Staff Selection Commission Sub Inspector Exam
Question : Two posts are 2 metres apart. Both posts are on the same side of a tree. If the angles of depressions of these posts when observed from the top of the tree are 45° and 60° respectively, then the height of the tree is:
Option 1: $(3-\sqrt{3})$ metres
Option 2: $(3+\sqrt{3})$ metres
Option 3: $(-3+\sqrt{3})$ metres
Option 4: $(3-\sqrt{2})$ metres
Correct Answer: $(3+\sqrt{3})$ metres
Solution : CD = 2 metres BD = $x$ metre AB = Tree = $h$ metre From ∆ ABC, tan 45° = $\frac{AB}{BC}$ ⇒ $1 = \frac{h}{x+2}$ $\therefore h = (x + 2)$ metre .....(i) From ∆ ABD, $\tan 60° = \frac{AB}{BD}$ ⇒ $\sqrt{3} = \frac{h}{x}$
Question : Onion is an example of the bulb which is a modified
Option 1: stem
Option 2: root
Option 3: leaf
Option 4: flower
Correct Answer: stem
Solution : The correct option is the stem.
The bulb of an onion is a modified underground stem that stores nutrients for the plant's growth, and reproduction. Scales are made up of layers of modified leaves. When growth resumes, the basal plate serves as an attachment
Question : Directions: In a certain code language, CHART is written as GDASS. How will INDEX be written in that language?
Option 1: MIDWF
Option 2: MJDWF
Option 3: MDJWF
Option 4: MWDJF
Correct Answer: MJDWF
Solution : Given: CHART is written as GDASS.
Add and subtract 1 from the place value of the letters of CHART and the middle letter of the word will remain the same then shuffle the position of the letters as shown below to get the required code.
Question : What would you call the area under the curve of a velocity-time graph included between itself and two-time ordinates?
Option 1: Velocity
Option 2: Displacement
Option 3: Acceleration
Option 4: Speed
Correct Answer: Displacement
Solution : The correct option is Displacement.
The area under the curve of a velocity-time graph, between the curve and two specific time axes, represents the displacement of an object during that time interval. This is based on the fact that the area under the velocity-time curve
Question : If 30% of (B – A) = 18% of (B + A), then the ratio A : B is equal to:
Option 1: 4 : 1
Option 2: 1 : 4
Option 3: 5 : 4
Option 4: 5 : 9
Correct Answer: 1 : 4
Solution : Given: 30% × (B – A) = 18% × (B + A) ⇒ $\frac{30}{100}$ × (B – A) = $\frac{18}{100}$ × (B + A) ⇒ 5 × (B – A) = 3 × (B + A) ⇒ 5B – 5A = 3B +
Question : The value of $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ is:
Option 1: $\cos A$
Option 2: $\tan A$
Option 3: $\cot A$
Option 4: $\sin A$
Correct Answer: $\sin A$
Solution : $(\operatorname{cosec}A+\cot A)(1 - \cos A)$ $=\left(\frac{1}{\sin A} + \frac{\cos A}{\sin A}\right)(1 - \cos A)$ $=\left(\frac{1 + \cos A}{\sin A}\right)(1 - \cos A)$ $=\frac{1 - \cos^2 A}{\sin A}$ $=\frac{\sin^2 A}{\sin A}$ [We know that $1 - \cos^2 A = \sin^2 A$] $=\sin A$ Hence, the
Question : A sum of INR 8,200 was divided among A, B, and C in such a way that A has INR 500 more than B, and C has INR 300 more than A. How much was A's share (in INR)?
Option 1: 2,300
Option 2: 3,100
Option 3: 2,800
Option 4: 2,000
Correct Answer: 2,800
Solution : Let the share of B be $x$. A = INR 500 more than B, so A $=x + 500$ C = INR 300 more than A, so C $=x + 500 + 300 = x+ 800$ According to the question, $x + (x + 500)
Question : The amount of oxygen in the atmosphere remains relatively constant because it is given off by
Option 1: oceans
Option 2: animals
Option 3: rocks
Option 4: plants
Correct Answer: plants
Solution : The correct option is plants.
Oxygen is cycled through the environment in a similar way to how water moves from the sky to the earth and back in the water cycle. Beginning with plants, the oxygen cycle begins. Through a process known as photosynthesis,
Question : If $a+\frac{1}{b}=b+\frac{1}{c}=c+\frac{1}{a}(a\neq b\neq c)$, then the value of $abc$ is:
Option 1: $\pm 1$
Option 2: $\pm 2$
Option 3: $0$
Option 4: $\pm \frac{1}{2}$
Correct Answer: $\pm 1$
Solution : $a+\frac{1}{b}=b+\frac{1}{c}$ ⇒ $(a-b) = \frac{(b-c)}{bc}$ ----------(i) $a+\frac{1}{b}=c+\frac{1}{a}$ ⇒ $(a-c) = \frac{(b-a)}{ba}$ ----------(ii) $b+\frac{1}{c}=c+\frac{1}{a}$ ⇒ $(b-c) = \frac{(c-a)}{ca}$ -----------(iii) Multiplying (i), (ii) and (iii), ⇒ $(a-b)(a-c)(b-c) = \frac{(b-c)(b-a)(c-a)}{bc×ba×ca}$ ⇒ $1 = \frac{1}{(abc)^2}$ ⇒ $abc = \pm 1$ Hence, the correct answer is $\pm 1$.
Question : Sour taste of "Coca cola" is due to the presence of
Option 1: Acetic acid
Option 2: Phosphoric acid
Option 3: Hydrochloric acid
Option 4: Formic acid
Correct Answer: Phosphoric acid
Solution : The correct answer is Phosphoric Acid.
Sour taste of coca cola is due to presence of phosphoric acid in it. Food grade phosphoric acid in an additive which gives acidic taste to the food and beverages and acts as a stabiliser and antioxidant. It
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