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.

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 $\sec 3\theta  - \tan 3\theta$.

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.

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 $\frac{92}{11}\ \text{hours}$.

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.
 

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.

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.

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 $1$.

Correct Answer: A, B and C only

Solution : The correct answer is A, B and C only.

A state's Legislative Council may not have fewer than 40 members or more than one-third of the State Assembly's total membership, as stated in Article 171 of the Constitution. One-third or less of the State Legislative Assembly's members may comprise the State Legislative Council. Its membership must, however, be less than forty. The State Legislative Council's Chairman and Deputy Chairman are chosen by these members.

Correct Answer: 5

Solution : Given:
4 × 9 × 3 = 4, 5 × 3 × 1 = 3

The pattern in the equation→4 × 9 × 3 = 4 is 4 + 9 + 3 = 16 = 4²
The pattern in the equation→5 × 3 × 1 = 3 is 5 + 3 + 1 = 9 = 3²

Here, the sign × means +.
Using the same pattern in equation 9 × 9 × 7
The equation becomes –
9 + 9 + 7 = 25 = 5²  
Therefore, the square root of 25 is equal to 5.

Hence, the first option is correct.