Staff Selection Commission Sub Inspector Exam
Question : If $a^2+b^2+c^2+216=12(a+b-2 c)$, then $\sqrt{a b-b c+c a}$ is:
Option 1: 8
Option 2: 3
Option 3: 6
Option 4: 4
Correct Answer: 6
Solution : Given: $a^2+b^2+c^2+216=12(a+b-2 c)$ Rearranging and simplifying ⇒ $a^2 - 12a + b^2 - 12b + c^2 + 24c + 216 = 0$ ⇒ $a^2 - 12a + 36 + b^2 - 12b + 36 + c^2 + 24c + 144 = 0$ ⇒ $(a -
Question : "A Century Is Not Enough" is an autobiography of:
Option 1: Rahul Dravid
Option 2: Sachin Tendulkar
Option 3: Anil Kumble
Option 4: Sourav Ganguly
Correct Answer: Sourav Ganguly
Solution : The correct answer is Sourav Ganguly.
The book "A Century is Not Enough: My Roller Coaster Ride to Success" is an autobiography of Sourav Ganguly with Gautam Bhattacharya. The book was published in 2018.
Question : If the angle of elevation of the Sun changes from 30° to 45°, the length of the shadow of a pillar decreases by 20 metres. The height of the pillar is:
Option 1: $20(\sqrt{3}-1)$ m
Option 2: $20(\sqrt{3}+1)$ m
Option 3: $10(\sqrt{3}-1)$ m
Option 4: $10(\sqrt{3}+1)$ m
Correct Answer: $10(\sqrt{3}+1)$ m
Solution : In $\Delta$ ABC $\tan 45°=\frac{AB}{BC}$ ⇒ $1=\frac{h}{BC}$ ⇒ $BC=h=AB$ In $\Delta$ ABD $\tan 30°=\frac{AB}{BD}$ ⇒ $\frac{1}{\sqrt3}=\frac{h}{h+20}$ ⇒ $h+20=h\sqrt{3}$ ⇒ $h=\frac{20}{\sqrt{3}–1}$ ⇒ $h=\frac{20}{\sqrt{3}–1}×\frac{\sqrt{3+1}}{\sqrt{3+1}}$ ⇒ $h=10(\sqrt{3}+1)$ m Hence, the correct answer is $10(\sqrt{3}+1)$ m.
Question : Directions: In the following question a series is given, with one number missing. select the missing number from the given alternatives. 4, 16, 36, 64, ?
Option 1: 81
Option 2: 121
Option 3: 100
Option 4: 729
Correct Answer: 100
Solution : Given: 4, 16, 36, 64,?
Each term is obtained by the squaring of consecutive even numbers – 22 = 4; 42 = 16; 62 = 36; 82 = 64; 102 = 100
So, 100 is the missing term in the
Question : In $\triangle \mathrm{ABC}, \mathrm{BD} \perp \mathrm{AC}$ at D. E is a point on BC such that $\angle \mathrm{BEA}=x^{\circ}$. If $\angle \mathrm{EAC}=62^{\circ}$ and $\angle \mathrm{EBD}=60^{\circ}$, then the value of $x$ is:
Option 1: $92^\circ$
Option 2: $78^\circ$
Option 3: $76^\circ$
Option 4: $68^\circ$
Correct Answer: $92^\circ$
Solution : In $\triangle AOD$, $\angle AOD + \angle ADO + \angle DAO = 180^\circ$ ⇒ $\angle AOD + 90^\circ + 62^\circ = 180^\circ$ ⇒ $\angle AOD = 180^\circ - 152^\circ$ ⇒ $\angle AOD = 28^\circ$ $\because \angle AOD$ and $\angle EOB$ are vertical opposite angles, $\angle
Question : Directions: In the following question, a sentence is given with a blank that is to be filled in with an appropriate word. Four alternatives are suggested; choose the correct alternative out of them as your answer.
Vishal couldn't ____ breakfast today.
Option 1: had
Option 2: have been
Option 3: have
Option 4: having
Correct Answer: have
Solution : The third option is the correct answer.
Have is the correct verb to use as the modal verb is always followed by the base form of the verb.
Therefore, the complete sentence is: Vishal couldn't have breakfast today.
Question : Let $\triangle {ABC} \sim \triangle {RPQ}$ and $\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{4}{9}$. If ${AB}=3 {~cm}, {BC}=4 {~cm}$ and ${AC}=5 {~cm}$, then ${PQ}$ (in ${cm}$ ) is equal to:
Option 1: 12
Option 2: 4.5
Option 3: 5
Option 4: 6
Solution : $\triangle$ ABC ∼ $\triangle$ RPQ $\frac{\operatorname{ar}(\triangle A B C)}{\operatorname{ar}(\triangle P Q R)}=\frac{4}{9}$ AB = 3 cm BC = 4 cm AC = 5 cm Concept used: $\triangle$ ABC ∼ $\triangle$ RPQ $\frac{\text{AB}}{\text{RP}} = \frac{\text{BC}}{\text{PQ}} = \frac{\text{AC}}{\text{QR}} = \sqrt{\frac{ar(\text{ABC})}{ar(\text{RPQ})}}$ $\frac{\text{AB}}{\text{RP}} = \sqrt{\frac{4}{9}}$ Calculation: $\frac{\text{AB}}{\text{RP}} = \frac{\text{BC}}{\text{PQ}}=
Question : A can complete a certain work in 35 days and B can complete the same work in 15 days. They worked together for 7 days, and then B left the work. In how many days will A alone complete 60% of the remaining work?
Option 1: 10
Option 2: 15
Option 3: 8
Option 4: 7
Correct Answer: 7
Solution : Given, A completes the work in 35 days. B completes the work in 15 days. A's 1 day's work $=\frac{1}{35}$ B's 1 day's work $=\frac{1}{15}$ So, (A + B)'s 1 day's work = $\frac{1}{35}+\frac{1}{15}=\frac{7 + 3}{105}=\frac{2}{21}$ ⇒ Work completed by A + B in 7
Question : If A is 48% more than B and C is 60% less than the sum of A and B, then A is what percentage more than C? (Correct to one decimal place.)
Option 1: 50.8
Option 2: 49.2
Option 3: 50.2
Option 4: 49.8
Correct Answer: 49.2
Solution : Given: A is 48% more than B and C is 60% less than the sum of A and B. Let the value of B be 100. Then, the value of A = $100\times \frac{148}{100}$ = 148 According to the question, C = 40% of (A
Question : The percentage marks obtained by 6 students in different subjects are given below. The maximum marks for each subject have been indicated in the table.
P
Q
R
S
T
U
70
90
85
75
65
60
44
40
32
50
88
54
58
45
92
64
80
72
55
25
38
30
35
42
48
The total marks obtained by student Q in Physics and Hindi are what percentage (rounded off to the nearest integer) more than the total marks obtained by student T in Geography and History?
Option 1: 45%
Option 2: 49%
Option 3: 56%
Option 4: 38%
Correct Answer: 45%
Solution : The total marks obtained by student Q in Physics and Hindi: In Physics, student Q scored 90% of 80 marks = 0.9 × 80 = 72 marks In Hindi, student Q scored 54% of 100 marks = 0.54 × 100 = 54 marks So, the
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
