Staff Selection Commission Combined Graduate Level Exam
Question : The ratio of the present ages of Ram and Ramesh is 3 : 5. After 7 years the ratio of their ages will be 4 : 5. Find the present age of Ramesh.
Option 1: 5 years
Option 2: 15 years
Option 3: 7 years
Option 4: 12 years
Correct Answer: 7 years
Solution : Let the present age of Ram and Ramesh be $3x$ and $5x$. According to the question, After 7 years, $\frac{3x+7}{5x+7}=\frac{4}{5}$ ⇒ $15x + 35 = 20x + 28$ ⇒ $35 - 28 = 20x - 15x$ ⇒ $5x = 7$ ⇒ $x = \frac{7}{5}$
Question : A fan is listed at Rs. 150 with a discount of 20%. What additional discount must be offered to the customer to bring the net price to Rs. 108?
Option 1: $11\frac{1}{9}$%
Option 2: $15$%
Option 3: $8$%
Option 4: $\text{None of these}$
Correct Answer: $\text{None of these}$
Solution : Marked price = Rs. 150 Discount = 20% of marked price = 20% of 150 = $\frac{20}{100}$ × 150 = Rs. 30 Price after initial discount = Rs. 150 – Rs. 30 = Rs. 120 Final price = Rs. 108 Additional discount to
Question : If $0°<\theta<90°$, the value of $\sin\theta+\cos\theta$ is:
Option 1: Equal to 1
Option 2: Greater than 1
Option 3: Less than 1
Option 4: Equal to 2
Correct Answer: Greater than 1
Solution : $\sin\theta+\cos\theta$ where $0°<\theta<90°$ Putting the value of $\theta=45°$, we have, $\sin 45°+\cos45°=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}$ ⇒ $\sin 45°+\cos45° =\frac{2}{\sqrt{2}}=\sqrt{2}$ Here, $\sqrt{2}=1.414>1$ Hence, the correct answer is greater than 1.
Question : $ABC$ is a triangle and $D$ is a point on the side $BC$. If $BC = 16\mathrm{~cm}$, $BD = 11 \mathrm{~cm}$ and $\angle ADC = \angle BAC$, then the length of $AC$ is equal to:
Option 1: $4 \sqrt{5} \mathrm{~cm}$
Option 2: $4 \mathrm{~cm}$
Option 3: $3 \sqrt{5} \mathrm{~cm}$
Option 4: $5 \mathrm{~cm}$
Correct Answer: $4 \sqrt{5} \mathrm{~cm}$
Solution :
We have, The $ABC$ is a triangle and $D$ is a point on the side $BC$. If $BC = 16 \mathrm{~cm}$, $BD = 11 \mathrm{~cm}$, $\angle ADC = \angle BAC$ (given), $\angle C$ is common angle and $AC$ is common side. So, $\triangle
Question : Directions: Three different positions of the same dice are shown. Find the number on the face opposite the face showing 3.
Option 1: 4
Option 2: 1
Option 3: 5
Option 4: 2
Correct Answer: 1
Solution : Taking dice positions of Figures 1 and 2 with 5 as the common face –
Moving clockwise from the common face with 5 –
Pairs of opposite faces –
So, the opposite face to the face containing 3 is 1. Hence, the second option is
Question : The following sentence has been split into four segments. Identify the segment that contains a grammatical error. You should / see a oculist; / your eyes look / worse today.
Option 1: your eyes look
Option 2: You should
Option 3: worse today
Option 4: see a oculist;
Correct Answer: see a oculist;
Solution : The correct choice is the fourth option.
Explanation: The use of a or an before a noun depends on the sound that follows it, not the actual letter. When a word begins with a vowel sound, you should use an instead of a
Question : 150 metres long train passes a telegraphic post in 12 seconds. Find the speed of the train (in km/h).
Option 1: 50
Option 2: 12.5
Option 3: 25
Option 4: 45
Correct Answer: 45
Solution : Given: The distance of the train is 150 m and its time taken is 12 seconds. We know that, $\text{Speed}=\frac{\text{Distance}}{\text{Time}}$ To convert m/s into km/h multiply by $\frac{18}{5}$ and we get, So, the speed of the train = $\frac{150}{12}\times \frac{18}{5}= 45$ km/h Hence, the correct
Question : Which of the following numbers is divisible by 24?
Option 1: 52668
Option 2: 49512
Option 3: 64760
Option 4: 26968
Correct Answer: 49512
Solution : To find: The number which is divisible by 24. We know, If a number is divisible by both 3 and 8 then it will be divisible by 24. If the sum of digits of a number is divisible by 3 then the number is divisible
Question : Study the given table and answer the question that follows. The table shows the number of students studying in six different classes at six different schools.
What is the respective ratio of students studying in class IX of schools Q and R together to those studying in class VI of schools S and T together?
Option 1: 181 : 127
Option 2: 143 : 150
Option 3: 150 : 143
Option 4: 127 : 181
Correct Answer: 150 : 143
Solution : Number of students studying in class IX of schools Q and R = 157 + 143 = 300 Number of students studying in class VI of schools S and T = 142 + 144 = 286 The ratio of class IX students in
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. VWX, BCD, HIJ, ?
Option 1: MOQ
Option 2: NOP
Option 3: GHI
Option 4: TUV
Correct Answer: NOP
Solution : Given: VWX, BCD, HIJ, ?
Add 6 to each letter of the given terms to obtain the next term in the series – First letter of the series→V + 6 = B; B + 6 = H; H + 6 = N Second letter of
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