Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: In the following question, a series is given with one number missing. Select the missing number from the given alternatives. 672, 666, 660, 654, ?
Option 1: 648
Option 2: 646
Option 3: 650
Option 4: 640
Correct Answer: 648
Solution : Given: 672, 666, 660, 654, ?
Here, subtract 6 from each number to get the next number. 672 – 6 = 666; 666 – 6 = 660; 660 – 6 = 654; 654 – 6 = 648
648 is the missing number of the series.
Question : Directions: The bar graph below shows the percentage distribution of a company's total expenditures under various expense heads during 2013. Study the graph and answer the given question.
If the total amount of expenditure of the company is N times the expenditure on research and development, then the value of N is:
Option 1: 5
Option 2: 18
Option 3: 20
Option 4: 27
Correct Answer: 20
Solution : Let the total expenditure be INR $100x$. According to the question, Expenditure on research and development = 5% = $\frac{5}{100} \times 100x$ $⇒100x = N \times \frac{5}{100} \times 100x$ $⇒ N = \frac{100}{5} = 20$% Hence, the correct answer is 20.
Question : On an item having a marked price of INR 1,600, successive discounts of $y$% and $z$% were offered. As a result, the item was sold for INR 1,056. Which of the options below CANNOT be a set of values for $y$ and $z$?
Option 1: $y=22, z=15.5$
Option 2: $y=4, z=31.25$
Option 3: $y=20, z=17.5$
Option 4: $y=12, z=25$
Correct Answer: $y=22, z=15.5$
Solution : Marked price = INR 1,600 Selling price = INR 1,056 Discount % = $\frac{\text{Discount}}{\text{Marked price}}\times 100$% Discount % = $\frac{1600-1056}{1600}\times 100 =34\%$ Single discount $=y + z - \frac{yz}{100}$ Single discount of 22 and 15.5 $=22+15.5-\frac{22\times 15.5}{100}$ $=37.5-3.41 = 34.09\%$ which is not equal
Question : Directions: Select the figure from the given options that can replace the question mark (?) in the following series.
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : According to the given figures – The figure in each box rotates by 90° in the clockwise direction. Therefore, the following figure will complete the given pattern –
Hence, the fourth option is correct.
Question : Directions: In the following question, choose the numbers similar to the given group of numbers. (580, 265, 373)
Option 1: 366
Option 2: 490
Option 3: 428
Option 4: 388
Correct Answer: 490
Solution : Given: (580, 265, 373)
The sum of the digits of the given number is the same. 580 = 5 + 8 + 0 = 13 265 = 2 + 6 + 5 = 13 373 = 3 + 7 + 3 = 13
Let's check
Question : What are the coordinates of the centroid of a triangle whose vertices are A (2, 5), B (–4, 0), and C (5, 4)?
Option 1: (–1, 3)
Option 2: (1, 3)
Option 3: (1, –3)
Option 4: (–1, –3)
Correct Answer: (1, 3)
Solution : Given: The vertices are A(2, 5), B(–4, 0), and C(5, 4). The centroid coordinates = $(x, y)$ = $\frac{(x_{1} + x_{2} + x_{3})}{3}, \frac{(y_{1} + y_{2} + y_{3})}{3}$. Centroid coordinates $(x, y)$ = $\frac{(2 – 4 + 5)}{3}, \frac{(5 + 0 + 4)}{3}$. Centroid
Question : A pipe can fill a tank in 24 hours. Due to a leakage at the bottom, it is filled in 36 hours. If the tank is half full, how much time will the leak take to empty the tank?
Option 1: 48 hours
Option 2: 72 hours
Option 3: 36 hours
Option 4: 24 hours
Correct Answer: 36 hours
Solution : Given: A pipe can fill a tank in 24 hours. Let the total work = LCM of 24 and 36 = 72 units One hour work of filling pipe = 72 $\div$ 24 = 3 units One hour of work filling pipe and the
Question : Directions: In the following question, which set of letters, when sequentially placed in the gaps in the given letter series, will complete it? X_ZX_YY_ZX_Z
Option 1: XXYY
Option 2: YXZY
Option 3: YYXY
Option 4: XXXY
Correct Answer: YXZY
Solution : Given: X_ZX_YY_ZX_Z
Divide the series into clusters of letters – X_Z / X _YY_ Z / X_Z Let's check each option – First option: XXYY; XXZ / XXYYYZ / XYZ (No repeated pattern found.) Second option: YXZY;
Question : Directions: Three of the following four are alike in a certain way and thus form a group. Which is the one that does NOT belong to that group? (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: 2 – 6
Option 2: 4 – 20
Option 3: 5 – 30
Option 4: 8 – 75
Correct Answer: 8 – 75
Solution : Let's check the options – First option: 2 – 6; 6 ÷ 2 = 3 Second option: 4 – 20; 20 ÷ 4 = 5 Third option: 5 – 30; 30 ÷ 5 = 6 Fourth option: 8 – 75
Question : Suhas, a tree, and an 11.25 m tall building are positioned such that their feet on the ground are collinear and the tree is located between Suhas and the building. The tree is located at a distance of 7.5 m from Suhas and a distance of 45 m from the building. Further, the eyes of Suhas, the top of the tree, and the top of the building fall in one line, and the eyes of Suhas are at a height of 1.8 m from the ground. Find the height (in m ) of the tree.
Option 1: 3.00 m
Option 2: 3.30 m
Option 3: 3.15 m
Option 4: 3.45 m
Correct Answer: 3.15 m
Solution : Given: All points are collinear. Height of Suhas be $a$ = 1.8 m Height of building be $b$ = 11.25 m Let the height of the tree be $c$ Distance between Suhas and tree be $x$ = 7.5 m Distance between tree and building
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