Staff Selection Commission Combined Higher Secondary Level Exam
Question : The radii of the two circles are 11 cm and 3 cm. The distance between their centres is 17 cm. What is the length of the direct common tangent?
Option 1: 12 cm
Option 2: 14 cm
Option 3: 16 cm
Option 4: 15 cm
Correct Answer: 15 cm
Solution : The radii of two circles are 11 cm and 3 cm. The distance between their centres is 17 cm. Length of the direct common tangent of two circles = $\sqrt{D^2-({r_{1}}-r{_{2}})^2}$ D = Distance between their centres $r{_{1}}$ = radius of the bigger circle $r{_{2}}$
Question : A man invested INR 4,500 at 5% per annum and INR 5,500 at 8% per annum simple interest. Both investments were for 4 years each. The amount received from the lower rate of interest is what percent (rounded off to the nearest integer) of the amount received from the higher rate of interest?
Option 1: 63%
Option 2: 74%
Option 3: 51%
Option 4: 48%
Correct Answer: 74%
Solution : A man invested Rs. 4,500 at 5% per annum and Rs. 5,500 at 8% per annum simple interest. For the first investment, Time = 4 years Principal = Rs. 4,500 Rate = 5% per annum Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ = $\frac{4500
Question : Find the single equivalent discount of 10% and 20%.
Option 1: 26%
Option 2: 28%
Option 3: 30%
Option 4: 32%
Correct Answer: 28%
Solution : Single equivalent discount = $(a+b-\frac{a×b}{100}$)%, where $a$% and $b$% are successive discounts. So, the single discount of two successive discounts of 10% and 20% $ = 10 + 20 - \frac{(10 \times 20) }{ 100} $ $=30-2$ $= 28\%$ Hence, the correct answer is 28%.
Question : If $\cot A+\cos A=p$ and $\cot A-\cos A=q$, then which of the following relation is correct?
Option 1: $\sqrt{\frac{1}{16pq}}=p^2+q^2$
Option 2: $\frac{1}{4pq}=p^2+q^2$
Option 3: $\sqrt{16pq}=p^2-q^2$
Option 4: $4pq=p^2+q^2$
Correct Answer: $\sqrt{16pq}=p^2-q^2$
Solution : Given: $\cot A+\cos A=p$ and $\cot A-\cos A=q$ $p^{2}=\cot^{2} A+\cos^{2} A+2\cot A.\cos A$ $q^{2}=\cot^{2} A+\cos^{2} A-2\cot A.\cos A$ ⇒ $p^{2}–q^{2}=4\cot A.\cos A$ Also, $pq=\cot^{2} A-\cos^{2} A$ $=\frac{\cos^{2} A–cos^{2}A.\sin^{2} A}{\sin^{2} A}$ $=\frac{\cos^{2} A(1–\sin^{2} A)}{\sin^{2} A}$ $=\cot^{2} A(1–\sin^{2} A)$ $=\cot^{2} A\cos^{2} A$ $=(\cot A\cos A)^{2}$ $\sqrt{pq}=\cot A\cos
Question : Select the option that can be used as a one-word substitute for the given group of words.
The constitutional right to vote.
Option 1: Franchise
Option 2: Polling
Option 3: Voting
Option 4: Buttoning
Correct Answer: Franchise
Solution : The correct choice is the first option.
Franchise, in a political context, refers to the right or privilege granted to eligible individuals to participate in elections or decision-making processes.
The meanings of the other options are as follows:
Question : Select the most appropriate ANTONYM of the given word.
Contemplate
Option 1: Ruminate
Option 2: Disregard
Option 3: Meditate
Option 4: Retract
Correct Answer: Disregard
Solution : The most appropriate choice is the second option.
Contemplate means to carefully consider or think about something deeply. Its antonym, disregard, means to pay no attention to or ignore something.
Question : Which one of the following is not a dimension of human development index?
Option 1: Life expectancy
Option 2: Knowledge
Option 3: Social Status
Option 4: Standard of living
Correct Answer: Social Status
Solution : The Correct Answer is- Social Status
The abbreviation HDI stands for Human Development Index. A statistical instrument called the Human Development Index is used to assess a nation's general progress in its social and economic spheres. Human Development Indicators, issued annually by the United
Question : Expand and simplify $(x+4)^2+(x-2)^2$.
Option 1: $2(x^2+2x+10)$
Option 2: $2(x^2+2x-10)$
Option 3: $2(x^2-2x+10)$
Option 4: $2(x^2-2x-10)$
Correct Answer: $2(x^2+2x+10)$
Solution : Given: $(x+4)^{2}+(x-2)^{2}$ $=(x^{2}+4^{2}+8x)+(x^{2}+2^{2}-4x)$ $=2x^{2}+20+4x$ $=2(x^{2}+2x+10)$ Hence, the correct answer is $2(x^2+2x+10)$.
Question : From which five-year plan onwards in India were fiscal and economic reforms, including liberalisation, adopted?
Option 1: Eighth Five-Year Plan
Option 2: Seventh Five-Year Plan
Option 3: Sixth Five-Year Plan
Option 4: Ninth Five-Year Plan
Correct Answer: Eighth Five-Year Plan
Solution : The correct answer is the Eighth Five-Year Plan.
The Eighth Five-Year Plan was executed from 1992 to 1997, and P. V. Narasimha Rao was the prime minister at that time. During this Eighth Five-Year Plan period, India achieved its highest annual growth
Question : Directions: In a certain code language, READ is written as 18514. How is RATE written in that code language?
Option 1: 181520
Option 2: 181025
Option 3: 181205
Option 4: 181914
Correct Answer: 181205
Solution : Given: READ is written as 18514.
Like, place values of the letters of READ, R→18; E→5; A→1; D→4 Similarly, place values of the letters of RATE, R→18; A→1; T→20; E→5
So, RATE is written as 181205. Hence, the third option is correct.
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