Correct Answer: $\sqrt{\frac{b+a}{b-a}}$

Solution : $b \sin \theta = a$
$\sin\theta = \frac{a}{b}$
So, Perpendicular = $a$ & Hypotenuse = $b$
$(Hypotenuse)^2= (Perpendicular)^2+ (Base)^2$
⇒ $b^2= a^2 + (Base)^2$
⇒ $(Base)^2 = b^2- a^2$
⇒ $(Base) = \sqrt{b^2- a^2}$
$\sec \theta = \frac{(Hypotenuse)}{(Base)}= \frac{b}{\sqrt{b^2- a^2}}$
$\tan \theta= \frac{(Perpendicular)}{(Base)}= \frac{a}{\sqrt{b^2- a^2}}$

Correct Answer: Madame Blavatsky

Solution : The correct answer is Madame Blavatsky.

A spiritual and mystic group is the Theosophical Society. Only in 1879 did this philosophy begin to take root in Indian culture. The society's main office was established in 1882 in Adyar, an Indian city close to Madras

Correct Answer: $(x+7)(x-2)$

Solution : Given: $x^{2}+5x-14$
After middle-term splitting,
$= x^{2}+7x-2x-14$
$= x(x+7)-2(x+7)$
$= (x+7)(x-2)$
Hence, the correct answer is $(x+7)(x-2)$.

Correct Answer: 27 km

Solution : Given:
Speed of A = 5 kmph; Speed of B = 4 kmph
Time = 3 hours

According to the instructions given, both A and B are standing at the same point, and from there they start moving in opposite directions at different speeds.

Correct Answer: Kathak

Solution : The correct option is Kathak.

Madhuri Dixit, the famous Indian actress, is a trained Kathak dancer. Kathak is one of the eight major classical dance forms of India. It originated in the state of Uttar Pradesh. Kathak has several distinct schools or styles known

Correct Answer: 100 + 5 – 10 × 250 ÷ 200 = 100

Solution : Given:
– stands for division, + stands for multiplication, ÷ stands for subtraction, and × stands for addition.

Replace the mathematical signs in the equations and solve the equations one by one.

Let's check the

Correct Answer: 16

Solution : Given: One number is 25% of another number. The larger number is 12 more than the smaller one.
Let the larger and the smaller numbers be $x$ and $y$ respectively.
now, $y$ = 25% of $x$
⇒ $y=\frac{x}{4}$
⇒ $x=4y$ .........................................(i)
The larger number is

Correct Answer: HBKP

Solution : Given:
AB_KPC_HKPEBH_PGBHK_

To fill the series we have to divide the series – AB_KP / C_HKP / EBH_P / GBHK_
Let's check each option –
First option: CDGP; ABCKP / CDHKP / EBHGP / GBHKP (No repeated

Correct Answer: $3\sqrt3$

Solution : Given: Side, $a$ = 6 cm
Let the height be $h$.
Area of the base of the hexagonal prism $=6 \times \frac{\sqrt3}{4}a^2=6 \times \frac{\sqrt3}{4} \times 6^2 = 54\sqrt3$
Total curved surface area of prism = 2 × (Area of base) + 6 × (Side of

Correct Answer: Prophane

Solution : The correct choice is the fourth option.

The incorrectly spelt word is prophane. The correct spelling is profane. It means "showing disrespect or contempt for sacred things".

The meanings of the other options are as follows:

• Reasonable means fair and sensible; based on