Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Select the combination of letters that when sequentially placed in the blanks of the given series will make the series logically complete. P_RSPG_SP_LSPM_S
Option 1: CWZO
Option 2: BWVQ
Option 3: ABXY
Option 4: QBWV
Correct Answer: QBWV
Solution : Given: P_RSPG_SP_LSPM_S
To fill the series we have to divide it – P_RS / PG_S / P_LS / PM_S Let's check each option – First option: CWZO; PCRS / PGWS / PZLS / PMOS (No, repeated pattern
Question : In a circle with centre $O$ and diameter $E F$, if the two chords $A E=A F$, then $ \angle A E F$ is:
Option 1: 80°
Option 2: 90°
Option 3: 45°
Option 4: 60°
Correct Answer: 45°
Solution : In a circle with centre O and diameter EF, if the two chords AE = AF, then they form an isosceles triangle. Also, we know that the angle in a semicircle is 90°. $⇒\angle EAF = 90°$ Let $\angle AEF = \angle AFE = x$
Question : In the following question, out of the given four alternatives, select the alternative which best expresses the meaning of the Idiom/Phrase.
To bridge the gap.
Option 1: To mend a broken bridge.
Option 2: To slander someone.
Option 3: To push people apart.
Option 4: To reduce differences and reconcile.
Correct Answer: To reduce differences and reconcile.
Solution : The correct choice is the fourth option.
To bridge the gap means to connect two things or make the difference between them smaller, which is correctly given in the fourth option, which states, "to reduce differences and reconcile".
Question : What is the direction of the southeast trade winds in India during the southwest monsoon season?
Option 1: South-easterly
Option 2: North-westerly
Option 3: South-westerly
Option 4: North-easterly
Correct Answer: South-westerly
Solution : The correct answer is South-westerly.
The southeast trade winds are caused by the warm subtropical areas of the southern oceans. They blow in a south-westerly direction as they pass the equator. The Coriolis effect and Ferrel's law are the primary causes of these trade winds.
Question : Directions: Each of the letters in the word JOURNAL are arranged in alphabetical order. How many letters are there in the English alphabetical series between the letter which is fourth from the left and the one which is second from the right in the new letter cluster thus formed?
Option 1: Six
Option 2: Three
Option 3: Five
Option 4: Four
Correct Answer: Three
Solution : Given: JOURNAL
When the letters of JOURNAL are arranged in alphabetical order, the letter cluster formed is AJLNORU. The letter which is fourth from the left is N. (AJLNORU) The letter which is second from the right is R. (AJLNORU) Letters
Question : What is the value of (22 + 1)(24+1)(28 + 1)(216 + 1) .........(2128 + 1)?
Option 1: $\frac{2^{256}-1}{2}$
Option 2: $\frac{2^{256}-1}{3}$
Option 3: $2^{256}-1$
Option 4: $\frac{2^{256}-1}{4}$
Correct Answer: $\frac{2^{256}-1}{3}$
Solution : $(2^2 + 1) (2^4 + 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} + 1)$ Divide by $(2^2 - 1)$ in numerator and denominator = $\frac{1}{(2^2 - 1)}[(2^2 - 1)(2^2 + 1) (2^4 + 1) (2^8 + 1) (2^{16} + 1) ........ (2^{128} +
Question : If the diagonals of a rhombus are 10 cm and 24 cm, then what is the perimeter of the rhombus?
Option 1: 50 cm
Option 2: 60 cm
Option 3: 56 cm
Option 4: 52 cm
Correct Answer: 52 cm
Solution : In a rhombus, the diagonals bisect each other at right angles. Therefore, we can form a right-angle triangle using half of each diagonal as the sides. Let the half diagonals as $a$ and $b$. $⇒a = \frac{10}{2} = 5 \text{ cm}$ $⇒b = \frac{24}{2}
Question : In a village election between three candidates, 80% of the voters cast their votes, out of which 3% votes were declared invalid. The winning candidate got 42680 votes which were 55% of the total valid votes. Find the number of valid votes received by the candidate who stood third, given that he received only 10% of the total valid votes.
Option 1: 7760
Option 2: 7700
Option 3: 7670
Option 4: 7680
Correct Answer: 7760
Solution : The winning candidate got 42680 votes, which was 55% of the total valid votes. The total valid votes = $\frac{42680}{0.55}$ = 77600 votes The candidate who stood third received only 10% of the total valid votes. The number of valid votes received by the third
Question : Directions: Select the option in which the numbers share the same relationship in the set as that shared by the numbers in the given set. (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.) (14, 17, 970) (15, 23, 1508)
Option 1: (17, 24, 1730)
Option 2: (16, 22, 1580)
Option 3: (18, 32, 2686)
Option 4: (19, 31, 2642)
Correct Answer: (17, 24, 1730)
Solution : Given: (14, 17, 970); (15, 23, 1508) The pattern is as follows – (14, 17, 970)→{(14)2 + (17)2} × 2 = {196 + 289} × 2 = 485 × 2 = 970 (15, 23, 1508)→{(15)2 + (23)2}
Question : If $x+\frac{1}{x}=2$, then find the value of $x^5+\frac{1}{x^5}$.
Option 1: 1
Option 2: 3
Option 3: 4
Option 4: 2
Correct Answer: 2
Solution : $x+\frac{1}{x}=2$ $⇒\frac{x^2+1}{x} = 2$ $⇒x^2+1 = 2x$ $⇒x^2+1-2x = 0$ $⇒(x-1)^2 = 0$ $⇒x-1 = 0$ $⇒x =1$ $\therefore x^5+\frac{1}{x^5} = 1+1 = 2$ Hence, the correct answer is 2.
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