Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $3a^{2}= b^{2}\neq0$, then the value of $\frac{\left (a+b \right)^{3}-\left (a-b \right)^{3}}{\left (a+b \right)^{2}+\left (a-b \right)^{2}}$ is:
Option 1: $\frac{3b}{2}$
Option 2: $b$
Option 3: $\frac{b}{2}$
Option 4: $\frac{2b}{3}$
Correct Answer: $\frac{3b}{2}$
Solution : Expression = $\frac{(a + b)^3 - (a - b)^3 }{(a + b)^2 + (a - b)^2} $ and $3a^{2}= b^{2}\neq0$ Using identities: $(a + b)^3=a^3 + b^3 + 3a^2b + 3ab^2$ and $(a - b)^3=a^3 - b^3 - 3a^2b + 3ab^2$, Now, $\frac{(a + b)^3
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."
We were (not) the wiser after hearing the explanation.
(1) none
(2) neither
(3) nevertheless
(4) No Improvement
Option 1: (1)
Option 2: (2)
Option 3: (3)
Option 4: (4)
Correct Answer: (1)
Solution : The sentence can be improved using the first option "none".
The sentence "We were none the wiser after hearing the explanation" is a common saying used to convey that the explanation did not provide any new insights.
The meanings of the other options are
Question : A transverse common tangent is drawn to two circles of radius 8.5 cm and 5.5 cm. The centres of the two circles are 18 cm apart. What is the length (in cm) of the tangent?
Option 1: $10 \sqrt{3}$
Option 2: $10 \sqrt{2}$
Option 3: $8 \sqrt{2}$
Option 4: $8 \sqrt{3}$
Correct Answer: $8 \sqrt{2}$
Solution : Given: The Radii of circles are 8.5 cm and 5.5 cm and the length between circles is 18 cm. $r_1=8.5\ \text{cm}$ $r_2=5.5\ \text{cm}$ $d=18\ \text{cm}$ The length of a transverse common tangent $=\sqrt{d^2−(r_1+r_2)^2}$ $=\sqrt{(18)^2−(8.5+5.5)^2}$ $=\sqrt{324−196}$ $=\sqrt{128}=8 \sqrt{2}\ \text{cm}$ Hence, the correct answer is $8
Question : Directions: A word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. A can be represented by 00, 21, etc., and S can be represented by 58, 98, etc. Similarly, you have to identify the set for the word given below. SLOW
Option 1: 58, 34, 66, 95
Option 2: 98, 04, 66, 96
Option 3: 58, 34, 66, 76
Option 4: 98, 04, 66, 95
Correct Answer: 98, 04, 66, 96
Solution : Given: SLOW
Number representations of each letter – S→56, 58, 98 L→04, 34 O→66 W→75, 96
First option: 58, 34, 66, 95; W cannot be represented by 95. Second option: 98, 04, 66, 96; All the letters of the word SLOW can
Question : The term 'tackle point' is associated with_____.
Option 1: Football
Option 2: Baseball
Option 3: Hockey
Option 4: Kabaddi
Correct Answer: Kabaddi
Solution : The correct answer is Kabaddi.
In Kabaddi, a tackle point is earned when a defender successfully tackles an opponent from the opposing team.
Other terms associated with Kabaddi are Defender, Rider, All Out, Touchpoint, etc.
Question : Directions: Select the missing number from the given responses.
Option 1: 8
Option 2: 31
Option 3: 32
Option 4: 36
Correct Answer: 8
Solution : Given:
The pattern can be observed running horizontally along the rows. First row: 26 – 6 = 20; 20 ÷ 4 = 5 Second row: 32 – 4 = 28; 28 ÷ 4 = 7 Third
Question : X, Y, and Z can complete a piece of work in 20, 12, and 28 days respectively. If all work together, the approximate number of days to complete the work will be:
Option 1: 6
Option 2: 7
Option 3: 4
Option 4: 5
Correct Answer: 6
Solution : The time taken by X, Y, and Z to complete the work is 20, 12, and 28 days respectively. Work done by X, Y, and Z in a day is $\frac{1}{20}$, $\frac{1}{12}$, and $\frac{1}{28}$ respectively. Work done by X, Y, and Z together in a
Question : Select the most appropriate option that can substitute the underlined words in the following sentence.
My parents had not call me yesterday.
Option 1: does not calling
Option 2: did not call
Option 3: do not call
Option 4: have not call
Correct Answer: did not call
Solution : The correct choice is the second option.
Since the action is related to the past event it should be stated in the simple past tense as per time reference. Did not call is the correct form in the case of the simple past
Question : Near which one of the following cities are Palitana temples located ?
Option 1: Bhavnagar
Option 2: Mount Abu
Option 3: Nasik
Option 4: Ujjain
Correct Answer: Bhavnagar
Solution : The correct answer is Bhavnagar
The Palitana Jain temples are found in Gujarat, India's Bhavnagar district, on Shatrunjaya, close to the city of Palitana. The Shatrunjaya Hill Palitana temples were built over a 900-year period beginning in the 11th century. Kumarpal Solanki, a well-known Jain
Question : Directions: What will come in place of the question mark (?) in the following equation if + and × are interchanged and – and ÷ are interchanged? 9 + 11 ÷ 2 × 36 – 12 = ?
Option 1: 103
Option 2: 98
Option 3: 109
Option 4: 100
Correct Answer: 100
Solution : Given: 9 + 11 ÷ 2 × 36 – 12 = ?
After interchanging + with ×, and – with ÷, the equation will be as follows – = 9 × 11 – 2 + 36 ÷ 12 = 9 × 11 – 2 +
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