Skip to main content
Back to TRANSFORMATIONS

Your Progress

0 / 112 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • TRANSFORMATIONS

Transformations practice · Easy

Try a question, then open “View answer” to check it. Sign in to submit answers and save progress.

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 91-112 of 112 questions
91 Easy
91 of 112
Application +4 | -1
The value of (cos⁡  A+cos⁡  Bsin⁡  A−sin⁡  B)n+(sin⁡  A+sin⁡  Bcos⁡  A−cos⁡  B)n{\left( {\frac{{\cos \,\,A + \cos \,\,B}}{{\sin \,\,A - \sin \,\,B}}} \right)^n} + {\left( {\frac{{\sin \,\,A + \sin \,\,B}}{{\cos \,\,A - \cos \,\,B}}} \right)^n} (where n  n\; is an even) is
View answer and explanation
Correct option: B
2  cot⁡n  (A−B2)2\,\,{\cot ^n}\,\,\left( {\frac{{A - B}}{2}} \right)
Option B (2  cot⁡n  (A−B2)2\,\,{\cot ^n}\,\,\left( {\frac{{A - B}}{2}} \right)) is correct because the expression simplifies to this form when n is even using trigonometric identities.
92 Easy
92 of 112
Application +4 | -1
The period of the function f(x)=∣sin⁡3x∣+∣cos⁡3x∣,f\left( x \right) = \left| {\sin 3x} \right| + \left| {\cos 3x} \right|, is
View answer and explanation
Correct option: B
  π6\frac{{\;\pi }}{6}
Option B (  π6\frac{{\;\pi }}{6}) is correct because it is the smallest value for which f(x+π6)=f(x)f(x + \frac{\pi}{6}) = f(x).
93 Easy
93 of 112
Analyzing +4 | -1
The maximum value of f(x)=sin⁡  x(1+cos⁡  x)f\left( x \right) = \sin \,\,x\left( {1 + \cos \,\,x} \right) is
View answer and explanation
Correct option: A
3 34\frac{{3\,\sqrt 3 }}{4}
Option A (3,34\frac{{3\\,\sqrt 3 }}{4}) is correct because it represents the maximum value of the function f(x)=sin⁡x(1+cos⁡x)f(x) = \sin x(1 + \cos x), which is found by taking the derivative, setting it to zero, and solving for x.
94 Easy
94 of 112
Application +4 | -1
The period of the function f(x)=sin⁡43x+cos⁡43xf\left( x \right) = {\sin ^4}3x + {\cos ^4}3x is
View answer and explanation
Correct option: C
π/6\pi /6
Option C (1−x31 - {x^3}) is correct because it is the inverse function obtained by swapping x and y and solving for y.
95 Easy
95 of 112
Analyzing +4 | -1
If cos⁡  θ=cos⁡  α  cos⁡  β\cos \,\,\theta = \cos \,\,\alpha \,\,\cos \,\,\beta, then tan⁡  (θ+α2)  tan⁡  (θ−α2)\tan \,\,\left( {\frac{{\theta + \alpha }}{2}} \right)\,\,\tan \,\,\left( {\frac{{\theta - \alpha }}{2}} \right) is equal to
View answer and explanation
Correct option: B
tan⁡2  β2{\tan ^2}\,\,\frac{\beta }{2}
Option B (tan⁡2β2{\tan ^2}\frac{\beta }{2}) is correct because simplifying the given expression using trigonometric identities leads to tan⁡2β2{\tan ^2}\frac{\beta }{2}.
96 Easy
96 of 112
Analyzing +4 | -1
3  cosec    20∘−sec⁡  20∘\sqrt 3 \,\,cosec\,\,\;20^\circ - \sec \,\,20^\circ is equal to
View answer and explanation
Correct option: C
4\mathrm{4}
Option C (4) is correct because simplifying the expression using trigonometric identities leads to the value 4.
97 Easy
97 of 112
Analyzing +4 | -1
The period of the function f(x)=∣sin⁡x∣+∣cos⁡x∣f\left( x \right) = \left| {\sin x} \right| + \left| {\cos x} \right| is
View answer and explanation
Correct option: B
π2{\frac{\pi }{2}}
Option B (π2\frac{\pi}{2}) is correct because the function repeats its values after an interval of π2\frac{\pi}{2}.
98 Easy
98 of 112
Analyzing +4 | -1
If α,   β,   γ,  δ\alpha ,\,\;\beta ,\,\;\gamma ,\,\,\delta are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity kk, then the value of

