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JEE • MATHEMATICS • TRANSFORMATIONS

Transformations practice · Mixed difficulty

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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.

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Showing 61-90 of 165 questions
61 Medium
61 of 165
Application +4 | -1
sin⁡  47∘+sin⁡  61∘−sin⁡  11∘−sin⁡  25∘\sin \,\,47^\circ + \sin \,\,61^\circ - \sin \,\,11^\circ - \sin \,\,25^\circ is equal to
View answer and explanation
Correct option: B
cos⁡  7∘\cos \,\,7^\circ
Option B (cos⁡ 7∘\cos \,7^\circ) is correct because the expression simplifies to cos⁡ 7∘\cos \,7^\circ using trigonometric identities.
62 Easy
62 of 165
Analyzing +4 | -1
If   y=1+4  sin⁡2  x  cos⁡2  x\;y = 1 + 4\,\,{\sin ^2}\,\,x\,\,{\cos ^2}\,\,x then

View answer and explanation
Correct option: A
1≤  y  ≤21 \le \,\,y\,\, \le 2
The correct answer is A (1≤y≤21 \le y \le 2) because by rewriting the equation and using the range of sin⁡22x\sin^2 2x, we can determine the range of y.
63 Easy
63 of 165
Application +4 | -1
If sin⁡  x+sin⁡  y=a\sin \,\,x + \sin \,\,y = a and cos⁡  x+cos⁡  y=b\cos \,\,x + \cos \,\,y = b, then tan⁡(a+y2)\tan \left( {\frac{{a + y}}{2}} \right) is equal to
View answer and explanation
Correct option: B
ab\frac{a}{b}
Option B (ab\frac{a}{b}) is correct because it is derived by dividing the sum-to-product formulas for sine and cosine.
64 Easy
64 of 165
Application +4 | -1
If A+B+C=180∘A+B+C=180^{\circ}, then cot⁡A+cot⁡B+cot⁡Ccot⁡Acot⁡Bcot⁡C\frac{\cot A+\cot B+\cot C}{\cot A \cot B \cot C} is equal to
View answer and explanation
Correct option: A
1
Option A (1) is correct because the given expression simplifies to 1 using the trigonometric identity for cot(A+B+C) when A+B+C = 180 degrees.
65 Easy
65 of 165
Application +4 | -1
The value of   cos⁡  π5  cos⁡  2 π5  cos⁡  4 π5  cos⁡  8 π5  \mathrm{\;}\cos \,\,\frac{\mathrm{\pi }}{5}\,\,\cos \,\,\frac{{2\,\mathrm{\pi }}}{5}\,\,\cos \,\,\frac{{4\,\mathrm{\pi }}}{5}\,\,\cos \,\,\frac{{8\,\mathrm{\pi }}}{5}\mathrm{\;} is equal to
View answer and explanation
Correct option: D
−116- \frac{1}{{16}}
Option D (−116- \frac{1}{{16}}) is correct because it is the result of applying the product-to-sine identity repeatedly and simplifying.
66 Medium
66 of 165
Analyzing +4 | -1
The period of the function f(x)=sin⁡2x+cos⁡4xf\left( x \right) = {\sin ^2}x + {\cos ^4}x is
View answer and explanation
Correct option: B
π2\frac{\pi }{2}
Option B (π2\frac{\pi}{2}) is correct because the period of the function is found by simplifying the function and identifying the period of the resulting trigonometric term.
67 Easy
67 of 165
Application +4 | -1
The period of the function sin⁡(πx2)+cos⁡(πx2)\sin \left( {\frac{{\pi x}}{2}} \right) + \cos \left( {\frac{{\pi x}}{2}} \right) is
View answer and explanation
Correct option: A
4
The correct answer is A (4) because the period of both sine and cosine functions with the given argument is 4, and the period of their sum is also 4.
68 Easy
68 of 165
Application +4 | -1
If cos⁡(θ+∅)=mcos  (θ−∅)\cos \left( {\theta + \emptyset } \right) = mcos\;\left( {\theta - \emptyset } \right), then tan⁡θ\tan \theta is equal to
View answer and explanation
Correct option: C
[(1−m)/(1+m)]  cot   ∅\left[ {\left( {1 - m} \right)/\left( {1 + m} \right)} \right]\,\,\mathrm{cot}\;\,\emptyset
Option C [(1−m)/(1+m)]cot   ∅\left[ {\left( {1 - m} \right)/\left( {1 + m} \right)} \right]\mathrm{cot}\;\,\emptyset is correct because it is derived by applying trigonometric identities and simplifying the given equation.
