Staff Selection Commission Combined Graduate Level Exam
Question : What is the diameter (in cm) of a sphere with a surface area of 6.16 sq. cm?
Option 1: 1.4
Option 2: 0.7
Option 3: 2.8
Option 4: 2.1
Correct Answer: 1.4
Solution : Let the radius be $r$. The total surface area of a sphere = $4\pi r^2$ ⇒ $6.16=4\pi r^2$ ⇒ $6.16=4×\frac{22}{7}×r^2$ ⇒ $r^2=\frac{49}{100}$ $\therefore r=0.7$ cm Diameter = $2×r=2×0.7=1.4$ cm Hence, the correct answer is 1.4.
Question : Which of the following states organises 'Lokrang', a five-day festival, beginning every year on 26 January?
Option 1: Arunachal Pradesh
Option 2: Himachal Pradesh
Option 3: Madhya Pradesh
Option 4: Uttar Pradesh
Correct Answer: Madhya Pradesh
Solution : The correct option is Madhya Pradesh.
The state that organises Lokrang, a five-day festival beginning every year on 26 January, is Madhya Pradesh. Lokrang is a cultural festival that celebrates the diverse folk traditions and art forms of India. It showcases a vibrant array
Question : Select the most appropriate meaning of the given idiom.
Go back to the drawing board.
Option 1: Mediate a task.
Option 2: Accomplish a task.
Option 3: Start over.
Option 4: Leave a work.
Correct Answer: Start over.
Solution : The correct choice is the third option.
This idiom means to start a task or project over from the beginning, often because the previous attempt was not successful or needs significant revision.
Question : What is the full form of DNA?
Option 1: Diribo nuclei acid
Option 2: Di nucleic acid
Option 3: Dual nitrogen acid
Option 4: Deoxyribonucleic acid
Correct Answer: Deoxyribonucleic acid
Solution : The correct option is Deoxyribonucleic acid
DNA, or deoxyribonucleic acid, is a complex molecule that contains the genetic information required for all known living species to grow, develop, function and reproduce. It has a double helix structure composed of a unique sequence of
Question : Directions: Which of the following numbers will replace the question mark (?) in the given series? 108, 99, 88, ?, 60, 43
Option 1: 76
Option 2: 75
Option 3: 78
Option 4: 77
Correct Answer: 75
Solution : Given: 108, 99, 88, ?, 60, 43
In the above-given series, subtract consecutive odd numbers (starting from 9) – 108 – 9 = 99; 99 – 11 = 88; 88 – 13 = 75; 75 – 15 = 60; 60 – 17 = 43
So,
Question : ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm. What is the ratio of the radius of the circle inscribed in it to the radius of the circle circumscribing $\triangle ABC$?
Option 1: $6–\sqrt{2}: 3 \sqrt{2}$
Option 2: $2–\sqrt{2}: \sqrt{2}$
Option 3: $6–3 \sqrt{2}: 1 \sqrt{2}$
Option 4: $6–3 \sqrt{2}: 6 \sqrt{2}$
Correct Answer: $2–\sqrt{2}: \sqrt{2}$
Solution : Given: ABC is an isosceles right-angle triangle. $\angle ABC = 90 ^{\circ}$ and AB = 12 cm. In $\triangle ABC$, $H^2=B^2+P^2$ (Using Pythagoras theorem). ⇒ $H^2=12^2+12^2$ ⇒ $H^2=144+144=288$ ⇒ $H=\sqrt{288}=12\sqrt2$ cm Inradius of inscribed circle of right angled triangle = $\frac{(P + B –
Question : Directions: Study the given pattern carefully and select the number that can replace the question mark (?) in it. (NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding/subtracting/multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.) (2, 2, 4); (1, 6, 6); (7, 2, ?)
Option 1: 14
Option 2: 2
Option 3: 7
Option 4: 12
Correct Answer: 14
Solution : Given: (2, 2, 4); (1, 6, 6); (7, 2, ?)
Like, (2, 2, 4)→2 × 2 = 4 (1, 6, 6)→1 × 6 = 6 Similarly, (7, 2, ?)→7 × 2 = 14
So, 14 is the required answer. Hence, the first option is correct.
Question : What is the value of $\frac{7}{2}+\frac{11}{3}+\frac{7}{6}+\frac{11}{15}+\frac{7}{12}+\frac{11}{35}+\ldots \ldots+\frac{7}{156}+\frac{11}{575}$?
Option 1: $\frac{3917}{355}$
Option 2: $\frac{3816}{325}$
Option 3: $\frac{3714}{345}$
Option 4: $\frac{3216}{315}$
Correct Answer: $\frac{3816}{325}$
Solution : Given: The series is $\frac{7}{2}+\frac{11}{3}+\frac{7}{6}+\frac{11}{15}+\frac{7}{12}+\frac{11}{35}+\ldots \ldots+\frac{7}{156}+\frac{11}{575}$. Determine the value of the series by solving two distinct series independently. The sum of the first series = $\frac{7}{2}+\frac{7}{6}+\frac{7}{12}+...+\frac{7}{156}$ ⇒ Sum = $7[1–(\frac{1}{2})+(\frac{1}{2}–\frac{1}{3})+(\frac{1}{3}–\frac{1}{4})+...+(\frac{1}{12}–\frac{1}{13})]$ ⇒ Sum = $7[1–\frac{1}{13}]$ ⇒ Sum = $7\times\frac{12}{13}=\frac{84}{13}$ The sum of the second series =
Question : If $x+\left [\frac{1}{(x+7)}\right]=0$, what is the value of $x-\left [\frac{1}{(x+7)}\right]$?
Option 1: $3\sqrt{5}$
Option 2: $3\sqrt{5}-7$
Option 3: $3\sqrt{5}+7$
Option 4: $8$
Correct Answer: $3\sqrt{5}-7$
Solution : Given: $x+[\frac{1}{(x+7)}]=0$ Adding both sides 7, we get, ⇒ $x+7+[\frac{1}{(x+7)}]=7$ Squaring both sides, we get, ⇒ $(x+7)^{2}+(\frac{1}{x+7})^{2}+2=49$ ⇒ $(x+7)^{2}+(\frac{1}{x+7})^{2}=47$ Subtracting 2 from both sides, $(x+7)^{2}+(\frac{1}{x+7})^{2}–2=47-2$ ⇒ $[(x+7)-(\frac{1}{x+7})]^{2}=45$ ⇒ $[(x+7)-(\frac{1}{x+7})]=\sqrt{45}$ ⇒ $[(x-\frac{1}{x+7})]=\sqrt{45}-7=\sqrt{9 \times5}-7=3\sqrt{5}–7$ Hence, the correct answer is $3\sqrt{5}-7$.
Question : What will be the remainder when $27^{27}+27$ is divided by 28?
Option 1: 28
Option 2: 27
Option 3: 25
Option 4: 26
Correct Answer: 26
Solution : $27^{27}+27$ can written as $27^{27}+1^{27}-1+27=(27^{27}+1^{27})+26$ We know that An + Bn is divisible by A + B when n is odd. Here n = 27 is an odd number. When $(27^{27}+1^{27})$ is divided by 28, the remainder will be 0. And, when $(27^{27}+1^{27})+26$
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