Question : Identify the option that arranges the following neighbouring countries of India according to their Human Development Index (HDI) ranks in 2021-22 in decreasing order.
a) Sri Lanka
b) Maldives
c) Bhutan
d) Bangladesh
Option 1: b-a-d-c
Option 2: a-b-c-d
Option 3: b-a-c-d
Option 4: a-b-d-c
Correct Answer: a-b-c-d
Solution : The correct option is a-b-c-d.
In 2021–22, neighbouring countries of India are arranged according to their Human Development Index (HDI) ranking:
a) Sri Lanka holds the highest HDI rank (73) with a value of 0.782, reflecting high development status.
b) The Maldives ranked second (90) with an HDI value of 0.747, also categorised under high development.
c) Bhutan follows (127) with an HDI value of 0.666, categorised under medium human development.
d) Bangladesh ranked lowest (129) with an HDI value of 0.661, also categorised under medium human development.
Answer laterQuestion : Select the most appropriate ANTONYM of the given word.
Pacify
Option 1: Placate
Option 2: Assuage
Option 3: Aggravate
Option 4: Quell
Correct Answer: Aggravate
Solution : The right option is the third option.
Pacify means to calm or soothe, while aggravate means to worsen or intensify a situation, making it the antonym in this context.
The meanings of other words are:
- Placate: This means to make someone less angry or hostile by making concessions or soothing gestures; to appease or calm.
- Assuage: This means to ease or alleviate a problem, discomfort, or pain; to make something less intense or severe.
- Quell: This means to suppress, pacify, or put an end to something, especially by using force or authority
Question : Who among the following has been appointed as the new Chairperson of the National Company Law Appellate Tribunal (NCLAT), for four years or until he attains the age of 70 years, whichever is the earliest in November 2021?
Option 1: Justice Vikram Nath
Option 2: Justice B.V. Nagarathna
Option 3: Justice Ashok Bhushan
Option 4: Justice Abhay Shreeniwas Oka
Correct Answer: Justice Ashok Bhushan
Solution : The correct option is Justice Ashok Bhushan.
Justice Ashok Bhushan, a former Supreme Court judge, was appointed as the new Chairperson of the National Company Law Appellate Tribunal (NCLAT) on November 8, 2021. His tenure is set for four years or until he reaches the age of 70, whichever comes first.
Question : Find the value of: $\sqrt{\frac{1 - \sin 3 \theta}{1 + \sin 3 \theta}}$
Option 1: $\sec 3 \theta - \tan 3 \theta$
Option 2: $(\sec 3 \theta - \tan 3 \theta)^3$
Option 3: $(\sec 3 \theta - \tan 3 \theta)^2$
Option 4: $\sec 3 \theta + \tan 3 \theta$
Correct Answer: $\sec 3 \theta - \tan 3 \theta$
Solution : $\sqrt{\frac{1 – \sin 3 \theta}{1 + \sin 3 \theta}}$
= $\sqrt{\frac{(1 – \sin 3 \theta)(1 – \sin 3\theta)}{(1 + \sin 3\theta)(1 – \sin 3\theta)}}$
= $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{1 – \sin^{2}3\theta}}$
= $\sqrt{\frac{(1 – \sin 3\theta)^{2}}{\cos^{2}3\theta}}$
= $\frac{1 - \sin 3\theta}{\cos 3\theta}$
= $\sec 3\theta - \tan 3\theta$
Hence, the correct answer is $\sec 3\theta - \tan 3\theta$.
Question : If $\left (x+\frac{1}{x}\right )=5$, find the value of $\frac{6x}{x^{2}+x+1}$.
Option 1: 3
Option 2: 2
Option 3: 1
Option 4: 0
Correct Answer: 1
Solution : Given: $\left (x+\frac{1}{x} \right)=5$
⇒ $\frac{x^2+1}{x}=5$
⇒ $x^2+1=5x$
Adding $x$ on both sides,
⇒ $x^2+1+x=5x+x$
⇒ $x^2+x+1=6x$
Now, put the value of $x^2+x+1=6x$ in the expression $\frac{6x}{x^{2}+x+1}$
So, $\frac{6x}{x^{2}+x+1}=\frac{6x}{6x}=1$
Hence, the correct answer is 1.