69 Easy
69 of 165
Analyzing +4 | -1
If in a triangle ABC,  a2−b2a2+b2=sin⁡  (A−B)sin⁡  (A+B)ABC,\,\,\frac{{{a^2} - {b^2}}}{{{a^2} + {b^2}}} = \frac{{\sin \,\,\left( {A - B} \right)}}{{\sin \,\,\left( {A + B} \right)}} , then the triangle is
View answer and explanation
Correct option: A
Right angled or isosceles
Right angled or isosceles is the correct answer because the given equation implies either A = B (isosceles) or a2+b2=c2a^2 + b^2 = c^2 (right-angled).
70 Easy
70 of 165
Application +4 | -1
If A+B+C=3 π2A + B + C = \frac{{3\,\pi }}{2}, then cos⁡  2A+cos⁡  2B+cos⁡  2C=\cos \,\,2A + \cos \,\,2B + \cos \,\,2C =
View answer and explanation
Correct option: D
1−4sin⁡A  sin⁡B  sin⁡C1 - 4\sin A\,\,\sin B\,\,\sin C
Option D (1−4sin⁡Asin⁡Bsin⁡C1 - 4\sin A\sin B\sin C) is correct because it is the simplified form of the given trigonometric expression using the condition A+B+C=3π2A + B + C = \frac{{3\pi }}{{2}}.
71 Easy
71 of 165
Analyzing +4 | -1
The period of the function f(x)=a{tan⁡(πx)+x−[x]}f\left( x \right) = {a^{\left\{ {\tan \left( {\pi x} \right) + x - \left[ x \right]} \right\}}}, where a>0a > 0 denotes the greatest integer function and x is a real number, is
View answer and explanation
Correct option: D
11
Option D 11 is correct because the fractional part of x and the tangent function both have a period of 1.
72 Easy
72 of 165
Application +4 | -1
The expression tan⁡2α+cot⁡2α{\tan ^2}\alpha + {\cot ^2}\alpha, is
View answer and explanation
Correct option: A
≥2\ge 2
Option A (≥2\ge 2) is correct because tan⁡2α+cot⁡2α{\tan ^2}\alpha + {\cot ^2}\alpha can be rewritten as a squared term plus 2, which is always greater than or equal to 2.
73 Easy
73 of 165
Application +4 | -1
If sin⁡α+sin⁡β=a\sin \alpha+\sin \beta=a and cos⁡α−cos⁡β=b\cos \alpha-\cos \beta=b, then tan⁡(α−β2)\tan \left(\frac{\alpha-\beta}{2}\right) is equal to
View answer and explanation
Correct option: B
−ba-\frac{b}{a}
Option B (−ba-\frac{b}{a}) is correct because it is derived from dividing the two given trigonometric equations after applying sum-to-product formulas.
74 Easy
74 of 165
Analyzing +4 | -1
Let f(x)f\left( x \right) be a real valued function defined by
f(x+λ)=1+[2−5f(x)+10{f(x)}2−10{f(x)}3+5{f(x)}4−{f(x)}5]1/5f\left( {x + \lambda } \right) = 1 + {\left[ {2 - 5f\left( x \right) + 10{{\left\{ {f\left( x \right)} \right\}}^2} - 10{{\left\{ {f\left( x \right)} \right\}}^3} + 5{{\left\{ {f\left( x \right)} \right\}}^4} - {{\left\{ {f\left( x \right)} \right\}}^5}} \right]^{1/5}} for all real x and some positive constant λ\lambda, then f(x)f\left( x \right) is
View answer and explanation
Correct option: B
A periodic function with period 2  λ2\;\lambda
The correct answer is A (A periodic function with period λ\lambda) because the function repeats its values after an interval of 2λ2\lambda, making it periodic.
75 Hard
75 of 165
Application +4 | -1
The value of cot⁡2  π9+cot⁡2  2 π9+cot⁡2  4 π9{\cot ^2}\,\,\frac{\pi }{9} + {\cot ^2}\,\,\frac{{2\,\pi }}{9} + {\cot ^2}\,\,\frac{{4\,\pi }}{9}, is
View answer and explanation
Correct option: B
3\mathrm{3}
Option B is correct because by using the identity for cot⁡2\cot^2 and simplifying, we can find the value to be 3.

