Staff Selection Commission Combined Graduate Level Exam
Question : Directions: Which of the following terms will replace the question mark (?) in the given series? AJRX, CNXF, ERDN, ?, IZPD
Option 1: HVJV
Option 2: GVJV
Option 3: HVIT
Option 4: GVKV
Correct Answer: GVJV
Solution : Given: AJRX, CNXF, ERDN, ?, IZPD
In the above-given series, add 2, 4, 6 and 8 to the place value of the first, second, third and fourth letters of the given terms. AJRX→A + 2 = C; J + 4 = N; R + 6
Question : If the numerical value of twice the curved surface area of a right circular cylinder is equal to the numerical value of its volume, then what is the numerical value of the radius of the base of the cylinder?
Option 1: 2
Option 2: 3
Option 3: 5
Option 4: 4
Correct Answer: 4
Solution : According to the question, $2\pi rh \times 2= \pi r^2h$ ⇒ $4 = r$ ⇒ $r = 4\ \mathrm{units}$ Hence, the correct answer is 4.
Question : A person saves $33 \frac{1}{3}\%$ of his income. If the savings increase by $22\%$ and the expenditure increases by $10\%$, then the percentage increase in his income is:
Option 1: 18%
Option 2: 14%
Option 3: 16%
Option 4: 22%
Correct Answer: 14%
Solution : Given: Savings of the man = $33\tfrac{1}{3}\% = \frac{1}{3}$rd of income Let the original income be $300x$ ⇒ Original Savings = $100x$ So, Original Expenditure $=300x-100x = 200x$ According to the question, New savings $=100x \times \frac{122}{100} = 122x$ New expenditure $=200x \times \frac{110}{100} =
Question : Directions: After interchanging the given two numbers and two signs what will be the values of equations (I) and (II) respectively? + and –, 6 and 9 I. 6 – 5 × 9 + 8 ÷ 2 II. 6 – 4 + 9 × 5 ÷ 3
Option 1: 17, 5
Option 2: 81, 16
Option 3: 35, 3
Option 4: 54, 5
Correct Answer: 35, 3
Solution : Given: I. 6 – 5 × 9 + 8 ÷ 2 II. 6 – 4 + 9 × 5 ÷ 3
Let's solve each equation after interchanging signs and numbers according to the instructions. On interchanging the signs and numbers in the first equation,
Question : Which of the following Sultans of the Tughlaq Dynasty issued copper coins instead of silver ones?
Option 1: Ghiyasuddin Tughlaq
Option 2: Muhammad bin Tughluq
Option 3: Firuz Shah Tughlaq
Option 4: Abu Bakr Shah
Correct Answer: Muhammad bin Tughluq
Solution : The correct answer is Muhammad bin Tughluq.
The Tughlaq Sultan who issued copper coins instead of silver ones was Muhammad bin Tughluq. During his reign, he introduced copper coins known as "tankas" to replace the silver coins. This decision, among other factors,
Question : A group of men decided to do a job in 11 days but 16 men left the work after each day. The work, as a result, was completed in 15 days. How many men were there initially in the group?
Option 1: 400
Option 2: 480
Option 3: 420
Option 4: 450
Correct Answer: 420
Solution : Given: A group of men decided to do a job in 11 days but 16 men left the work after each day. Total time taken to complete the work = 15 days Let there be $x$ number of men in the group with efficiency of
Question : If $\sec\theta+\tan\theta=m\left (> 1 \right)$, then the value of $\sin\theta$ is $\left (0^{\circ} < \theta<90^{\circ} \right)$:
Option 1: $\frac{1-m^{2}}{1+m^{2}}$
Option 2: $\frac{m^{2}-1}{m^{2}+1}$
Option 3: $\frac{m^{2}+1}{m^{2}-1}$
Option 4: $\frac{1+m^{2}}{1-m^{2}}$
Correct Answer: $\frac{m^{2}-1}{m^{2}+1}$
Solution : Given: $\sec\theta+\tan\theta=m$ ⇒ $1+\sin\theta=m\cos\theta$ Squaring both sides, $1+2\sin\theta+\sin^{2}\theta=m^{2}\cos^{2}\theta$ ⇒ $1+2\sin\theta+\sin^{2}\theta=m^{2}(1-\sin^{2}\theta)$ ⇒ $(1+m^{2})\sin^{2}\theta+2\sin\theta+(1-m^{2})=0$ ⇒ $\sin\theta = \frac{-2\pm\sqrt{2^2-4(1+m^2)(1-m^2)}}{2(1+m^{2})}$ ⇒ $\sin\theta =\frac{-2\pm 2m^2}{2(1+m^{2})}$ ⇒ $\sin\theta =\frac{m^2-1^2}{(1+m^{2})}$ and $\sin\theta =-1$ ⇒ $\sin\theta=\frac{m^{2}-1}{m^{2}+1},-1$ Hence, the correct answer is $\frac{m^{2}-1}{m^{2}+1}$.
Question : If $x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$, then the value of $\frac{\sqrt{3}-x}{\sqrt{3}+x}$ (corrected to two decimal places) is:
Option 1: 0.25
Option 2: 0.17
Option 3: 0.19
Option 4: 0.27
Correct Answer: 0.27
Solution : $x=\sqrt{1+\frac{\sqrt{3}}{2}}-\sqrt{1-\frac{\sqrt{3}}{2}}$ Squaring both sides, we get, $⇒x^2=1+\frac{\sqrt{3}}{2}+1-\frac{\sqrt{3}}{2}-2(\sqrt{1-\frac{3}{4}})$ $⇒x^2=1$ $x=1$ or $x=-1$ Taking $x=1$, we get, $⇒\frac{\sqrt{3}-x}{\sqrt{3}+x}$ $=\frac{\sqrt{3}-1}{\sqrt{3}+1}$ $=\frac{\sqrt{3}-1}{\sqrt{3}+1}\times\frac{\sqrt{3}-1}{\sqrt{3}+1}$ $=\frac{(\sqrt{3}-1)^2}{3-1}$ $=2-\sqrt{3}$ $=2-1.73$ [As the value of $\sqrt3=1.73$] $=0.27$ Hence, the correct answer is 0.27.
Question : Wheat worth Rs. 80 per kg and Rs. 50 per kg is mixed with a third variety in the ratio $1:2:3$. If the mixture is worth Rs.75 per kg, then the price of the third variety per kg will be equal to:
Option 1: Rs. 95
Option 2: Rs. 85
Option 3: Rs. 80
Option 4: Rs. 90
Correct Answer: Rs. 90
Solution : Let the price of the third variety be Rs. $x$ per kg. The ratio of varieties of rice in the mixture is $1 : 2 : 3$. Let the amount of the first, second, and third varieties of rice in the mixture be 1
Question : Select the most appropriate collocating word to fill in the blank.
The girl has ________ chances winning the match.
Option 1: bountiful
Option 2: high
Option 3: light
Option 4: hefty
Correct Answer: high
Solution : The correct choice is the second option.
The word chances is often collocated with "high" to convey a likelihood or probability of success. In this context, the phrase "high chances" indicates a favourable or significant probability of winning the match.
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