4sin⁡  α2+3sin⁡  β2+2sin⁡  γ2+sin⁡  δ24\sin \,\,\frac{\alpha }{2} + 3\sin \,\,\frac{\beta }{2} + 2\sin \,\,\frac{\gamma }{2} + \sin \,\,\frac{\delta }{2} is equal to
View answer and explanation
Correct option: B
2 1+k2\,\sqrt {1 + k}
Option B (2 1+k2\,\sqrt {1 + k}) is correct because by using the properties of sine and trigonometric identities, we can simplify the expression to 21+k2\sqrt{1+k}.
99 Easy
99 of 112
Application +4 | -1
If cos⁡  A=34\cos \,\,A = \frac{3}{4}, then 32  sin⁡  (A2)  sin⁡  (5 A2)=32\,\,\sin \,\,\left( {\frac{A}{2}} \right)\,\,\sin \,\,\left( {\frac{{5\,A}}{2}} \right) =
View answer and explanation
Correct option: C
11
Option C (11) is correct because by using product-to-sum identities and substituting the given value of cos⁡A\cos A, the expression simplifies to 11.
100 Easy
100 of 112
Application +4 | -1
If xcos⁡  θ=ycos⁡  (θ−2π3)=zcos⁡  (θ+2π3)\frac{x}{{\cos \,\,\theta }} = \frac{y}{{\cos \,\,\left( {\theta - \frac{{2\pi }}{3}} \right)}} = \frac{z}{{\cos \,\,\left( {\theta + \frac{{2\pi }}{3}} \right)}} then x+y+z=x + y + z =
View answer and explanation
Correct option: B
0
Option B (0) is correct because the sum of the cosines in the denominator simplifies to zero, making x + y + z = 0.
101 Easy
101 of 112
Analyzing +4 | -1
If in a Δ ABC\Delta \,ABC,
(sin⁡  A+sin⁡  B+sin⁡C)  (sin⁡  A+sin⁡  B−sin⁡  C)=3  sin⁡  A  sin⁡  B\left( {\sin \,\,A + \sin \,\,B + \sin C} \right)\,\,\left( {\sin \,\,A + \sin \,\,B - \sin \,\,C} \right) = 3\,\,\sin \,\,A\,\,\sin \,\,B
View answer and explanation
Correct option: C
C=60∘C = 60^\circ
Option C (C=60∘C = 60^\circ) is correct because by simplifying the given equation using trigonometric identities, we find that cos⁡C=1/2\cos C = 1/2, which implies C=60∘C = 60^\circ.
102 Easy
102 of 112
Application +4 | -1
If sin⁡  θ=sin⁡  15∘+sin⁡  45∘\sin \,\,\theta = \sin \,\,15^\circ + \sin \,\,45^\circ ,where 0∘<θ<90∘0^\circ < \theta < 90^\circ, then θ\theta is equal to0
View answer and explanation
Correct option: D
75∘75^\circ
Option D (75∘75^\circ) is correct because sin⁡θ=sin⁡15∘+sin⁡45∘\sin \theta = \sin 15^\circ + \sin 45^\circ simplifies to sin⁡θ=sin⁡75∘\sin \theta = \sin 75^\circ, leading to θ=75∘\theta = 75^\circ.
103 Easy
103 of 112
Application +4 | -1
96cos⁡π33cos⁡2π33cos⁡4π33cos⁡8π33cos⁡16π3396 \cos \frac{\pi}{33} \cos \frac{2 \pi}{33} \cos \frac{4 \pi}{33} \cos \frac{8 \pi}{33} \cos \frac{16 \pi}{33} is equal to
View answer and explanation
Correct option: A
3
Option A (3) is correct because it involves using the identity for the product of cosines and simplifying the expression.
104 Easy
104 of 112
Application +4 | -1
If   sin⁡  A−sin⁡  Ccos⁡  C−cos⁡  A=cot⁡  B,   then   A, B,C\;\frac{{\sin \,\,A - \sin \,\,C}}{{\cos \,\,C - \cos \,\,A}} = \cot \,\,B,\,\;\mathrm{then}\;\,A,\,B,C are in

View answer and explanation
Correct option: A
AP
Option A (AP) is correct because the given condition implies that BB is the arithmetic mean of AA and CC, which is the definition of an arithmetic progression.
105 Easy
105 of 112
Application +4 | -1
16sin⁡(20∘)sin⁡(40∘)sin⁡(80∘)16\sin \left( {20^\circ } \right)\sin \left( {40^\circ } \right)\sin \left( {80^\circ } \right) is equal to:
View answer and explanation
Correct option: B
232\sqrt 3
Option B (232\sqrt 3) is correct because the expression simplifies using the trigonometric identity 4sin⁡θsin⁡(60°−θ)sin⁡(60°+θ)=sin⁡3θ4\sin \theta \sin(60°-\theta)\sin(60°+\theta) = \sin 3\theta.

