comparison to 1996 (rounded off to the nearest integer)?
Option 1: 27%
Option 2: 25%
Option 3: 24%
Option 4: 26%
Correct Answer: 25%
Solution : Percentage increase in the total production of all types of two-wheelers in 1998 in comparison to 1996 = $\frac{334-268}{268}×100$ = 24.63% $\approx$ 25% Hence, the correct answer is 25%.
Question : Select the correct active form of the given sentence. Her wooden almirah has been destroyed by the termites.
Option 1: The termites destroyed her wooden almirah.
Option 2: The termites could destroy her wooden almirah.
Option 3: The termites had destroyed her wooden almirah.
Option 4: The termites have destroyed her wooden almirah.
Correct Answer: The termites have destroyed her wooden almirah.
Solution : The correct choice is the fourth option.
Active voice emphasises the doer of the action, while passive voice emphasises the receiver. To convert passive to active, we make the subject perform the action and rephrase the verb.
The structure
Question : Ram can copy 60 pages in 15 hours. If Ram and Riya together can copy 180 pages in 30 hours, in how many hours can Riya copy 20 pages?
Option 1: 29 hours
Option 2: 12 hours
Option 3: 20 hours
Option 4: 10 hours
Correct Answer: 10 hours
Solution : Given: Ram can copy 60 pages in 15 hours. Total pages = Pages per hour × Time Ram's rate is $\frac{60}{15} = 4$ pages per hour. Together, Ram and Riya can copy 180 pages in 30 hours. So, their combined rate (Ram + Riya)
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