CUET · MATHS · PYQ PAPER 2025
If a line makes angles \(\alpha, \beta, \gamma\) with the positive directions of the coordinate axes, then the value of \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma\) is
- A 1
- B 2
- C -1
- D -2
Answer & Solution
Correct Answer
(C) -1
Step-by-step Solution
Detailed explanation
\(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma = 1\) \(\cos 2 \alpha+\cos 2 \beta+\cos 2 \gamma = (2\cos^2 \alpha - 1) + (2\cos^2 \beta - 1) + (2\cos^2 \gamma - 1)\) \( = 2(\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma) - 3\) \( = 2(1) - 3\) \( = -1\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from MATHS
- The window of the house is in the form of a rectangle surmounted by a semi-circular portion, having a perimeter of 10 m as shown in figure.
If \(x\) and \(y\) represent the length and breadth of rectangular region, then relation between \(x\) and \(y\) is:CUET 2023 Hard - If \(A\) is a square matrix such that \(A^2=A\), then the value of \((I-A)^2-(I+A)^3\) is :CUET 2023 Easy
- Match List - I with List - II. Evaluate the integrals.
\(List - I\) \(List - II\) (A) \(\int_0^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x\) \((I)\) \(2 \pi\) (B) \(\int_0^{1 / 2} \frac{d x}{\sqrt{x-x^2}}\) \((II)\) \(\frac{\pi}{4}\) (C) \(\int_{-\pi}^\pi x \sin x d x\) \((III)\) \(0\) (D) \(\int_0^1 \frac{1}{1+x^2} d x\) \((IV)\) \(\frac{\pi}{2}\) CUET 2023 Easy - The side of an equilateral triangle increases at the rate of \(3 cm / sec\), then the rate at which the area of the triangle increases when the side is 4 cm , is :CUET 2023 Medium
- (A) f(x) = |x| is continuous function on R (the set of real numbers)
(B) f(x) = [x] is continuous function on R
(C) f(x) = sin x is continuous function on R
(D) f(x) = tanx is continuous function on R
(E) f(x) = sinx + cosx is continuous function on RCUET 2023 Easy - If \(u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)\) and \(v=\tan ^{-1} x, x \in(-1,1)\), then \(\frac{d u}{d v}\) is equal to:CUET 2023 Hard
More PYQs from CUET
- In the conversion of ethanol to ethene, the first step of the reaction involves the formation ofCUET 2025 Medium
- Germanium is a semiconductor because:CUET 2023 Hard
-
These structures represent which particular kind of halides :CUET 2023 Easy - Which of the following can not be used as specimen for DNA finger printing?CUET 2023 Hard
- Which one of the followings is responsible for producing the large holes in "Swiss cheese"?CUET 2023 Medium
- Amoebic dysentery is caused by:CUET 2023 Medium