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
106 Easy
106 of 112
Application +4 | -1
The value of 2  cos⁡  x−cos⁡  3x−cos⁡  5x  2\,\,\cos \,\,x - \cos \,\,3x - \cos \,\,5x\mathrm{\;} is equal to
View answer and explanation
Correct option: A
16  cos⁡3 x  sin⁡2 x16\,\,{\cos ^3}\,x\,\,{\sin ^2}\,x
Option A (16  cos⁡3 x  sin⁡2 x16\,\,{\cos ^3}\,x\,\,{\sin ^2}\,x) is correct because by using trigonometric identities and factoring, the expression simplifies to 16  cos⁡3 x  sin⁡2 x16\,\,{\cos ^3}\,x\,\,{\sin ^2}\,x.
107 Easy
107 of 112
Application +4 | -1
The least value of cosec2 x+25  sec⁡2 x\mathrm{cose}{\mathrm{c}^2}\,x + 25\,\,{\sec ^2}\,x is
View answer and explanation
Correct option: D
38
Option D (38) is correct because the minimum value of the expression is obtained by completing the square and finding the minimum value of the squared term.
108 Easy
108 of 112
Understanding +4 | -1
The function f(x)=∣cos⁡x∣f\left( x \right) = \left| {\cos x} \right| is periodic with period
View answer and explanation
Correct option: B
π\pi
Option B (π\pi) is correct because the period of ∣cos⁡x∣|\cos x| is π\pi.
109 Easy
109 of 112
Analyzing +4 | -1
In aΔ ABC,  cos⁡(B+2C+3A2)+cos⁡(A−B2)\Delta \,ABC,\,\,\cos \left( {\frac{{B + 2C + 3A}}{2}} \right) + \cos \left( {\frac{{A - B}}{2}} \right) is equal to
View answer and explanation
Correct option: B
0
Option B (0) is correct because by using the identity A+B+C=πA+B+C = \pi and simplifying the expression, we can show that the sum of the cosines equals 0.
110 Easy
110 of 112
Application +4 | -1
The sum   S=sin  θ+sin⁡  2θ+...+sin⁡  nθ  \mathrm{\;S} = \mathrm{sin}\,\,\mathrm{\theta } + \sin \,\,2\mathrm{\theta } + ... + \sin \,\,n\mathrm{\theta \;} equals
View answer and explanation
Correct option: A
sin⁡  12  (n+1)  θ  sin⁡  nθ2/sin⁡  θ2\sin \,\,\frac{1}{2}\,\,\left( {n + 1} \right)\,\,\mathrm{\theta }\,\,\sin \,\,\frac{{n\mathrm{\theta }}}{2}/\sin \,\,\frac{\mathrm{\theta }}{2}
Option A (sin⁡12(n+1)θsin⁡nθ2/sin⁡θ2\sin \frac{1}{2}\left( {n + 1} \right)\theta \sin \frac{{n\theta }}{2}/\sin \frac{{\theta }}{2}) is correct because it represents the sum of a sine series using the appropriate trigonometric formula.
111 Easy
111 of 112
Application +4 | -1
The maximum value of cos⁡2A+cos⁡2B−cos⁡2C{\cos ^2}A + {\cos ^2}B - {\cos ^2}C, is
View answer and explanation
Correct option: D
2
Option D (2) is correct because the maximum value is attained when cos²A and cos²B are maximized (equal to 1) and cos²C is minimized (equal to 0).
112 Easy
112 of 112
Analyzing +4 | -1
The equation sin⁡4θ+cos⁡4θ=a{\sin ^4}\theta + {\cos ^4}\theta = a has a real solution if
View answer and explanation
Correct option: A
a∈[1/2,1]a \in \left[ {1/2,1} \right]
Option A is correct because it finds the range of 'a' for which the equation has real solutions by using trigonometric identities and the range of cosine function.
Revision notes and key takeaways

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

Showing 91-112 of 112 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - TRANSFORMATIONS MCQs (All) 165 MCQs → ENGINEERING MATHEMATICS - TRANSFORMATIONS MCQs (Hard) 8 MCQs → ENGINEERING MATHEMATICS - TRANSFORMATIONS MCQs (Medium) 45 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
📚 Switch Set (EASY)
Chapter Sets
ALL 165 MCQs EASY 112 MCQs HARD 8 MCQs MEDIUM 45 MCQs
0 /112
0✓ 0✗
0% Accuracy
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 →