Skip to main content
Back to TRIGONOMETRY RATIOS

Your Progress

0 / 394 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • TRIGONOMETRY RATIOS

Trigonometry ratios practice · Mixed difficulty

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 241-270 of 394 questions

Preparing practice and saved progress…

241 Easy
241 of 394
Application +4 | -1
sin⁡2  5∘+sin⁡2  10∘+sin⁡2  15∘+...+sin⁡2  90∘{\sin ^2}\,\,5^\circ + {\sin ^2}\,\,10^\circ + {\sin ^2}\,\,15^\circ + ... + {\sin ^2}\,\,90^\circ is equal to
View answer and explanation
Correct option: C
9  129\,\,\frac{1}{2}
Option A (2) is correct because if sin x + cosec x = 2, then sin x = 1, and therefore sin^n x + cosec^n x = 1 + 1 = 2.
242 Medium
242 of 394
Application +4 | -1
The value of (1+cos⁡π6)(1+cos⁡π3)(1+cos⁡2π3)\left(1+\cos \frac{\pi}{6}\right)\left(1+\cos \frac{\pi}{3}\right)\left(1+\cos \frac{2 \pi}{3}\right) (1+cos⁡7π6)\left(1+\cos \frac{7 \pi}{6}\right) is
View answer and explanation
Correct option: A
3/163 / 16
Option A (3/163 / 16) is correct because substituting the values of the cosine functions and simplifying the expression leads to the result 3/163/16.
243 Easy
243 of 394
Application +4 | -1
If π2<θ<π\frac{\pi }{2} < \theta < \pi, then 1−sin⁡  θ1+sin⁡  θ+1+sin⁡  θ1−sin⁡  θ\sqrt {\frac{{1 - \sin \,\,\theta }}{{1 + \sin \,\,\theta }}} + \sqrt {\frac{{1 + \sin \,\,\theta }}{{1 - \sin \,\,\theta }}} is equal to
View answer and explanation
Correct option: B
− 2  sec⁡  θ- \,2\,\,\sec \,\,\theta
Option B ( − 2sec⁡θ\ - \,2\sec \theta) is correct because the expression simplifies to −2sec⁡θ-2\sec \theta when π2<θ<π\frac{\pi}{2} < \theta < \pi, considering the sign of cos⁡θ\cos \theta in the second quadrant.
244 Medium
244 of 394
Analyzing +4 | -1
If sec⁡  α\sec \,\,\alpha and cosec    α\mathrm{cosec}\;\,\,\alpha are the roots of the equation x2−ax+b=0{x^2} - ax + b = 0, then
View answer and explanation
Correct option: B
a2=b(b+2){a^2} = b\left( {b + 2} \right)
Option B (a2=b(b+2){a^2} = b(b + 2)) is correct because by using Vieta's formulas to find the sum and product of the roots and then applying the trigonometric identity sin⁡2α+cos⁡2α=1{\sin^2 \alpha + \cos^2 \alpha = 1}, we can derive the given relation.
245 Easy
245 of 394
Understanding +4 | -1
If sin⁡θ=−12\sin \theta=-\frac{1}{\sqrt{2}} and tan⁡θ=1\tan \theta=1, then θ\theta lies in which quadrant
View answer and explanation
Correct option: C
Third
Option C (Third) is correct because sine is negative and tangent is positive only in the third quadrant.
246 Easy
246 of 394
Application +4 | -1
At what time between 2 and 3 ' OO clock, both the hands will be at right angle?
View answer and explanation
Correct option: A
1641116 \frac{4}{11} minutes past 2
Option A (1641116 \frac{4}{11} minutes past 2) is correct because it is derived from the relative speed concept of the hour and minute hands and solving for the time when the angle between them is 90 degrees.
247 Medium
247 of 394
Application +4 | -1
The value of cos⁡4(π8)+cos⁡4(3π8)+cos⁡4(5π8)+cos⁡4\cos ^4\left(\frac{\pi}{8}\right)+\cos ^4\left(\frac{3 \pi}{8}\right)+\cos ^4\left(\frac{5 \pi}{8}\right)+\cos ^4 (7π8)\left(\frac{7 \pi}{8}\right) is
View answer and explanation
Correct option: C
3/23 / 2
Option C (3/2) is correct because by using trigonometric identities and simplifying, the expression cos⁡4(π8)+cos⁡4(3π8)+cos⁡4(5π8)+cos⁡4(7π8)\cos^4(\frac{\pi}{8}) + \cos^4(\frac{3\pi}{8}) + \cos^4(\frac{5\pi}{8}) + \cos^4(\frac{7\pi}{8}) simplifies to 32\frac{3}{2}.
248 Medium
248 of 394
Analyzing +4 | -1
If   2sin⁡  α1+cos⁡  α+sin⁡  α=x,    then   1−cos⁡  α−sin⁡  αcos⁡  α  \;\frac{{2\sin \,\,\alpha }}{{1 + \cos \,\,\alpha + \sin \,\,\alpha }} = x,\,\,\;\mathrm{then}\;\,\frac{{1 - \cos \,\,\alpha - \sin \,\,\alpha }}{{\cos \,\,\alpha }}\; is equal to