Question : Two pipes, S1 and S2, can alone fill an empty tank in 15 hours and 20 hours, respectively. Pipe S3 alone can empty that filled tank in 40 hours. Firstly, both pipes, S1 and S2, are opened and after 2 hours, pipe S3 is also opened. In how much time will the tank be filled after S3 is opened?
Option 1: $\frac{90}{17}\ \text{hours}$
Option 2: $\frac{89}{12}\ \text{hours}$
Option 3: $\frac{90}{13}\ \text{hours}$
Option 4: $\frac{92}{11}\ \text{hours}$
Correct Answer: $\frac{92}{11}\ \text{hours}$
Solution : Let the capacity of the tank be 120 units (LCM of 15, 20, and 40)
Pipe A fills = $\frac{120}{15}$ = 8 units per hour
Pipe B fills = $\frac{120}{15}$ = 6 units per hour
Pipe C empties = $\frac{120}{40}$ = 3 units per hour
A and B in 2 hours fill (8 + 6) × 2 units of the tank = 28 units of the tank
Remaining units of the tank to be filled = 120 – 28 = 92 units/hour
After 2 hours, C joins.
So, units of the tank filled by A, B, and C = (8 + 6 – 3) = 11 units/hour
So, the time needed to fill the remaining tank = $\frac{92}{11}$ hours
Hence, the correct answer is $\frac{92}{11}\ \text{hours}$.
Question : Washing of peeled vegetables removes the vitamin
Option 1: A
Option 2: C
Option 3: D
Option 4: E
Correct Answer: C
Solution : The correct option is Vitamin C.
Some vitamin C is lost when vegetables are washed. Because vitamin C is a water-soluble vitamin, it dissolves in water. When you wash vegetables, part of the vitamin C is washed away. The quantity of vitamin C lost during washing is determined by several factors, including the kind of vegetable, the length of time it is washed, and the temperature of the water. Leafy vegetables, such as spinach and kale, lose more vitamin C than root vegetables, such as carrots and potatoes.
Question : The perimeter of an isosceles triangle is 100 cm. If the base is 36 cm, find its semi-perimeter (in centimetres).
Option 1: 64 cm
Option 2: 60 cm
Option 3: 45 cm
Option 4: 50 cm
Correct Answer: 50 cm
Solution : Semi-perimeter of a triangle $= (\frac{\text{Perimeter}}{2})$
= $\frac{100}{2}$
= 50 cm
Hence, the correct answer is 50 cm.
Question : If $14 : 30 :: 7 : x$, then what is the value of $x$?
Option 1: 15
Option 2: 21
Option 3: 9
Option 4: 12
Correct Answer: 15
Solution : $14 : 30 :: 7 : x$
⇒ $\frac{14}{30}=\frac{7}{x}$
⇒ $x = \frac{7\times 30}{14}$
⇒ $x= 15$
Hence, the correct answer is 15.
Question : The length, breadth, and height of a wooden box with a lid are 10 cm, 9 cm, and 7 cm, respectively. The total inner surface of the closed box is 262 cm2. The thickness of the wood (in cm) is:
Option 1: $2$
Option 2: $3$
Option 3: $\frac{23}{3}$
Option 4: $1$
Correct Answer: $1$
Solution : Given: Inner surface area = 262 cm2
The length, breadth, and height are 10 cm, 9 cm, and 7 cm, respectively.
Let the thickness of the wood be $x$ cm.
Surface area of the cuboid = 2(length × breadth + length × height + breadth × height)
Area of inner surface $= 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10- 2x)(7 - 2x)$
$⇒ 262 = 2(9 - 2x)(10 - 2x) + 2(9 -2x)(7 - 2x) + 2(10 - 2x)(7- 2x)$
Putting the value of $x = 1,$ the above equation is satisfied.
Hence, the correct answer is $1$.
