Staff Selection Commission Combined Higher Secondary Level Exam
Question : If $a + b + c = 6$ and $a^2+b^2+c^2=40$, then what is the value of $a^3+b^3+c^3-3abc$?
Option 1: 212
Option 2: 252
Option 3: 232
Option 4: 206
Correct Answer: 252
Solution : Given that $a + b + c = 6$ and $a^2+b^2+c^2=40$, $(a+b+c)^2 = a^2 + b^2 + c^2 + 2(ab+bc+ac)$. $⇒6^2 = 40 + 2(ab+bc+ac)$ $⇒ab+bc+ac = -2$ $a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ac)$ $⇒a^3+b^3+c^3-3abc=6 \times (40 +2)$ $⇒a^3+b^3+c^3-3abc=6 \times 42 $ $⇒a^3+b^3+c^3-3abc=252 $ Hence, the correct answer is 252.
Question : If $a: b=3: 7$, then $(2 a+3 b):(3 a+2 b)$ is:
Option 1: $27:23$
Option 2: $23:29$
Option 3: $21:29$
Option 4: $21:23$
Correct Answer: $27:23$
Solution : Given $a:b=3:7$ Let $a=3k$ and $b=7k$ for some constant $k$. Now, $(2 a+3 b):(3 a+2 b)$ $=\{2(3k)+3(7k)\}:\{3(3k)+2(7k)\}$ $=(6k+21k):(9k+14k)$ $=27k:23k$ $=27:23$ Hence, the correct answer is $27:23$.
Question : A circle with centre O has a chord AB that is 20 cm in length. If the radius of the circle is 12 cm, then the area of triangle AOB is:
Option 1: $20 \sqrt{15}$ cm2
Option 2: $22 \sqrt{11}$ cm2
Option 3: $20 \sqrt{11}$ cm2
Option 4: $22 \sqrt{15}$ cm2
Correct Answer: $20 \sqrt{11}$ cm2
Solution : The area of triangle AOB, $ = \frac{1}{2} \times \text{base} \times \text{height}$ In triangle AOB, AB is the base and the height is the perpendicular drawn from the centre O to the chord AB. Use the Pythagorean theorem, $OD = \sqrt{12^2 -
Question : The pie chart given below shows the number of girls in six schools. The total number of girls in all these six schools is 5000. Number of girls in a particular school is shown as a percentage of total number of girls in all these six schools.
What is the ratio of the number of girls in school A to the number of girls in school E?
Option 1: 5 : 8
Option 2: 10 : 9
Option 3: 6 : 7
Option 4: 9 : 10
Correct Answer: 10 : 9
Solution : Total = 5000 We have to find the ratio of the number of girls in school A to the number of girls in school E Number of girls in school A = 20% of 5000 $=\frac{20}{100}\times 5000 = 1000$ Number of girls in
Question : Improve the underlined part of the sentence. Choose ‘No improvement’ as an answer if the sentence is grammatically correct. The dog will whine at the door when he wants to go out.
Option 1: wants to gone
Option 2: want to go
Option 3: No improvement
Option 4: wants to going
Correct Answer: No improvement
Solution : The correct choice is the third option.
The underlined segment is grammatically correct and contextually meaningful.
Therefore, the correct answer is no improvement.
Question : Choose the correct meaning of the underlined word in the given sentence.
My friend works as a florist at the shop down the street.
Option 1: A person who sells and arranges cut flowers
Option 2: A person who sells sweets
Option 3: Someone who grows flowers
Option 4: Someone who works in a bank
Correct Answer: A person who sells and arranges cut flowers
Solution : The first option is the correct answer.
In the context of the sentence, a florist is described as working at a shop down the street, indicating involvement in the business of selling and arranging flowers. A florist refers
Question : Directions: Select the related letter cluster from the given alternatives. SPINSTER : ROHMRSDQ :: SEMESTER : ?
Option 1: RDDLRSDQ
Option 2: RDLDSRDQ
Option 3: RDLDRSDQ
Option 4: RDLDRDSQ
Correct Answer: RDLDRSDQ
Solution : Given: SPINSTER : ROHMRSDQ :: SEMESTER : ?
Like, for SPINSTER – S – 1 = R; P – 1 = O; I – 1 = H; N – 1 = M; S – 1 = R; T – 1 = S; E – 1
Question : Directions: What will come in the place of (?) in the following equation, if × and – are interchanged and also + and ÷ are interchanged? 12 + 4 – 2 × 5 ÷ 4 = ?
Option 1: 6
Option 2: 5
Option 3: 3
Option 4: 4
Correct Answer: 5
Solution : Given: 12 + 4 – 2 × 5 ÷ 4 = ?
On interchanging the mathematical signs, we get – 12 ÷ 4 × 2 – 5 + 4 = ? = 3 × 2 – 5 + 4 = 6 – 5 + 4
Question : What will be the average of the first 8 positive even numbers divisible by 9?
Option 1: 45
Option 2: 72
Option 3: 81
Option 4: 63
Correct Answer: 81
Solution : We know that even numbers are divisible by 2. The sum of the numbers = 9 × 2( 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8) [We know that the sum of the first n natural number =
Question : A dealer offers a discount of 10% on the marked price of an article and still makes a profit of 20%. If the cost price of the article is INR 540, then find the marked price (in INR) of the article.
Option 1: 810
Option 2: 750
Option 3: 720
Option 4: 690
Correct Answer: 720
Solution : Given, Cost Price = INR 540, Profit Percentage = 20%, Discount Percentage = 10% Here cost price is denoted by CP, the selling price is denoted by SP, and MP denotes the marked price. Profit = Profit Percentage × CP ⇒ Profit = 0.20 ×
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
