Staff Selection Commission Combined Graduate Level Exam
Question : If $(x-5)^2+(y-2)^2+(z-9)^2=0$, then value of $(x+y-z)$ is:
Option 1: 16
Option 2: –1
Option 3: –2
Option 4: 12
Correct Answer: –2
Solution : Given: $(x-5)^2+(y-2)^2+(z-9)^2=0$ So, $x=5, y=2, z=9$ Therefore, $x+y-z = (5+2-9) = -2$ Hence, the correct answer is –2.
Question : Directions: In a certain code language, BELOVED is coded as 65, and FLOWER is coded as 79. How will QUIVER be coded in that language?
Option 1: 92
Option 2: 94
Option 3: 91
Option 4: 90
Correct Answer: 92
Solution : Given: BELOVED is coded as 65, and FLOWER is coded as 79.
Add the place values of the letters of BELOVED and FLOWER to get their required codes. BELOVED; B→2; E→5; L→12; O→15; V→22; E→5; D→4 Add the pace values→2 + 5 + 12 +
Question : Which of the following is not a nitrogenous fertiliser?
Option 1: Ammonium sulphate
Option 2: Urea
Option 3: Ammonium Thiosulphate
Option 4: Superphosphate
Correct Answer: Superphosphate
Solution : The correct option is Superphosphate.
The term "superphosphate" does not refer to nitrogenous fertiliser. It is a sort of phosphate fertiliser that gives plants phosphorous but no nitrogen. Nitrogenous fertilisers, on the other hand, such as Urea, and Ammonium sulphate, include nitrogen as a
Question : The marked price of a piano was Rs. 15,000. At the time of sale, there were successive discounts of 20%, 10%, and 10% respectively on it. The sale price was:
Option 1: Rs. 9,720
Option 2: Rs. 9,750
Option 3: Rs. 9,760
Option 4: Rs. 9,780
Correct Answer: Rs. 9,720
Solution : Single discount of 20% and 10% = $20 + 10 - \frac{20\times 10}{100} = 28\%$ Now single discount of 20%, 10%, and 10% = $28 + 10 - \frac{28\times 10}{100} = 35.2\%$ SP of the piano = $15000×\frac{100\:–\:35.2}{100}$ = Rs. 9,720 Hence, the correct
Question : Directions: Which of the following interchanges of numbers and mathematical signs would make the given equation correct? 729 × 81 ÷ 20 + 16 − 6 = 50
Option 1: 6 and 20, × and ÷
Option 2: 20 and 50, + and −
Option 3: 16 and 50, × and +
Option 4: 16 and 20, + and ÷
Correct Answer: 6 and 20, × and ÷
Solution : Given: 729 × 81 ÷ 20 + 16 − 6 = 50
Let's check the given options – First option: 6 and 20, × and ÷ On interchanging the signs and numbers, we get – ⇒ 729 ÷ 81 ×
Question : Find the value of the following expression. $12\left(\sin^4 \theta+\cos^4 \theta\right)+18\left(\sin^6 \theta+\cos^6 \theta\right)+78 \sin^2 \theta \cos^2 \theta$
Option 1: 30
Option 2: 40
Option 3: 10
Option 4: 20
Correct Answer: 30
Solution : $12(\sin^4 \theta+\cos^4 \theta)+18(\sin^6 \theta+\cos^6 \theta)+78 \sin^2 \theta \cos^2 \theta$ $=12[(\sin^2 \theta+\cos^2\theta)^2-2\sin^2 \theta \cos^2 \theta]+18[(\sin^2 \theta+\cos^2 \theta)^3-3\sin^2 \theta \cos^2 \theta(\sin^2 \theta+\cos^2\theta)]+78 \sin^2 \theta \cos^2 \theta$ $=12[1-2\sin^2 \theta \cos^2 \theta]+18[1-3\sin^2 \theta \cos^2 \theta]+78 \sin^2 \theta \cos^2 \theta$ $= 12-24\sin^2 \theta \cos^2 \theta+18-54\sin^2 \theta \cos^2 \theta+78 \sin^2 \theta
Question : The Revolutionary Socialist Party was established in _______.
Option 1: 1936
Option 2: 1925
Option 3: 1940
Option 4: 1929
Correct Answer: 1940
Solution : The correct answer is 1940.
The Revolutionary Socialist Party was established in 1940. It had its roots in the Bengali liberation movement and the Hindustan Socialist Republican Army. Tridib Chaudhuri was the founder of this party.
Question : Value of $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ is:
Option 1: 1
Option 2: 2
Option 3: –1
Option 4: 0
Correct Answer: 1
Solution : $\sec^2\theta-\frac{\sin^2\theta-2\sin^4\theta}{2\cos^4\theta-\cos^2\theta}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(2\cos^2\theta-1)}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta[2(1-\sin^2\theta)-1]}$ $=\sec^2\theta-\frac{\sin^2\theta(1-2\sin^2\theta)}{\cos^2\theta(1-2\sin^2\theta)}$ $=\sec^2\theta-\tan^2\theta$ $=1$ Hence, the correct answer is 1.
Question : Directions: In the following question, out of the four alternatives, select the alternative that will improve the bracketed part of the sentence. In case no improvement is needed, select "No Improvement".
(The meeting adjourned abruptly) by the chairperson after about an hour of intense deliberation.
(1) The meeting was adjourned abruptly
(2) The meeting was abruptly adjourned
(3)The meeting was adjourned abrupt
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The correct choice is the first option.
Explanation: The sentence is in the passive voice,(the voice in which the object experiences an action rather than the person that acts).
The structure for a passive sentence is: "Object + form of the be verb (in
Question : A, B, and C can do a job working alone in 6, 9, and 18 days, respectively. They all worked together for one day, and then A and B quit. How many days does C working alone take to complete the remainder of the job?
Option 1: 9
Option 2: 6
Option 3: 12
Option 4: 10
Correct Answer: 12
Solution : Given: A, B, and C can do a job working alone in 6, 9, and 18 days, respectively. One day's work for A = $\frac{1}{6}$ B's one day's work = $\frac{1}{9}$ C's one day's work = $\frac{1}{18}$ Let for $x$ days, C worked alone. A
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