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Correct Answer: 2

Solution : Given: $2apq=(p+q)^{2}-(p-q)^{2}$
⇒ $2apq=4pq$
$\therefore a=\frac{4pq}{2pq} =2$
Hence, the correct answer is 2.

Correct Answer: 2

Solution : Given: $(1+\sec20°+\cot70°)(1 – \operatorname{cosec}20°+\tan70°)$
= $(1+\sec20°+\tan20°)(1-\operatorname{cosec}20°+\cot20°)$
= $(1+\frac{1}{\cos20°}+\frac{\sin20°}{\cos20°})(1–\frac{1}{\sin20°}+\frac{\cos20°}{\sin20°})$
= $(\frac{\cos20°+1+\sin20°}{\cos20°})(\frac{\sin20°–1+\cos20°}{\sin20°})$
= $\frac{(\sin20°+\cos20°)^{2}–1^{2}}{\cos20°\sin20°}$
= $\frac{\sin^{2}20°+\cos^{2}20°+2\sin20°\cos20°–1}{\cos20°\sin20°}$
= $\frac{2\sin20°\cos20°}{\cos20°\sin20°}$
= $2$
Hence, the correct answer is 2.

Correct Answer: $112 \sqrt{3}$

Solution : Given, $x+\frac{1}{x}=-14$
Squaring both sides, we get,
⇒ $x^2+\frac{1}{x^2}+2=196$
⇒ $x^2+\frac{1}{x^2}=196-2=194$
Subtracting 2 from both sides, we get,
$x^2+\frac{1}{x^2}-2=194-2$
⇒ $(x-\frac{1}{x})^2=192$
⇒ $x-\frac{1}{x}=-\sqrt{192}$ [as $x<-1$]
Now $x^2-\frac{1}{x^2}$
$=(x-\frac{1}{x})(x+\frac{1}{x})$
$=(-\sqrt{192})\times (-14)$
$=8\sqrt3\times 14 = 112\sqrt3$
Hence, the correct answer is $112\sqrt3$.

Correct Answer: Seven

Solution : The correct answer is Seven.

Seven fundamental rights were initially recognized by the Indian Constitution. The property right was abolished as a fundamental right in 1978 with the passage of the 44th Constitutional Amendment. It gained constitutional protection under Article 300A.

Correct Answer: Border Roads Organisation

Solution : The correct answer is Border Roads Organisation.

The Border Roads Organisation has built the 9 km long Atal Tunnel. It is a highway tunnel built under the Rohtang Pass on the Leh to Manali highway in Himachal Pradesh. It is named after the

Correct Answer: Shah Alam II

Solution : The correct answer is Shah Alam II.

The third Battle of Panipat was fought in 1761 between the Durrani Kingdom of Afghanistan, led by Ahmad Shah Abdali, and the Marathas. In this war, Ahmad Shah Abdali emerged victorious, leading to the decline of

Correct Answer: 14

Solution : Given: $(a+b+c)=17$ and $\left(a^2+b^2+c^2\right)=101$
We know that $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ac$
Squaring both sides, we get
⇒ $a^2+b^2+c^2+2ab+2bc+2ac=289$
⇒ $101+2ab+2bc+2ac=289$
⇒ $2ab+2bc+2ac=188$
Now, $(a-b)^2+(b-c)^2+(c-a)^2$
= $2a^2+2b^2+2c^2-2ab-2bc-2ac$
= $2\times101-188$
= $202-188=14$
Hence, the correct answer is 14.

Correct Answer: 6 metres

Solution : Given: The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower.
$ \angle C$ and $ \angle D$ are complementary.
We know that $\tan\theta=\frac{\text{Perpendicular}}{\text{Base}}$ and $\tan

Correct Answer: bone

Solution : The correct answer is bone.

Osteocytes are found in the bone tissue. The bone tissue consists of various cell types, including osteoblasts, osteoclasts, and osteocytes. Osteoblasts are responsible for bone formation.

Correct Answer: Drongo

Solution : The correct option is drongo.

The drongo, a clever bird found in Asia and Africa, is known for its exceptional mimicry skills. Using its imitative talents, the drongo mimics the calls of other birds to create false alarms, causing them to flee and