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Staff Selection Commission Sub Inspector Exam

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Question : If $s-\frac{1}{s-8}=20$, then the value of $(s-8)^3-\frac{1}{(s-8)^3}$ is:

Option 1: 1324

Option 2: 1764

Option 3: 1864

Option 4: 1944

Team Careers360 24th Jan, 2024

Correct Answer: 1764


Solution : Given: $s-\frac{1}{s-8}=20$
⇒ $s-8-\frac{1}{s-8}=12$
⇒ $(s-8-\frac{1}{s-8})^3=12^3$
⇒ $(s-8)^3-(\frac{1}{s-8})^3-3×(s-8)×\frac{1}{(s-8)}(s-8-\frac{1}{s-8})=1728$
⇒ $(s-8)^3-(\frac{1}{s-8})^3-3×12=1728$
$\therefore(s-8)^3-(\frac{1}{s-8})^3= 1764$
Hence, the correct answer is 1764.

18 Views

Question : Who was the last sultan of the Lodi Dynasty?

Option 1: Khizr Khan

Option 2: Sikander Lodi

Option 3: Ibrahim Lodi

Option 4: Bahlol Lodi

Team Careers360 23rd Jan, 2024

Correct Answer: Ibrahim Lodi


Solution : The correct answer is Ibrahim Lodi.

Ibrahim Khan Lodi, the final ruler of the Lodi Sultanate in Delhi (r. 1517–1526), possessed commendable warrior skills but lacked political acumen. His premature pursuit of royal absolutism and reliance on repression without administrative strengthening led to

24 Views

Question : Directions: Select the option related to the fifth letter cluster in the same way the second letter cluster is related to the first letter cluster and the fourth letter cluster is related to the third letter cluster.
LIST : JNGKQURV :: MOAN : KOMQYCLP :: PLUM : ?

Option 1: NRJNKOSW

Option 2: NRJNSWKO

Option 3: NRSWKOJN

Option 4: NRSWJNKO

Team Careers360 23rd Jan, 2024

Correct Answer: NRJNSWKO


Solution : Given:
LIST : JNGKQURV :: MOAN : KOMQYCLP :: PLUM : ?

Subtract and add 2, to the place value of each letter of LIST and MOAN, to get the related letter cluster as shown below –

So, LIST is related to JNGKQURV.
And, MOAN

131 Views

Question : Directions: In a language FIFTY is written as CACTY, CAR as POL, TAR as TOL how can TARIFF be written in that language?

Option 1: TOEFDD

Option 2: TOEFEL

Option 3: TOLACC

Option 4: TOLADD

Team Careers360 25th Jan, 2024

Correct Answer: TOLACC


Solution : Given:
FIFTY is written as CACTY, CAR is written as POL and TAR is written as TOL.

Like in, FIFTY is written as CACTY –

F I F T Y
C A C T Y

And in, CAR is written as POL –

C A
21 Views

Question : If $4-2 \sin ^2 \theta-5 \cos \theta=0,0^{\circ}<\theta<90^{\circ}$, then the value of $\cos \theta+\tan \theta$ is:

Option 1: $\frac{2-\sqrt{3}}{2}$

Option 2: $\frac{1+2 \sqrt{3}}{2}$

Option 3: $\frac{2+\sqrt{3}}{2}$

Option 4: $\frac{1-2 \sqrt{3}}{2}$

Team Careers360 19th Jan, 2024

Correct Answer: $\frac{1+2 \sqrt{3}}{2}$


Solution : Given: $4-2 \sin ^2 \theta-5 \cos \theta=0$
⇒ $4-2(1- \cos ^2 \theta)-5 \cos \theta=0$
⇒ $4-2+ 2\cos ^2 \theta-5 \cos \theta=0$
⇒ $2\cos ^2 \theta-5 \cos \theta+2=0$
⇒ $2\cos ^2 \theta-4 \cos \theta- \cos \theta+2=0$
⇒ $2\cos \theta(\cos \theta-2) - 1(\cos \theta-2) = 0$

119 Views

Question : In an election between two candidates, the difference between the candidates who won and lost was 2,500 votes. The candidate who won got 75% of the votes, and there were no invalid votes. The total number of votes polled by the losing candidate was:

Option 1: 1875

Option 2: 5000

Option 3: 1250

Option 4: 3750

Team Careers360 22nd Jan, 2024

Correct Answer: 1250


Solution : Let V be the total number of votes polled.
The winning candidate received 75% of the votes, which is 0.75V.
⇒ The losing candidate received the remaining 25% of the votes, which is 0.25V.
The difference between the votes of the winning and losing candidates

22 Views

Question : Which atomic number element of the periodic table is named after Alfred Nobel, the inventor of dynamite and the founder of the Nobel Prize?

Option 1: 102

Option 2: 100

Option 3: 105

Option 4: 108

Team Careers360 24th Jan, 2024

Correct Answer: 102


Solution : The correct option is 102.

The element named after Alfred Nobel is Nobelium, and its atomic number is 102. Nobelium is a synthetic element, meaning it is not found in nature and has to be produced in a laboratory. It was first synthesised in

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