View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the given expression simplifies to −x-x, which is not among the provided options.
249 Easy
249 of 394
Application +4 | -1
If 0<θ<π/20 < \theta<\pi / 2, and f(θ)=(1+cot⁡θ−cosec⁡θ)f(\theta)=(1+\cot \theta-\operatorname{cosec} \theta) (1+tan⁡θ+sec⁡θ)(1+\tan \theta+\sec \theta), then f(π/4)f(\pi / 4) is equal to
View answer and explanation
Correct option: C
2
Option C (2) is correct because the expression simplifies to a constant value of 2 after applying trigonometric identities.
250 Medium
250 of 394
Application +4 | -1
If the line of action of the resultant of two forces PP and QQ divides the angle between them in the ratio 1: 2 then the magnitude of resultant is
View answer and explanation
Correct option: D
P2−Q2Q\frac{{P}^2-{Q}^2}{{Q}}
Option D (P2−Q2Q\frac{{P}^2-{Q}^2}{{Q}}) is correct because it is derived by using the sine rule and trigonometric identities to relate the forces and the angles.
251 Easy
251 of 394
Application +4 | -1
If cos⁡  x+cos⁡2x=1\cos \,\,x + {\cos ^2}x = 1, then the value of sin⁡12x+3  sin⁡10x+3  sin⁡8x+sin⁡6x−1{\sin ^{12}}x + 3\,\,{\sin ^{10}}x + 3\,\,{\sin ^8}x + {\sin ^6}x - 1, is equal to
View answer and explanation
Correct option: D
0\mathrm{0}
Option D (0) is correct because the expression simplifies to 0 after substituting cos x = sin²x.
252 Easy
252 of 394
Application +4 | -1
If cosec⁡θ=p+qp−q\operatorname{cosec} \theta=\frac{p+q}{p-q} where p>q>0p>q>0, then ∣cot⁡(π4+θ2)∣\left|\cot \left(\frac{\pi}{4}+\frac{\theta}{2}\right)\right| is equal to:
View answer and explanation
Correct option: A
pq\sqrt{\frac{p}{q}}
The correct answer is A (pq\sqrt{\frac{p}{q}}) because by using trigonometric identities and the given information, we can simplify the expression to obtain the result.
253 Easy
253 of 394
Application +4 | -1
The value of 3+cot⁡76∘cot⁡16∘cot⁡76∘+cot⁡16∘\frac{3+\cot 76^{\circ} \cot 16^{\circ}}{\cot 76^{\circ}+\cot 16^{\circ}} is
View answer and explanation
Correct option: D
cot⁡44∘\cot 44^{\circ}
Option D (cot⁡44∘\cot 44^{\circ}) is correct because the expression simplifies to tan⁡46∘\tan 46^{\circ}, which is equal to cot⁡44∘\cot 44^{\circ}, using trigonometric identities.
254 Medium
254 of 394
Application +4 | -1
Range of cos⁡2x−10cos⁡x+25+2\sqrt{\cos ^2 x-10 \cos x+25}+2 is
View answer and explanation
Correct option: C
[6,8][6,8]
Option C ([6,8]) is correct because simplifying the expression cos⁡2x−10cos⁡x+25+2\sqrt{{\cos ^2 x-10 \cos x+25}}+2 leads to the range [6,8].
255 Easy
255 of 394
Application +4 | -1
The value of cos⁡(270∘+θ)⋅cos⁡(90∘−θ)−\cos \left(270^{\circ}+\theta\right) \cdot \cos \left(90^{\circ}-\theta\right)- sin⁡(270∘−θ)cos⁡θ\sin \left(270^{\circ}-\theta\right) \cos \theta is
View answer and explanation
Correct option: D
1
Option D (1) is correct because after applying trigonometric identities and simplifying, the expression reduces to sin⁡2θ+cos⁡2θ\sin^2 \theta + \cos^2 \theta, which equals 1.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
256 Easy
256 of 394
Application +4 | -1
cos⁡2(π6+θ)−sin⁡2(π6−θ)=\cos ^2\left(\frac{\pi}{6}+\theta\right)-\sin ^2\left(\frac{\pi}{6}-\theta\right)=
