Comprehension

Consider the following for the three (03) items that follow: Let , and

What is equal to?

This question was previously asked in
NDA-I (Mathematics) Official Paper (Held On: 13 Apr, 2025)
View all NDA Papers >
  1. 1/2
  2. 1
  3. 3/2
  4. 2

Answer (Detailed Solution Below)

Option 3 : 3/2
Free
UPSC NDA 01/2025 General Ability Full (GAT) Full Mock Test
6.1 K Users
150 Questions 600 Marks 150 Mins

Detailed Solution

Download Solution PDF

Calculation:

Given,

The expression to simplify is \(p^2 + q^2 + r^2\), where:

\(p^2 + q^2 + r^2\)

\(q = \sin(25^\circ) \)

\(r = \sin(-95^\circ) = -\cos(5^\circ) \)

We are given that p + q + r = 0 . Using the identity for squaring a sum:

\( (p + q + r)^2 = p^2 + q^2 + r^2 + 2(pq + qr + rp) \)

Since p + q + r = 0, we substitute this into the identity:

\( 0 = p^2 + q^2 + r^2 + 2(pq + qr + rp) \)

From previous calculations, we know that:

\( pq + qr + rp = -\frac{3}{4} \).

Substitute this value into the equation:

\( 0 = p^2 + q^2 + r^2 + 2\left( -\frac{3}{4} \right) \)

Simplifying:

\( 0 = p^2 + q^2 + r^2 - \frac{3}{2} \)

\( p^2 + q^2 + r^2 = \frac{3}{2} \).

Hence, the correct answer is Option 3.

Latest NDA Updates

Last updated on Jul 8, 2025

->UPSC NDA Application Correction Window is open from 7th July to 9th July 2025.

->UPSC had extended the UPSC NDA 2 Registration Date till 20th June 2025.

-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.

->The NDA exam date 2025 has been announced. The written examination will be held on 14th September 2025.

-> The selection process for the NDA exam includes a Written Exam and SSB Interview.

-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100. 

-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential. 

Get Free Access Now
Hot Links: happy teen patti teen patti gold apk download teen patti real money app teen patti vungo