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SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs INDEFINITE INTEGRATION 1179 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs
76 Easy
76 of 165
Application +4 | -1
The maximum value of 3  cos⁡  x+4  sin⁡  x+53\,\,\cos \,\,x + 4\,\,\sin \,\,x + 5 is
View answer and explanation
Correct option: D
None of these
None of these is correct because the maximum value of the expression is 10, which is not among the options.
77 Medium
77 of 165
Analyzing +4 | -1
cos⁡  xcos⁡  (x−2y)=λ  ⇒tan⁡  (x−y)tan⁡y\frac{{\cos \,\,x}}{{\cos \,\,\left( {x - 2y} \right)}} = \lambda \; \Rightarrow \tan \,\,\left( {x - y} \right)\tan y is equal to
View answer and explanation
Correct option: B
1−λ1+λ\frac{{1 - \lambda }}{{1 + \lambda }}
Option B (1−λ1+λ\frac{{1 - \lambda }}{{1 + \lambda }}) is correct because it is derived by applying trigonometric identities to simplify the given expression.
78 Easy
78 of 165
Analyzing +4 | -1
The period of the function

f(x)=sin⁡8x  cosx−sin⁡6x  cos3xcos⁡2xcos⁡x−sin⁡3xsin⁡4xf\left( x \right) = \frac{{\sin 8\mathrm{x\;cosx} - \sin 6\mathrm{x\;cos}3\mathrm{x}}}{{\cos 2\mathrm{x}\cos \mathrm{x} - \sin 3\mathrm{x}\sin 4\mathrm{x}}} is
View answer and explanation
Correct option: C
π2\frac{\pi }{2}
Option C (π2\frac{\pi}{{2}}) is correct because the given function simplifies to tan⁡2x\tan 2x, and the period of tan⁡kx\tan kx is π∣k∣.\frac{\pi}{{|k|}}.
79 Easy
79 of 165
Application +4 | -1
The value of cos⁡  π15  cos⁡  2 π15  cos⁡  2 π15  cos⁡  8 π15\cos \,\,\frac{\pi }{{15}}\,\,\cos \,\,\frac{{2\,\pi }}{{15}}\,\,\cos \,\,\frac{{2\,\pi }}{{15}}\,\,\cos \,\,\frac{{8\,\pi }}{{15}} is
View answer and explanation
Correct option: B
−116- \frac{1}{{16}}
Option B (-116\frac{1}{{16}}) is correct because by repeatedly using the product-to-sum trigonometric identities, the expression simplifies to -116\frac{1}{{16}}.
80 Easy
80 of 165
Application +4 | -1
The range of f(x)=cos⁡x−sin⁡xf\left( x \right) = \cos x - \sin x is
View answer and explanation
Correct option: D
[−2,  2]\left[ { - \sqrt 2 ,\;\sqrt 2 } \right]
Option D ([−2,;2]\left[ { - \sqrt 2 ,\\;\sqrt 2 } \right]) is correct because it represents the range of the function, which is a sinusoidal function with amplitude 2\sqrt{2}.
81 Easy
81 of 165
Analyzing +4 | -1
The maximum value of 12  sin⁡  θ−9  sin⁡2  θ12\,\,\sin \,\,\theta - 9\,\,{\sin ^2}\,\,\theta is
View answer and explanation
Correct option: B
4\mathrm{4}
Option B (4) is correct because the maximum value of the given expression is 4, obtained by completing the square.
82 Hard
82 of 165
Analyzing +4 | -1
If sin⁡3x sin   3x=∑m=0n Cm cos⁡  mx{\sin ^3}x\,sin\;\,3x = \sum \limits_{m = 0}^n \,{C_m}\,\cos \,\,mx is an identity in xx, where C0,   C1,…,  Cn{C_0},\;\,{C_1}, \ldots ,\,\,{C_n} are constants and Cn≠0{C_n} \ne 0, then the value of nn equals
View answer and explanation
Correct option: C
6
Option C (6) is correct because expanding sin⁡3xsin⁡3x\sin^3 x \sin 3x and using trigonometric identities results in a sum of cosine terms up to cos⁡6x\cos 6x, making n = 6.
