RRB NTPC Graduate CBT 1 21 Jun 2025 Shift 3 – Question Paper

Concept: Mohenjo-daro is one of the largest cities of the Harappan (Indus Valley) Civilisation.

1. Mohenjo-daro lies in Larkana district of Sindh (Pakistan), on the right bank of the Indus.
2. It was excavated by R.D. Banerji in 1922; the Great Bath and the Dancing Girl bronze come from here.
3. Harappa lies on the Ravi; Ganga and Yamuna are far east of the Harappan core.

Yaad rakhein: Mohenjo-daro = Sindh = Indus; Harappa = Ravi; Lothal = Bhogava; Kalibangan = Ghaggar.

Answer: (D) Indus

Concept: Use $(1-\sin A)(1+\sin A)={\cos }^{2}A$ and ${\sec }^{2}A-1={\tan }^{2}A$.

1. $\frac{2\cos A}{1-\sin A}+\frac{2\cos A}{1+\sin A}=\frac{2\cos A(1+\sin A+1-\sin A)}{1-{\sin }^{2}A}=\frac{4\cos A}{{\cos }^{2}A}=4\sec A$
2. $3\sqrt{{\sec }^{2}A-1}=3\sqrt{{\tan }^{2}A}=3\tan A$
3. Product $=4\sec A\times 3\tan A=12\sec A\tan A$

Trick: Put $A=0^{\circ }$: bracket $=4$, root part $=0$ → value 0; only $12\sec A\tan A$ (and $12\tan A$) give 0, and at $A={45}^{\circ }$ the value is $12\sqrt{2}$, which fits $12\sec A\tan A$.

Answer: (A) $12\sec A\tan A$

Concept: Check every symbol: the element just before it must be an odd number and the element just after it must NOT be an even number.

1. & : 7 before, 9 after → ✔
2. ^ : 9 before, # after → ✔
3. * : 1 before, 5 after → ✔ ; ≺ : 5 before but 2 after → ✘
4. $ : 3 before, @ after → ✔ ; others (#, ≡, ∆, @) are not preceded by an odd number.
5. Total = 4, i.e. more than three.

Trick: First list symbols after odd numbers (&, ^, *, ≺, $), then strike out those followed by an even number (≺).

Answer: (D) More than three