Staff Selection Commission Sub Inspector Exam
Question : Directions: Four pairs of numbers have been given, out of which three are alike in some manner, while one is different. Choose out the odd one.
Option 1: 25 : 16 : 9
Option 2: 64 : 100 : 18
Option 3: 81 : 9 : 19
Option 4: 16 : 64 : 12
Correct Answer: 81 : 9 : 19
Solution : Let's check each option – First option: 25 : 16 : 9→√(25) + √(16) = 5 + 4 = 9 Second option: 64 : 100 : 18→√(64) + √(100) = 8 + 10 = 18 Third option: 81 : 9 :
Question : Directions: Six characters A, B, C, 1, 2, and 3 are written on different faces of a dice. Two positions of this dice are shown in the figure. Find the character on the face opposite to C.
Option 1: 2
Option 2: 1
Option 3: 3
Option 4: B
Correct Answer: 3
Solution : Taking dice positions 1 and 2 with A as the common face.
Moving clockwise from the common face with A –
So, the opposite pairs are –
Therefore, the opposite face of the C is 3. Hence, the third option is correct.
Question : PT is a tangent at the point R on a circle with centre O. SQ is a diameter, which when produced meets the tangent PT at P. If $\angle$SPT = 32$^\circ$, then what will be the measure of $\angle$QRP?
Option 1: $58^\circ$
Option 2: $30^\circ$
Option 3: $29^\circ$
Option 4: $32^\circ$
Correct Answer: $29^\circ$
Solution : Given, $\angle SPT = 32^\circ$ $OR$ is perpendicular to $PT$, so $\angle ORP = 90^\circ$ Let $\angle QRP = \theta$ As we know, the sum of two interior opposite angles of a triangle is equal to its exterior angle. So, $\angle OQR = 32^\circ +
Question : Select the option that can be used as a one-word substitute for the given group of words.
A place for storage of arms and ammunition
Option 1: Wardrobe
Option 2: Warehouse
Option 3: Granary
Option 4: Arsenal
Correct Answer: Arsenal
Solution : The fourth option is correct.
Arsenal is a place where weapons and military equipment are made or stored. This makes it the correct one-word substitute.
The meanings of the other options are as follows:
Question : In a test consisting of 120 questions, Anuradha answered 65% of the first 60 questions correctly. What percentage of the remaining questions does she need to answer correctly to score 75% in the test?
Option 1: 80
Option 2: 85
Option 3: 84
Option 4: 90
Correct Answer: 85
Solution : Let the remaining correct questions be $x$. According to the question, $60 \times \frac{65}{100} + x = 120 \times \frac{75}{100}$ ⇒ $39 + x = 90$ ⇒ $x = 90 - 39= 51$ So, the required percentage = $\frac{51}{60} \times 100$ = 85% Hence, the
Question : Find the area of a triangle whose length of two sides are 4 cm and 5 cm and the angle between them is 45°.
Option 1: $4 \sqrt{2} \mathrm{~cm}^2$
Option 2: $7 \sqrt{2} \mathrm{~cm}^2$
Option 3: $5 \sqrt{2} \mathrm{~cm}^2$
Option 4: $6 \sqrt{2} \mathrm{~cm}^2$
Correct Answer: $5 \sqrt{2} \mathrm{~cm}^2$
Solution : Given: 1st side = 4 cm 2nd side = 5 cm Angle between them = $45^\circ$ We know that, Area of triangle = $\frac{1}{2}\times\text{1st side × 2nd side}\times\sin\theta$ = $\frac{1}{2}\times4\times5\times\sin45^\circ$ = $10\times\frac{1}{\sqrt2}$ = $5\sqrt2$ Hence, the correct answer is $5\sqrt2\ cm^2$.
Question : Which one of the following organisations is directly related to child welfare?
Option 1: UNESCO
Option 2: UNICEF
Option 3: WHO
Option 4: WTO
Correct Answer: UNICEF
Solution : The correct option is UNICEF.
The United Nations organization UNICEF, also known as the United Nations International Children's Emergency Fund, is devoted to advancing and defending the rights and welfare of children everywhere. On December 11, 1946, the United Nations General Assembly established UNICEF to
Question : If $x=a\sec\theta$ and $y=b\tan\theta$, then $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=?$
Option 1: 1
Option 2: 2
Option 4: 4
Correct Answer: 1
Solution : Given: $x=a\sec\theta$ and $y=b\tan\theta$ ⇒ $\frac{x^{2}}{a^{2}}=\frac{a^{2}\sec^{2}\theta}{a^{2}}=\sec^{2}\theta$ ⇒ $\frac{y^{2}}{b^{2}}=\frac{b^{2}\tan^{2}\theta}{b^{2}}=\tan^{2}\theta$ The value of $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=\sec^{2}\theta-\tan^{2}\theta=1$ Hence, the correct answer is 1.
Question : Select the most appropriate synonym of the given word.
Chaos
Option 1: Insanity
Option 2: Tidiness
Option 3: Disarray
Option 4: Certainty
Correct Answer: Disarray
Solution : The third option is correct.
Chaos refers to a state of complete disorder and confusion, often characterised by a lack of organisation or predictability. On the other hand, disarray is a synonym that specifically captures the essence of disorder and lack of arrangement.
The meanings
Question : The cost of a pencil is $33\frac{1}{3}$% less than the cost price of a pen. If a man sells 4 pencils at the cost price of 5 pens, what is his profit percentage?
Option 1: 50
Option 2: 66.66
Option 3: 75
Option 4: 87.5
Correct Answer: 87.5
Solution : Let $x$ be the cost price of a pen. Cost price of a pencil $= x - 33\frac{1}{3}$% of $x$ = $x - \frac{1}{3}x = \frac{2}{3}x$ Cost price of 4 pencils = $4 × \frac{2}{3}x$ = $\frac{8}{3}x$ Selling price of 4 pencils = cost price
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