83 Medium
83 of 165
Analyzing +4 | -1
The smallest positive value of xx (in degree) for which tan⁡(x+100∘)=tan⁡(x+50∘)tan⁡xtan⁡(x−50∘)\tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan x \tan \left(x-50^{\circ}\right), is
View answer and explanation
Correct option: D
30∘30^{\circ}
Option D (30∘30^{\circ}) is correct because it is the smallest positive value of xx that satisfies the given trigonometric equation.
84 Medium
84 of 165
Application +4 | -1
If α+β+γ=2θ\alpha + \beta + \gamma = 2\theta, then cos⁡  θ+cos⁡  (θ−α)+cos⁡  (θ−β)+cos⁡  (θ−γ)\cos \,\,\theta + \cos \,\,\left( {\theta - \alpha } \right) + \cos \,\,\left( {\theta - \beta } \right) + \cos \,\,\left( {\theta - \gamma } \right) is equal to
View answer and explanation
Correct option: B
4  cos⁡  α2  .  cos⁡  β2  .  cos⁡  γ24\,\,\cos \,\,\frac{\alpha }{2}\,\,.\,\,\cos \,\,\frac{\beta }{2}\,\,.\,\,\cos \,\,\frac{\gamma }{2}
Option B is correct because it correctly simplifies the given trigonometric expression using sum-to-product formulas and the given condition.
85 Easy
85 of 165
Application +4 | -1
For α,β∈(0,π/2)\alpha, \beta \in(0, \pi / 2), let 3sin⁡(α+β)=2sin⁡(α−β)3 \sin (\alpha+\beta)=2 \sin (\alpha-\beta) and a real number kk be such that tan⁡α=ktan⁡β\tan \alpha=k \tan \beta. Then, the value of kk is equal to
View answer and explanation
Correct option: B
−5-5
Option B (-5) is correct because it involves using trigonometric identities to simplify the given equation and find the relationship between tan⁡α\tan \alpha and tan⁡β\tan \beta.
86 Easy
86 of 165
Application +4 | -1
sin⁡  65∘+sin⁡  43∘−sin⁡  29∘−sin⁡  7∘\sin \,\,65^\circ + \sin \,\,43^\circ - \sin \,\,29^\circ - \sin \,\,7^\circ is equal to
View answer and explanation
Correct option: D
None of these
Option C (3/2) is correct because it is the result of applying the sine rule and componendo and dividendo.
87 Easy
87 of 165
Application +4 | -1
The period of the function f(θ)=sin⁡θ3+cos⁡θ2f\left( \mathrm{\theta } \right) = \sin \frac{\mathrm{\theta }}{3} + \cos \frac{\mathrm{\theta }}{2} is
View answer and explanation
Correct option: D
12π12\pi
Option D is correct because the period of the sum of two trigonometric functions is the LCM of their individual periods.
88 Easy
88 of 165
Application +4 | -1
The function f(x)=sin⁡πx2+2cos⁡πx3−tan⁡πx4f\left( x \right) = \sin \frac{{\pi x}}{2} + 2\cos \frac{{\pi x}}{3} - \tan \frac{{\pi x}}{4} is periodic with period
View answer and explanation
Correct option: D
12
Option D (12) is correct because the period of the sum of periodic functions is the least common multiple (LCM) of their individual periods, which in this case is LCM(4, 6, 4) = 12.
89 Easy
89 of 165
Application +4 | -1
The period of the function f(x)=sin⁡(sin⁡x5)f\left( x \right) = \sin \left( {\sin \frac{x}{5}} \right) is
View answer and explanation
Correct option: C
10π10\pi
Option C (10π10\pi) is correct because it is the smallest value for which f(x+10π)=f(x)f(x + 10\pi) = f(x).
90 Easy
90 of 165
Application +4 | -1
If sin⁡  (x+3α)=3 sin⁡(α−x)\sin \,\,\left( {x + 3\alpha } \right) = 3\,\sin \left( {\alpha - x} \right), then
View answer and explanation
Correct option: C
tan⁡  x=tan⁡3  α\tan \,\,x = {\tan ^3}\,\,\alpha
Option C (tan⁡ x=tan⁡3 α\tan \,x = {\tan ^3}\,\alpha) is correct because it is derived by applying componendo and dividendo and trigonometric identities to the given equation.
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