Staff Selection Commission Combined Graduate Level Exam
Question : The numerator of a fraction is a multiple of two numbers. One of the numbers is greater than the other by 2. The greater number is smaller than the denominator by 4. If the denominator $7 + c (c > –7)$ is a constant, then the minimum value of the fraction is:
Option 1: 5
Option 2: $\frac{1}{5}$
Option 3: –5
Option 4: $-\frac{1}{5}$
Correct Answer: $-\frac{1}{5}$
Solution : Let the first number be $x$. Then, the second number would be $(x+2)$. According to the question, ⇒ $x + 2+ 4 = 7 + c$ ⇒ $x + 6 = 7 + c$ ⇒ $x = 1 + c$ Fraction is $\frac{{x}({x}+2)}{7+{c}}= \frac{(1+c)(3+c)}{7+c}$ For
Question : A car priced INR 6,50,000 is bought by making a down payment. On the balance, a simple interest of 10% is charged in a lump sum and the money is to be paid in 20 equal annual instalments of INR 25,000. How much is the down payment?
Option 1: INR 1,55,945
Option 2: INR 1,95,455
Option 3: INR 1,94,555
Option 4: INR 1,45,955
Correct Answer: INR 1,95,455
Solution : Let the downpayment be of INR $x$. Hence from the above data, we get the following relation, $(650000 - x)\times (1 + \frac{10}{100}) = 20\times 25000$ $⇒650000 - x = 20\times 25000 \times \frac{10}{11} ≈ 454545$ $⇒x = 650000 - 454545 = 1,95,455$ $⇒x
Question : Direction: In the following question, identify the diagram that represents the best relationship among classes given below.
Fruits, Apples, Oranges
Option 1:
Option 2:
Option 3:
Option 4:
Correct Answer:
Solution : Both apples and oranges are fruits. But, apples and oranges are not related to each other in any way.
So, All apples are fruits; All oranges are fruits; No apples are oranges.
Based on the above statements, the Venn diagram will be
Hence, second option is
Question : O is a point in the interior of $\triangle \mathrm{ABC}$ such that OA = 12 cm, OC = 9 cm, $\angle A O B=\angle B O C=\angle C O A$ and $\angle A B C=60^{\circ}$. What is the length (in cm) of OB?
Option 1: $6 \sqrt{3}$
Option 2: $4 \sqrt{6}$
Option 3: $4 \sqrt{3}$
Option 4: $6 \sqrt{2}$
Correct Answer: $6 \sqrt{3}$
Solution :
O is a point in the interior of $\triangle \mathrm{ABC}$ OA = 12 cm OC = 9 cm $\angle A O B=\angle B O C=\angle C O A$ $\angle A B C=60^{\circ}$ $\angle A O B=\angle B O C=\angle C O A=\frac{360^{\circ}}{3} = 120^{\circ}$
Question : Identify the segment in the sentence which contains a grammatical error. This jewellery box is made from silver and is an antique piece.
Option 1: This jewellery box
Option 2: is made from silver
Option 3: and is
Option 4: an antique piece
Correct Answer: is made from silver
Solution : The correct choice is the second option.
Explanation: The error is in the use of the preposition "from" in connection with the material of the jewellery box. The correct preposition to use when talking about the material from which something is
Question : Jawahar Tunnel one of the largest in India is located in the State of
Option 1: Jammu and Kashmir
Option 2: Maharashtra
Option 3: Karnataka
Option 4: Himachal Pradesh
Correct Answer: Jammu and Kashmir
Solution : The correct option is Jammu and Kashmir.
The Jawahar Tunnel is a road tunnel located in Jammu and Kashmir, India. It is a vital transit route in the area. The tunnel connects the villages of Banihal and Qazigund by passing through the Pir
Question : Direction: In this question, a word is represented by only one set of numbers as given in any one of the alternatives. The sets of numbers given in the alternatives are represented by two classes of alphabets as in the two matrices, given below. The columns and rows of Matrix (I) are numbered from 0 to 4 and that of Matrix (II) are numbered from 5 to 9. A letter from these matrices can be represented first by its row and next by its column, e.g. A can be represented by 01,13, etc. and B can be represented by 58, 69, etc. Similarly, you have to identify the set for the word FINE.
Option 1: 00, 04, 02, 56
Option 2: 12, 10, 13, 67
Option 3: 24, 59, 31, 78
Option 4: 31, 32, 33, 87
Correct Answer: 00, 04, 02, 56
Solution : Given – FINE
Option first: 00, 04, 02, 56
FINE
The first set represents the word FINE.
Option second: 12, 10, 13, 67
FIAE
Option third: 24, 59, 31, 78
ATAT
Option fourth: 31, 32, 33, 87
FINT
Hence, third option is
Question : If $x=\frac{6pq}{p+q}$, then the value of $\frac{x+3p}{x–3p}+\frac{x+3q}{x–3q}$ is:
Option 1: 6
Option 2: 8
Option 3: 2
Option 4: 3
Correct Answer: 2
Solution : Given: $x=\frac{6pq}{p+q}$ ⇒ $x=\frac{6pq}{p+q}$ and $x=\frac{6pq}{p+q}$ ⇒ $\frac{x}{3p}=\frac{2q}{p+q}$ and $\frac{x}{3q}=\frac{2p}{p+q}$ Applying componendo and dividendo in the above expressions, we get, ⇒ $\frac{x+3p}{x–3p}=\frac{2q+p+q}{2q–(p+q)}$ and $\frac{x+3q}{x–3q}=\frac{2p+p+q}{2p–(p+q)}$ ⇒ $\frac{x+3p}{x–3p}=\frac{p+3q}{q–p}$ and $\frac{x+3q}{x–3q}=\frac{3p+q}{p–q}$ The value of the given expression $\frac{x+3p}{x–3p}+\frac{x+3q}{x–3q}$ is as follows, $\frac{x+3p}{x–3p}+\frac{x+3q}{x–3q}=\frac{p+3q}{q–p}-\frac{3p+q}{q–p}$ $=\frac{p+3q–3p–q}{q–p}$ $=\frac{2(q-p)}{q-p}$ $=2$ Hence, the correct
Question : Which of the following festivals is not associated with Sikkim?
Option 1: Losar
Option 2: Lohri
Option 3: Sakewa
Option 4: Yenya
Correct Answer: Lohri
Solution : The correct option is Lohri.
Lohri is not associated with the state of Sikkim. Lohri is a winter festival celebrated in North India, particularly in the Punjab region. It is usually observed on January 13th every year.
Question : A shopkeeper sells an item at a profit of 15% and uses a weight which is 20% less. Find his actual profit percentage.
Option 1: 42.5%
Option 2: 50%
Option 3: 40%
Option 4: 43.75%
Correct Answer: 43.75%
Solution : Given: A shopkeeper sells an item at a profit of 15%. False weight used = 20% less than the actual weight Let the cost price of 100 gm = Rs. 100 if the cost price of 1 gm is Re. 1 Selling price of 100
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