Staff Selection Commission Combined Graduate Level Exam
Question : If $\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$, then what is the value of $(x+y+z)^3$?
Option 1: 0
Option 2: 1
Option 3: 2
Option 4: 3
Correct Answer: 0
Solution : Given:$\frac{x^2}{yz}+\frac{y^2}{zx}+\frac{z^2}{xy}=3$ We know the identity, if $(x+y+z)=0$, then $(x^3+y^3+z^3)=3xyz$ Take the LCM of the given expression, we get– $\frac{x^3+y^3+z^3}{xyz}=3$ ${x^3+y^3+z^3}=3(xyz)$ So, $(x+y+z)=0$ The value of $(x+y+z)^3=0$ Hence, the correct answer is 0.
Question : Raman spends 80% of his income. If his income is increased by 25% and the expenditure increases by 10%, what will be the percentage increase in his savings?
Option 1: 17%
Option 2: 70%
Option 3: 77%
Option 4: 85%
Correct Answer: 85%
Solution : Let Raman's income be Rs. 100. Raman spends 80% = $\frac{80}{100}× 100$ = Rs. 80 Raman's savings = 100 – 80 = Rs. 20 If his income is increased by 25%, New income $=\frac{125}{100} × 100 = 125$ If his expenditure increases by 10%, New
Question : A person deposited INR 500 for 3 years, INR 650 for 5 years, and INR 1,250 for 7 years. He received a total simple interest of INR 1,620. The rate of interest per annum is:
Option 1: 12%
Option 2: 13%
Option 3: 10.8%
Option 4: 11%
Correct Answer: 12%
Solution : Given: A person deposited INR 500 for 3 years, INR 650 for 5 years, and INR 1,250 for 7 years. Total Simple Interest = INR 1,620 Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$ According to the question, ⇒ $1620=\frac{500×R×3}{100}+\frac{650×R×5}{100}+\frac{1250×R×7}{100}$ ⇒ $1620=15R+\frac{65R}{2}+\frac{175R}{2}$ ⇒ $1620=\frac{30R+65R+175R}{2}$ ⇒
Question : In a triangle PQR, S, and T are the points on PQ and PR, respectively, such that ST || QR and $\frac{\text{PS}}{\text{SQ}} = \frac{3}{5}$ and PR = 6 cm. Then PT is:
Option 1: 2 cm
Option 2: 2.25 cm
Option 3: 3.5 cm
Option 4: 4 cm
Correct Answer: 2.25 cm
Solution : Given: In $\triangle$PQR, QR || ST $\frac{\text{PS}}{\text{SQ}} = \frac{3}{5}$ Let PS = 3 units, SQ = 5 units So, PQ = 3 + 5 = 8 units PR = 6 cm In ∆ PST and ∆ PQR, ∵ QR | | ST ∵ $\angle$S
Question : Directions: Fair is related to Righteous in the same way as Cunning is related to ____.
Option 1: Person
Option 2: Personality
Option 3: Deceit
Option 4: Character
Correct Answer: Deceit
Solution : Given: Fair is related to Righteous.
Like, righteous is the synonym of fair which means to do everything morally right. Similarly, deceit is the synonym of cunning which means to cheat.
Hence, the third option is correct.
Question : From point H, at 6:30 pm, a train starts moving towards point K at the speed of 90 km/hr. Another train starts moving from point K at 7:30 p.m. towards point H at the speed of 72 km/hr. Both trains meet at 11:30 p.m. at point J. What is the ratio of the distance HJ and KJ?
Option 1: 25 : 16
Option 2: 5 : 16
Option 3: 36 : 25
Option 4: 31 : 19
Correct Answer: 25 : 16
Solution : Given, H to K = 6:30 pm at 90 km/hr K to H = 7: 30 pm at 72 km/hr J = 11: 30 pm The time between 6:30 pm and 11:30 pm = 5 hours ⇒ Distance between point H and J
Question : Directions: A sentence or a part of the sentence is printed in bold. Below are alternatives to the bold part that may improve the sentence. Choose the correct alternative. In case no improvement is needed, choose "No Improvement".
But understanding what constitutes such a miracle diet, and making sure that patients get it, isn't as straightforward as it seems.
Option 1: 1
Option 2: 2
Option 3: 3
Option 4: 4
Correct Answer: 1
Solution : The correct choice is the first option.
This alternative provides the correct adjective form miraculous to describe the type of diet.
Miraculous means highly extraordinary or seemingly supernatural, which aligns with the context of the sentence.
So, the correct sentence is: But understanding what constitutes
Question : Directions: Select the word pair that best represents a similar relationship to the one expressed in the pair of words given below. (The words must be considered meaningful English words and not be related to each other based on the number of letters/consonants/vowels in the word.) Dog : Kennel
Option 1: Bee : Hive
Option 2: Hare : Den
Option 3: Lion : Burrow
Option 4: Spider : Shed
Correct Answer: Bee : Hive
Solution : Given: Dog : Kennel (Kennel is the shelter for dogs.)
Let's check the options – First option: Bee : Hive; Hive is the shelter for bees. Second option: Hare : Den; Den is the shelter for lions. Third option: Lion : Burrow; Burrow
Question : The Security Council of UN consists of
Option 1: 5 permanent and 10 non-permanent members
Option 2: 10 permanent and 5 non-permanent members
Option 3: 15 permanent members
Option 4: 15 non-permanent members
Correct Answer: 5 permanent and 10 non-permanent members
Solution : The correct option is 5 permanent and 10 non-permanent members.
The United Nations Security Council is made up of 15 members, with China, France, Russia, the United Kingdom, and the United States serving as its five permanent members. The General
Question : Directions: A series is given below with one term missing. Choose the correct alternative from the given ones that will complete the series. CAT, DBT, ECT, ?
Option 1: DCT
Option 2: FDT
Option 3: FCT
Option 4: FAT
Correct Answer: FDT
Solution : Given: CAT, DBT, ECT, ?
In the given series, add 1 to the place value of the first and second letters, and T is constant in all the given terms – CAT→C + 1 = D; A + 1 = B; T DBT→D + 1
The Question containing Inaapropriate or Abusive Words
Question lacks the basic details making it difficult to answer
Topic Tagged to the Question are not relevant to Question
Question drives traffic to external sites for promotional or commercial purposes
The Question is not relevant to User
And never miss an important update
