Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Four number pairs have been given. Out of which three are alike in some manner and one is different. Select a different one. (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.)
Option 1: 14 : 210
Option 2: 25 : 650
Option 3: 11 : 132
Option 4: 19 : 342
Correct Answer: 19 : 342
Solution : Let's check the options – First option: 14 : 210→210 ÷ 14 = 15→(14 + 1) Second option: 25 : 650→650 ÷ 25 = 26→(25 + 1) Third option: 11 : 132→132 ÷ 11 = 12→(11 + 1) Fourth option: 19 : 342→342
Question : Three people A, B, and C worked together and finished a work in 9 days. If A alone can finish the same work in 18 days, and B alone in 30 days, then the number of days C alone will take is:
Option 1: 36 days
Option 2: 45 days
Option 3: 40 days
Option 4: 54 days
Correct Answer: 45 days
Solution : Let $x$ be the total work. A alone can finish the same work in 18 days. So 1 day's work of A = $\frac{1}{18}$ of the work B alone can finish the same work in 30 days. So 1 day's work of B =
Question : The radius of the incircle of a triangle whose sides are 9 cm, 12 cm, and 15 cm is:
Option 1: 9 cm
Option 2: 13 cm
Option 3: 3 cm
Option 4: 6 cm
Correct Answer: 3 cm
Solution : Checking for the triangle by using Pythagoras theorem. $9^2 + 12^2 = 15^2$ Thus, The triangle is right-angled. Given, AB = 9, BC = 12 cm OD = OE = OF = $x$ cm (radius of the circle) And, BEOD is a square. AD
Question : If $x^2-5\sqrt{5}x+1=0$ and $x > 0$, what is the value of $(x^3-\frac{1}{x^3})$?
Option 1: 1331
Option 2: 1364
Option 3: 1296
Option 4: 1244
Correct Answer: 1364
Solution : Given: $x^2-5\sqrt{5}x+1=0$, and $x >0$ Dividing by $x$ on both sides, we get $x-5\sqrt{5}+\frac{1}{x}=0$ ⇒ $x+\frac{1}{x}=5\sqrt{5}$ Squaring both sides, we get ⇒ $(x+\frac{1}{x})^2=(5\sqrt{5})^2=125$ We know that $(x-\frac{1}{x})^2=(x+\frac{1}{x})^2-4$ ⇒ $(x-\frac{1}{x})^2=125-4=121$ ⇒ $(x-\frac{1}{x})=11$ Now, $(x-\frac{1}{x})^3=x^3-\frac{1}{x^3}-3×x×\frac{1}{x}(x-\frac{1}{x})$ ⇒ $11^3=x^3-\frac{1}{x^3}-3×11$ ⇒ $x^3-\frac{1}{x^3}=1331+33$ $\therefore x^3-\frac{1}{x^3}=1364$ Hence, the correct answer is 1364.
Question : The National Film Awards have been administered since _____.
Option 1: 1973
Option 2: 1980
Option 3: 1987
Option 4: 1994
Correct Answer: 1973
Solution : The correct option is 1973.
Since its establishment in 1954, the National Film Awards has held the distinction of being India's foremost film award ceremony. Since 1973, it, along with the International Film Festival of India and the Indian Panorama, has been overseen by the
Question : Select the option with the correct spellings to replace the underlined words in the given sentence.
His charesmatic attitude is admirble.
Option 1: karismatic; admerable
Option 2: charismatic; admarable
Option 3: karismatic; admirable
Option 4: charismatic; admirable
Correct Answer: charismatic; admirable
Solution : The correct choice is the fourth option.
Charismatic: Having, exhibiting, or based on charisma or charism
Admirable: Deserving the highest esteem
Therefore, the correct spelling will be charismatic and admirable.
Question : A, B, and C started a business with their investments in the ratio 1 : 2 : 4. After 6 months A increased his capital by 50% and B invested twice the amount as before, while C withdrew $\frac{1}{4}$th of his investment. The ratio of their profits at the end of the year was:
Option 1: 10 : 5 : 9
Option 2: 5 : 12 : 14
Option 3: 6 : 9 : 17
Option 4: 5 : 14 : 16
Correct Answer: 5 : 12 : 14
Solution : The ratio of investments of A, B, and C = 1 : 2 : 4 Let the investments of A, B, and C be k, 2k, and 4k. Ratio of profit = Ratio of investment × Ratio of time The ratio
Question : Directions: Select the related letter cluster from the given alternatives. OFFICIAL : QHHKEKCN :: LANGUAGE : ?
Option 1: NCPWICIG
Option 2: NCPIWCIG
Option 3: NCPIWICG
Option 4: NCPIWCGI
Correct Answer: NCPIWCIG
Solution : Given: OFFICIAL : QHHKEKCN :: LANGUAGE : ?
Like, for OFFICIAL – O + 2 = Q; F + 2 = H; F + 2 = H; I + 2 = K; C + 2 = E; I + 2 = K; A + 2
Question : Who won the Best Actress in Leading Role award in the 75th BAFTA ceremony?
Option 1: Jennifer Lawrence
Option 2: Kate Winslet
Option 3: Joanna Scanlan
Option 4: Gigi Hadid
Correct Answer: Joanna Scanlan
Solution : The correct answer is Joanna Scanlan.
At the 75th British Academy Film Awards (BAFTAs) ceremony held on March 13, 2022, Joanna Scanlan won the Best Actress in a Leading Role award. Her win was for her outstanding performance in the movie "After Love,"
Question : Directions: In a certain code language, A + B means A is the mother of B, A – B means A is the father of B, A × B means A is the husband of B, A ÷ B means A is the sister of B. Based on the above, how is Q related to L if Q × C + R ÷ G – L?
Option 1: Mother's father
Option 2: Father's father
Option 3: Father's son
Option 4: Father's brother
Correct Answer: Father's father
Solution : As per the given information, the family tree will be as follows –
Here, the quadrilateral represents the male, and the circular figure represents the female in the figure.
So, Q is the father's father (grandfather) of L. Hence, the second option is correct.
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