Correct Answer: 2

Solution : Given:
$x=a(\sin\theta+\cos\theta), y=b(\sin\theta-\cos\theta)$
So, $\frac{x}{a}=(\sin\theta+\cos\theta), \frac{y}{a}=(\sin\theta-\cos\theta)$
Now, $\frac{x^2}{a^2}+\frac{y^2}{b^2}$
= $(\sin\theta+\cos\theta)^2+(\sin\theta-\cos\theta)^2$
= $\sin^2\theta+2×\sin\theta×\cos\theta+\cos^2\theta+\sin^2\theta-2×\sin\theta×\cos\theta+\cos^2\theta$
= $\sin^2\theta+\cos^2\theta+\sin^2\theta+\cos^2\theta$
= $1+1$
= $2$
Hence, the correct answer is $2$.

Correct Answer: ÷ and ×

Solution : Given:
95 × 5 + 19 ÷ 2 − 21 = 36

Replace the given symbols in the options one by one with the original symbols in the given equation.
First option: ÷ and ×
⇒ 95 ÷ 5 + 19 × 2

Correct Answer: HIPLM

Solution : For APPLE to become ETTPI, each letter is shifted four positions forward –

• A becomes E (A + 4)
• P becomes T (P + 4)
• P becomes T (P + 4)
• L becomes I (L + 4)
• E becomes C (E + 4)

Now, using

Correct Answer: Raj Krishna

Solution : The correct answer is Raj Krishna.

Some of the early economists who coined the term used the word "Hindu" to suggest that the slow growth was due to the Hindu outlook of contentedness and hopelessness. In 1978, Professor Raj Krishna, an economist from

Correct Answer: Histology

Solution : Given:
Fungi : Mycology :: Tissue : ?

The study of fungi is known as Mycology.
Similarly, the study of tissue is known as Histology.

Hence, the third option is correct.

Correct Answer: Stigma

Solution : The correct option is Stigma.

Saffron is obtained from the stigma of the saffron crocus (Crocus sativus) flower, which is the female reproductive part. The stigmas are carefully collected, dried, and used to make saffron, which is a prized spice. Jammu and Kashmir, and

Correct Answer: 40 km/hr

Solution : Given: The speed of the boat is 30 km/hr and 60 km/hr for the same distance.
So, average speed = $\frac{2xy}{x+y}$, where $x$ and $y$ are two given speeds of the boat (for the same distance).
Putting the values $x$ = 30 and $y$

Correct Answer: 758

Solution : Given: $x+y+z = 22$ and $xy+yz+zx = 35$
We know that $(x+y+z)^2 = x^2+y^2+z^2+2(xy+yz+zx)$
⇒ $22^2 = x^2+y^2+z^2+2\times 35$
⇒ $484 = x^2+y^2+z^2+70$
⇒ $x^2+y^2+z^2 = 484-70 = 414$
So, $(x-y)^2+(y-z)^2+(z-x)^2 = 2[x^2+y^2+z^2-(xy+yz+zx)]$
⇒ $(x-y)^2+(y-z)^2+(z-x)^2 = 2[414-35]$
$\therefore(x-y)^2+(y-z)^2+(z-x)^2 = 758$
Hence, the correct answer is

Correct Answer:  Only assumption I is valid

Solution : Given:

Statement

If people are intelligent, they should be creative.

Now, let's assess the assumptions:

I. Creativity and intelligence are related.
This assumption is supported by the statement. The statement implies that there is a relationship between intelligence and creativity. It

Correct Answer: 44

Solution : Single equivalent discount = $(a+b-\frac{a×b}{100}$)%, where $a$% and $b$% are successive discounts.
So, the single discount of two successive discounts of 20% and 30%
$=20+30-\frac{20×30}{100}=44\%$
Hence, the correct answer is 44.