Correct Answer: $-\frac{9}{50}$

Solution : Given: $\sin t+\cos t=\frac{4}{5}$
Squaring both sides, we have,
⇒ $(\sin t+\cos t)^{2}=(\frac{4}{5})^{2}$
⇒ $\sin^{2} t+\cos^{2} t+2\sin t.\cos t=\frac{16}{25}$
We know that $\sin^{2} t+\cos^{2}=1$
⇒ $1+2\sin t.\cos t=\frac{16}{25}$
⇒ $2\sin t.\cos t=\frac{16}{25}–1$
⇒ $2\sin t.\cos t=-\frac{9}{25}$
⇒ $\sin t.\cos t=-\frac{9}{50}$
Hence, the correct answer is

Correct Answer: (2)

Solution : The error lies in the second part of the sentence.

The rules of the first conditional should be applied here, and the modal would should be used in the sentence to express a polite request. As per the first conditional, the condition must be in

Correct Answer: 208 cm

Solution : We know,
The volume of a cone = $\frac{1}{3}πr^2h$, where r is the radius of the cone
The volume of a sphere = $\frac{4}{3}πR^3$, where r is the radius of the sphere
According to the question,
$\frac{4}{3}πR^3 = \frac13πr^2h$
Let the height of the

Correct Answer: 66

Solution : Add the multiplication of numbers given in diagonal blocks, to get the number of centre blocks.

In the first figure – (4 × 3) + (5 × 2) = 12 + 10 = 22
In the second figure – (1 × 2) + (7

Correct Answer: 16 : 25

Solution : Here,
Remaining acid = Initial quantity × $(1–\frac{\text{Quantity taken out}}{\text{Original quantity}})^{\text{number of times removed}}$
⇒ Remaining acid $=20×(1-\frac{4}{20})^2=20×\frac{4}{5}×\frac{4}{5}= 12.8$ L
So, the required ratio
= (12.8) : (20)
= 128 : 200
= 16 : 25
Hence, the correct answer is 16 :

Correct Answer:  +, ÷, –, × 

Solution : Given:
55 * 63 * 9 * 8 * 3 = 38

Let's check the given options –
First option: ÷, ×, –, + 
⇒ 55 ÷ 63 × 9 – 8 + 3 = 38
Solving the L.H.S. of the equation

Correct Answer: Slege

Solution : The correct choice is the second option.

The correct spelling is sledge. It is an object or a vehicle that has long narrow strips of wood or metal under it and is used for travelling on snow.

The meanings of the other options

Correct Answer: 138^th Session held in Tokyo

Solution : The correct option is the 138^th Session held in Tokyo.

Brisbane was chosen to host the 2032 Olympics and Paralympics at the 138th Session of the IOC Executive Board Meeting on July 21, 2021, in Tokyo, Japan. The

Correct Answer: 24 cm

Solution :
The radii of the circles are 15 cm and 13 cm.
Distance between the centres = 14 cm
AB = 15 cm and BC = 13 cm, and AC = 14 cm
Let OC = $x$ and AO = $(14 - x)$
Now in

Correct Answer: 25%

Solution : Let the cost price of an article be 100.
⇒ profit = 100 × 55% = 55
Now, selling price = 100 + 55 = 155
New cost price = 100 + 100 × 24% = 124
So, new profit = 155 – 124 =