Staff Selection Commission Combined Higher Secondary Level Exam
Question : Directions: Select the number from among the given options that can replace the question mark (?) in the following series. –4, –1, 4, ?, 20, 31, 44
Option 1: 15
Option 2: 17
Option 3: 11
Option 4: 18
Correct Answer: 11
Solution : Given: –4, –1, 4, ?, 20, 31, 44
Add consecutive odd numbers in the previous term to obtain the next term. –4 + 3 = –1; –1 + 5 = 4; 4 + 7 = 11; 11 + 9 = 20; 20 + 11 =
Question : If $a-b=9$ and $a b=20$, then $a^2+b^2$:
Option 1: 111
Option 2: 115
Option 3: 121
Option 4: 118
Correct Answer: 121
Solution : Given, $a-b=9$ and $a b=20$ We have to find the value of $a^2+b^2$. Consider, $a-b=9$ Squaring both sides, $(a-b)^2=9^2$ ⇒ $a^2+b^2-2ab=81$ ⇒ $a^2+b^2-2\times 20 = 81$ ⇒ $a^2+b^2-40=81$ ⇒ $a^2+b^2=81+40$ ⇒ $a^2+b^2=121$ Hence, the correct answer is 121.
Question : What is the equation of the line if its slope is $\frac{–2}{5}$ and it passes through the point $(1,–3)$?
Option 1: $2x+5y=17$
Option 2: $2x–5y=–13$
Option 3: $2x–5y=17$
Option 4: $2x+5y=–13$
Correct Answer: $2x+5y=–13$
Solution : Given: Slope = $-\frac{2}{5}$ Passing through the point $(1,–3)$. The equation of the line with slope $m$ is $y=mx+c$ Putting the values of $m$ and $(x,y)$, ⇒ $ –3= -\frac{2}{5}×1+c$ ⇒ $c= \frac{2}{5}-3$ ⇒ $c=-\frac{13}{5}$ So, the equation is $y=-\frac{2}{5}x+(-\frac{13}{5})$ ⇒ $5y=–2x–13$ ⇒ $2x+5y=–13$ Hence,
Question : Directions: The subjective number of applicants for the year 2008 an 2009 in a college is given in the following chart. Study the graph and answer the questions.
The number of Physics seeking applicants increased by:
Option 1: 17.26%
Option 2: 18.89%
Option 3: 19.25%
Option 4: 21.08%
Correct Answer: 17.26%
Solution : Applicants in physics in 2008 = 1240 Applicants in physics in 2009 = 1454 Difference = 1454 – 1240 = 214 Percentage increased = $\frac{\text{Difference}}{\text{Applicants in 2008}}\times100$ = $\frac{214}{1240}\times100$ = 17.26% Hence, the correct answer is 17.26%.
Question : Select the most appropriate SYNONYM of the given word.
Indispensable
Option 1: Destructive
Option 2: Imperative
Option 3: Drastic
Option 4: Invariable
Correct Answer: Imperative
Solution : The correct choice is the second option.
Indispensable means absolutely necessary or essential. Imperative also conveys the sense of something crucial or essential, making it an appropriate synonym in this context.
The meanings of the other options are as follows:
Question : Select the most appropriate synonym of the given word. Elaborate
Option 1: Easy
Option 2: Complex
Option 3: Simple
Option 4: Plain
Correct Answer: Complex
Solution : The second option is the correct choice.
The most appropriate synonym for elaborate is complex. Elaborate refers to detailed and intricate explanations or plans. Similarly, complex denotes a high level of intricacy or difficulty, making it a suitable synonym in this context.
The meanings of
Question : If $\tan(5\theta-10^\circ)=\cot(5\varphi+20^\circ)$, then the value of $(\theta+\varphi)$ is:
Option 1: $16^\circ$
Option 2: $18^\circ$
Option 3: $15^\circ$
Option 4: $20^\circ$
Correct Answer: $16^\circ$
Solution : $\tan(5\theta-10^\circ)=\cot(5\varphi+20^\circ)$ ⇒ $\cot(90^\circ-5\theta+10^\circ)=\cot(5\varphi+20^\circ)$ ⇒ $90^\circ-5\theta+10^\circ=5\varphi+20^\circ$ ⇒ $100^\circ-20^\circ= 5(\theta+\varphi)$ ⇒ $(\theta+\varphi)= 16^\circ$ Hence, the correct answer is $16^\circ$.
Question : If $\theta$ is an acute angle and $\sin \theta=\frac{13}{19}$, what is the value of $\cos \theta?$
Option 1: $\frac{6}{19}$
Option 2: $\frac{10 \sqrt{2}}{19}$
Option 3: $\frac{14}{19}$
Option 4: $\frac{8 \sqrt{3}}{19}$
Correct Answer: $\frac{8 \sqrt{3}}{19}$
Solution : Given: $\sin \theta=\frac{13}{19}$ We know, $\cos\theta=\sqrt{1-\sin^2\theta}$ $⇒\cos\theta=\sqrt{1-(\frac{13}{19})^2}$ $⇒\cos\theta=\sqrt{1-\frac{169}{361}}$ $⇒\cos\theta=\sqrt{\frac{192}{361}}$ $\therefore \cos\theta=\frac{8\sqrt3}{19}$ Hence, the correct answer is $\frac{8\sqrt3}{19}$.
Question : Directions: Select the set in which the numbers are related in the same way as the numbers of the given sets. (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.) 12 : 92 : 8 16 : 92 : 6
Option 1: 9 : 122 : 14
Option 2: 13 : 60 : 5
Option 3: 15 : 184 : 12
Option 4: 8 : 109 : 14
Correct Answer: 9 : 122 : 14
Solution : Given : 12 : 92 : 8; 16 : 92 : 6
Subtract 4 from the product of the first and the third numbers to obtain the second number. ⇒ 12 : 92 : 8→(12 × 8) – 4 = 96
Question : Directions: Select the option figure in which the given figure is embedded. (rotation is NOT allowed)
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Since the rotation is restricted. So, the embedded figure will have the same orientation as the main figure. By comparison of all the option figures, the given question figure is embedded only in the first option figure.
Hence, the first option is correct.
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