Correct Answer: 7.98

Solution : Downstream speed = (10 + 4.5) = 14.5 km/hr
Upstream speed = (10 – 4.5) = 5.5 km/hr
Let the distance be $x$ km.
According to the question,
$\frac{x}{14.5}+\frac{x}{5.5}=2$
⇒ $\frac{10x}{145}+\frac{10x}{55}=2$
⇒ $550x+1450x=2×145×55$
⇒ $2000x=2×145×55$
⇒ $x=\frac{2×145×55}{2000}$
⇒ $x= 7.975 \approx 7.98$ km
Hence, the

Correct Answer: 36 

Solution : Let's check the options —

First option: 36; 36 is not divisible by 16. This option is different from the other options.

Second option: 96; 96 ÷ 16 = 6. 96 is divisible by 16.

Third option: 16; 16 ÷ 16 = 1. 16 is

Correct Answer: 42 : 4

Solution : Let's check the options —

First option: 42 : 4; 42 is not divisible by 4. This option is different from the other options.

Second option: 48 : 6; 48 ÷ 6 = 8. 48 is divisible by 6.

Third option: 32 :

Correct Answer: Bharatiya Jnanapeeth Trust

Solution : The correct answer is Bharatiya Jnanapeeth Trust. mo

The Bharatiya Jnanpeeth Trust, bestows the Moortidevi Award to an Indian writer each year. It was instituted in the year 1961 but was first awarded in 1983. It has a cash reward of 4 lakh

Correct Answer: 6

Solution : Given: Number = 148109326
The last three digits of the given number are 326.
When 326 is divided by 8 gave a remainder of 6.
So, 148109326 – 6 = 148109320 is completely divisible by 8.
So, the smallest required number is 6.
Hence, the

Correct Answer: Directive Principles of State Policy

Solution : The Correct Answer is Directive Principles of State Policy

The Directive Principles of State Policy (DPSP) are found in Part IV of the Indian Constitution, Articles 36–51. These tenets seek to create a welfare state in India and guarantee socioeconomic

Correct Answer: $-\cos ^2 \theta \sin ^2 \theta$

Solution : $\frac{\tan ^6 \theta-\sec ^6 \theta+3 \sec ^2 \theta \tan ^2 \theta}{\tan ^2 \theta+\cot ^2 \theta+2}$
Since $0^{\circ}<\theta<90^{\circ}$, putting $\theta=45^{\circ}$
$\frac{\tan ^6 45^{\circ}-\sec ^6 45^{\circ}+3 \sec ^2 45^{\circ} \tan ^2 45^{\circ}}{\tan ^2 45^{\circ}+\cot ^245^{\circ}+2}$
$=\frac{1-(\sqrt2)^6+ 3\times (\sqrt2)^2\times 1}{1+1+2}$
$=\frac{1-8+6}{1+1+2}=-\frac{1}{4}$
From option

Correct Answer: 15

Solution : The figure can be labeled as shown below –

There are a total of 15 triangles in the figure. They are AHB, AHD, BHC, DHC, ABD, BCD, BAC, ADC, EHC, CHF, GHF, CHG, BHE, DHG, DHF.

Hence, the second option is correct.

Correct Answer: $\frac{1}{679}$

Solution : $\frac{432^2+247^2-432 \times 247}{432^3+247^3}$
Using identity $x^3+y^3 = (x+y)(x^2+y^2-x \times y)$, 
$\frac{432^2+247^2-432 \times 247}{(432+247)(432^2+247^2-432 \times 247)}$
$=\frac{1}{(432+247)}$
$= \frac{1}{679}$
Hence, the correct answer is $\frac{1}{679}$.

Correct Answer: equipped

Solution : The most appropriate option to fill in the blank is the fourth option.

Explanation: The word technically in the sentence indicates that the industry is being described in terms of technical aspects. The adjective equipped fits well in this context, suggesting that the Indian tea