Staff Selection Commission Combined Graduate Level Exam
Question : If $\cos \theta=\frac{\sqrt{3}}{2}$, then $\tan ^2 \theta \cos ^2 \theta=?$
Option 1: $\frac{1}{\sqrt{3}}$
Option 2: $\frac{1}{4}$
Option 3: $\frac{1}{2}$
Option 4: $\sqrt{3}$
Correct Answer: $\frac{1}{4}$
Solution : We have, $\cos \theta = \frac{\sqrt{3}}{2}$ ⇒ $\cos \theta = \cos 30^\circ$ ⇒ $\theta = 30^\circ$ Now, $\tan^2 \theta \cos^2 \theta=\tan^2 30^\circ \cos^2 30^\circ= (\frac{1}{\sqrt3})^2 ×(\frac{\sqrt{3}}{2})^2$ $= \frac{1}{4}$ Hence, the correct answer is $\frac{1}{4}$.
Question : A man can cover a certain distance in 3 hours and 36 minutes if he walks at a rate of 5 km/h. If he covers the same distance on a bicycle at a rate of 24 km/h, then the time taken by him in minutes is:
Option 1: 40
Option 2: 45
Option 3: 50
Option 4: 55
Correct Answer: 45
Solution : Let the time taken by him on a bicycle be $x$ hour. Distance covered by him by walking = $5×3\frac{36}{60}=5×\frac{18}{5}=18$ km. Distance covered by him on the bicycle = 24$x$ km. According to the question, 24$x$ = 18 ⇒ $x = \frac{18}{24}$ hour = $\frac{18}{24}×60$
Question : Shiva’s monthly salary is Rs.75,000. He spends Rs.12,000 on household items, Rs.14,000 on LIC and mutual funds, Rs.15,000 on his children’s education, and keeps Rs.10,000 for miscellaneous expenses. His savings are Rs.21,000 per month and he donates the rest of the amount to an orphanage. The percentage of his income that he donates is:
Option 1: 3%
Option 2: 6%
Option 3: 8%
Option 4: 4%
Correct Answer: 4%
Solution : Percentage Donated = $\frac{\text{Amount Donated}}{\text{Total Income}}\times 100$ First, let's calculate the total expenses: Total Expenses = Household items + LIC and mutual funds + Children's education + Miscellaneous expenses Total Expenses = Rs. 12,000 + Rs. 14,000 + Rs. 15,000 + Rs. 10,000 = Rs.
Question : Select the option that contains a grammatical error in the underlined portion.
When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Option 1: When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Option 2: When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Option 3: When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Option 4: When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Correct Answer: When Mrs. Sinha came to see Varanasi in 2019, Nupur has already been teaching there for five years.
Solution : The correct choice is the second option.
The past perfect tense "had already been teaching" should have been used as it indicates an action that was completed before
Question : Match the columns (As per Census 2011).
Option 1: 1-a, 2-b, 3-c
Option 2: 1-b, 2-a, 3-c
Option 3: 1-a, 2-c, 3-b
Option 4: 1-c, 2-b, 3-a
Correct Answer: 1-a, 2-b, 3-c
Solution : The correct answer is 1-a, 2-b, 3-c.
Kerala - a. Highest sex ratio. The sex ratio of Kerala is 1084, one of the highest sex ratios in India whereas 943 is the sex ratio of India.
Haryana - b. Lowest sex ratio. Haryana
Question : In an examination, the average marks obtained by John in English, Maths, Hindi and Drawing were 50. His average marks in Maths, Science, Social Studies and Craft were 70. If the average marks in all seven subjects are 58, his score in Maths is:
Option 1: 50
Option 2: 52
Option 3: 60
Option 4: 74
Correct Answer: 74
Solution : Given: The average marks of John in English, Maths, Hindi and Drawing = 50 $\therefore$ The sum of marks in English, Maths, Hindi and Drawing = 50 × 4 = 200 The average marks in Maths, Science, Social Studies and Craft = 70 $\therefore$ The
Question : Directions: Select the correct combination of mathematical signs to sequentially replace the * signs and to balance the given equation. 25 * 82 * 12 * 6 * 8 * 91
Option 1: –, ×, +, ÷, =
Option 2: ÷, +, –, ×, =
Option 3: +, –, ÷, ×, =
Option 4: ×, +, ÷, –, =
Correct Answer: +, –, ÷, ×, =
Solution : Given: 25 * 82 * 12 * 6 * 8 * 91
Replace the * sign given in the equation with the assigned signs in the options one by one – First option: –, ×, +, ÷, = 25 – 82
Question : Lake Kolleru is situated in which of the following states?
Option 1: Andhra Pradesh
Option 2: Tamil Nadu
Option 3: Karnataka
Option 4: Kerala
Correct Answer: Andhra Pradesh
Solution : The correct option is Andhra Pradesh.
The location of Lake Kolleru is in Andhra Pradesh State. Situated in Andhra Pradesh between the districts of Krishna and West Godavari, it is one of the biggest freshwater lakes in the nation. It is designated as
Question : The Sundarbans or the 'Mangrove' forests are found in
Option 1: Kutch Peninsula
Option 2: Western Ghats
Option 3: Konkan Coast
Option 4: Deltaic West Bengal
Correct Answer: Deltaic West Bengal
Solution : The correct option is - Deltaic West Bengal.
One of the biggest forests in the world, the Sundarbans mangrove forest is located on the Bay of Bengal's Ganges, Brahmaputra, and Meghna river deltas. The region that comprises 40% of the area is in
Question : The volume of a cylinder is 4312 cm3. Its curved surface area is one-third of its total surface area. Its curved surface area (in cm2) is: (Take $\pi=\frac{22}{7}$ )
Option 1: 572 cm2
Option 2: 528 cm2
Option 3: 660 cm2
Option 4: 616 cm2
Correct Answer: 616 cm2
Solution : According to the question, Curved surface area = $\frac{\text{Total surface area}}{3}$ ⇒ $2\pi rh = \frac{2\pi r(h + r)}{3}$ ⇒ $3h = (h + r)$ ⇒ $2h = r$ Now, The volume of a cylinder = 4312 cm3 ⇒ $\pi r^2h =
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