View answer and explanation
Correct option: A
12cos⁡2θ\frac{1}{2} \cos 2 \theta
Option A 12cos⁡2θ\frac{{1}}{{2}} \cos 2 \theta is correct because it is obtained by applying the trigonometric identity for the difference of squares of cosines and sines.
257 Easy
257 of 394
Understanding +4 | -1
In a cyclic quadrilateral ABCDABCD, he value of cos⁡  A+cos⁡  B+cos⁡  C+cos⁡  D\cos \,\,A + \cos \,\,B + \cos \,\,C + \cos \,\,D, is
View answer and explanation
Correct option: B
0\mathrm{0}
Option B (0) is correct because in a cyclic quadrilateral, opposite angles are supplementary (A + C = 180° and B + D = 180°), leading to cos A = -cos C and cos B = -cos D, thus their sum is zero.
258 Hard
258 of 394
Application +4 | -1
How many times do the hands of the watch form a right angle during a complete day?
View answer and explanation
Correct option: D
44
Option D (44) is correct because the hands of a watch form a right angle 44 times during a complete day.
259 Easy
259 of 394
Application +4 | -1
The value of cos⁡255∘+sin⁡195∘\cos 255^{\circ}+\sin 195^{\circ} is
View answer and explanation
Correct option: C
−(3−12)-\left(\frac{\sqrt{3}-1}{\sqrt{2}}\right)
Option C (-(3−12\frac{\sqrt{3}-1}{\sqrt{2}})) is correct because it is the simplified value of the given trigonometric expression.
260 Easy
260 of 394
Application +4 | -1
The value of
sin⁡2  5∘+sin⁡2  10∘+sin⁡2  15∘+…  +sin⁡2  85∘+sin⁡2  90∘{\sin ^2}\,\,5^\circ + {\sin ^2}\,\,10^\circ + {\sin ^2}\,\,15^\circ + \ldots \,\, + {\sin ^2}\,\,85^\circ + {\sin ^2}\,\,90^\circ, is
View answer and explanation
Correct option: C
9  129\,\,\frac{1}{2}
Option C (9 129\,\frac{1}{2}) is the correct answer because by pairing terms and using trigonometric identities, the sum simplifies to this value.
261 Hard
261 of 394
Application +4 | -1
The set of values of xx in (−π,π)\left( { - \pi ,\pi } \right) satisfying the inequation ∣4sin⁡x−1∣<5\left| {4\sin x - 1} \right| < \sqrt 5 is
View answer and explanation
Correct option: A
(− π/10,   3π/10)\left( { - \,\pi /10,\;\,3\pi /10} \right)
Option A (− π/10,    3π/10)\left( { - \,\pi /10,\;\,\,3\pi /10} \right) is correct because it represents the interval of xx values that satisfy the inequality ∣4sin⁡x−1∣<5\left| {4\sin x - 1} \right| < \sqrt 5 within the given range of (−π,π)\left( { - \pi ,\pi } \right).
262 Medium
262 of 394
Application +4 | -1
If 0<x<π0 < x < \pi and cos⁡x+sin⁡x=12\cos x+\sin x=\frac{1}{2}, then tan⁡x\tan \mathrm{x} is
View answer and explanation
Correct option: C
−(4+7)3-\frac{(4+\sqrt{7})}{3}
Option C is correct because solving the trigonometric equation and considering the domain 0 < x < π leads to the correct value for tan x.
263 Medium
263 of 394
Application +4 | -1
If cos⁡xa=sin⁡xb\frac{\cos x}{a}=\frac{\sin x}{b} then ∣acos⁡2x+bsin⁡2x∣|a \cos 2 x+b \sin 2 x| is equal to
View answer and explanation
Correct option: D
None of these
Option D (None of these) is correct because the expression simplifies to ∣a∣|a| using trigonometric identities and the given condition.
264 Medium
264 of 394
Application +4 | -1
2sin⁡(π22)sin⁡(3π22)sin⁡(5π22)sin⁡(7π22)sin⁡(9π22)2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\frac{7 \pi}{22}\right) \sin \left(\frac{9 \pi}{22}\right) is equal to:
View answer and explanation
Correct option: B
116\frac{1}{16}
Option B (116\frac{1}{16}) is correct because by using trigonometric identities, the expression simplifies to 116\frac{1}{16}.
265 Medium
265 of 394
Application +4 | -1
What is cos⁡20∘+cos⁡100∘+cos⁡140∘\cos 20^{\circ}+\cos 100^{\circ}+\cos 140^{\circ} equal to ?
View answer and explanation
Correct option: D
0
Option D (0) is correct because using the sum-to-product trigonometric identity, the expression simplifies to zero.
266 Easy
266 of 394
Application +4 | -1
Value of sin⁡πn+sin⁡3πn+sin⁡5πn+……\sin \frac{\pi}{n}+\sin \frac{3 \pi}{n}+\sin \frac{5 \pi}{n}+\ldots \ldots to nn terms is:
View answer and explanation
Correct option: B
0
Option B (0) is correct because the given series is a sum of sines in an arithmetic progression, and using the formula for the sum, the expression simplifies to 0.
267 Easy
267 of 394
Application +4 | -1
sin⁡2(π8+A2)−sin⁡2(π8−A2)\sin ^2\left(\frac{\pi}{8}+\frac{A}{2}\right)-\sin ^2\left(\frac{\pi}{8}-\frac{A}{2}\right) is equal to:
View answer and explanation
Correct option: A
(1/2)sin⁡A(1 / \sqrt{2}) \sin A
Option A (12sin⁡A\frac{1}{\sqrt{2}} \sin A) is correct because using the identity sin⁡2A−sin⁡2B=sin⁡(A−B)sin⁡(A+B)\sin^2 A - \sin^2 B = \sin(A-B)\sin(A+B), the expression simplifies to 12sin⁡A\frac{1}{\sqrt{2}} \sin A.
268 Easy
268 of 394
Application +4 | -1
Value of cos⁡(3π2+x)cos⁡(2π+x)[cot⁡(3π2−x)+cot⁡(2π+x)]\cos \left(\frac{3 \pi}{2}+x\right) \cos (2 \pi+x)\left[\cot \left(\frac{3 \pi}{2}-x\right)+\cot (2 \pi+x)\right] is
View answer and explanation
Correct option: A
1
Option A (1) is correct because the given expression simplifies to 1 using trigonometric identities.
269 Medium
269 of 394
Application +4 | -1
If 12cot⁡2θ−31cosec⁡θ+32=012 \cot ^2 \theta-31 \operatorname{cosec} \theta+32=0, then the value of sin⁡θ\sin \theta is
View answer and explanation
Correct option: C
4/54 / 5 or 3/43 / 4
Option C (4/54/5 or 3/43/4) is correct because solving the trigonometric equation 12cot⁡2θ−31cosec⁡θ+32=012 \cot ^2 \theta-31 \operatorname{cosec} \theta+32=0 leads to sin⁡θ=3/4\sin \theta = 3/4 or 4/54/5.
270 Easy
270 of 394
Application +4 | -1
If tan⁡  θ=x−14x\tan \,\,\theta = x - \frac{1}{{4x}}, then sec⁡  θ−tan⁡  θ\sec \,\,\theta - \tan \,\,\theta is equal to
View answer and explanation
Correct option: A
− 2x,  12x- \,2x,\,\,\frac{1}{{2x}}
Option A ( − 2x, 12x\ - \,2x,\,\frac{{1}}{{2x}}) is correct because it is derived by using trigonometric identities and solving for sec⁡ θ−tan⁡ θ\sec \,\theta - \tan \,\theta.
Revision notes and key takeaways

Review TRIGONOMETRY RATIOS in your textbook or class notes, then use this set to check your understanding.

Showing 241-270 of 394 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Easy) 218 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Hard) 19 MCQs → ENGINEERING MATHEMATICS - TRIGONOMETRY RATIOS MCQs (Medium) 157 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → INDEFINITE INTEGRATION 1179 MCQs

Your practice

0 / 394 answered · 394 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →