Correct Answer: 1911-1921

Solution : The correct option is 1911-1921.

India experienced its sole negative population growth in the 1911-1921 decade, declining by 0.31%. Factors included the devastating Spanish Flu Pandemic of 1918, which caused around 18 million deaths, the repercussions of World War I impacting the economy and causing food shortages and natural disasters, such as earthquakes and floods, compounding the hardships.

Correct Answer: $\cos \left(\frac{\pi}{3}+x\right)$

Solution : Given, $\frac{\cos x-\sqrt{3} \sin x}{2}$
= $\frac{1}{2} \cos x-\frac{\sqrt3}{2}\sin x$
= $\cos x \cos \frac{\pi}{3} - \sin \frac{\pi}{3} \sin x$ [$\because\cos \frac{\pi}{3}=\frac{1}{2}$ and $\sin \frac{\pi}{3}=\frac{\sqrt3}{2}$]
= $\cos( \frac{\pi}{3}+x)$
Hence, the correct answer is $\cos( \frac{\pi}{3}+x)$.

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Correct Answer: 5, 2, 1, 3, 4

Solution : Given:
1. Patriot 2. Pastor 3. Patron 4. Pattern 5. Pastern

Step 1: Since all the words start with the same letter P, so move on to the next letter.
Step 2: The second letter of each word is the same, i.e., a. So, move on to the next letter.
Step 3: The third letter of each word is either t or s. The arrangement can be – (Pastor, Pastern), (Patriot, Patron, Pattern).
Step 4: The fourth letter of (Pastor, Pastern) is the same. So, move on to the next letter.
Step 5: Compare the fifth letter of (Pastor, Pastern). Pastern will come before Pastor as e comes before o according to the alphabetical system.
Step 6: Compare the fourth letter of (Patriot, Patron, and Pattern). (Patriot, Patron) will come before Pattern as r comes before t according to the alphabetical system.
Step 7: Compare the fifth letter of (Patriot, Patron) Patriot will come before Patron as i comes before o. So, move on to the next letter.

So, the sequence is Pastern, Pastor, Patriot, Patron, Pattern, or 5, 2, 1, 3, 4. Hence, the second option is correct.

Correct Answer: two years

Solution : The correct option is two years.

The Rowlatt Act of 1919 conferred extensive powers upon the British colonial government in India to suppress political activities perceived as seditious. This legislation granted authorities the ability to detain individuals deemed politically suspect without providing them the right to trial for a period of up to two years.

Correct Answer: Blood Coagulation

Solution : The correct answer is Blood coagulation.

It is involved in the coagulation of blood. It is one of 13 clotting factors that cooperate to produce a blood clot, and halt bleeding. Specifically, the Christmas factor is associated with the intrinsic process of coagulation. Blood that comes into contact with an unexpected surface, such as a broken blood vessel or piece of tissue, activates the intrinsic pathway. In the presence of an active intrinsic route, factor IX, also referred to as factor IXa, is produced.

Correct Answer: It was a great but risky idea

Solution : “But” expresses an opposite or different point of view. On the other hand, “And” means also or in addition to. Further, once the article has been used before the connector, it is not required again. Hence, “It was a great but risky idea” is the answer.

Correct Answer: Progesterone

Solution : The correct answer is Progesterone.

Progesterone is the hormone used as an oral contraceptive. It is a female sex hormone that is used as a progestin to prevent conception. It acts by inhibiting egg release from the ovaries (ovulation) and altering the cervical mucus and uterine lining.

Correct Answer: Both statements are correct.
  

Solution : The correct answer is (a) Both statements are correct.

Statement 1 is correct. A budget is often considered a tertiary plan because it is a detailed and specific financial plan that supports the broader strategic and operational plans of an organization.

Statement 2 is correct. Budgeting involves the process of planning and controlling financial activities by setting specific financial targets, allocating resources, and monitoring actual performance against the budgeted figures.

Therefore, both statements 1 and 2 are correct.