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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 121-150 of 165 questions
121 Easy
121 of 165
Application +4 | -1
The period of the function f(x)=cosec23x+cot⁡4xf\left( x \right) = \mathrm{cose}{\mathrm{c}^2}3x + \cot 4x is
View answer and explanation
Correct option: D
π\pi
Option D (π\pi) is correct because it is the least common multiple of the periods of the individual functions, which are π3\frac{\pi}{3} and π4\frac{\pi}{4}.
122 Easy
122 of 165
Application +4 | -1
Maximum value of sin⁡θ+cos⁡θ\sin \theta + \cos \theta in [0,   π2]\left[ {0,\;\,\frac{\pi }{2}} \right] is

View answer and explanation
Correct option: A
2\sqrt 2
Option A (2\sqrt 2) is correct because the maximum value of sin⁡θ+cos⁡θ\sin \theta + \cos \theta is 2\sqrt 2 and occurs at θ=π4\theta = \frac{\pi}{4} within the given interval.
123 Easy
123 of 165
Application +4 | -1
The value of sin⁡  55∘−cos⁡  55∘sin⁡  10∘\frac{{\sin \,\,55^\circ - \cos \,\,55^\circ }}{{\sin \,\,10^\circ }} is
View answer and explanation
Correct option: D
2\sqrt 2
Option D (2\sqrt{2}) is correct because the expression simplifies to 2\sqrt{2} after applying the sine subtraction formula and using the value of cos⁡45∘\cos 45^\circ.
124 Medium
124 of 165
Analyzing +4 | -1
If cos⁡  (α+β)sin⁡  (γ+δ)=cos⁡  (α−β)sin⁡  (γ−δ)\cos \,\,\left( {\alpha + \beta } \right)\sin \,\,\left( {\gamma + \delta } \right) = \cos \,\,\left( {\alpha - \beta } \right)\sin \,\,\left( {\gamma - \delta } \right), then cot⁡α  cot⁡β  cot⁡γ\cot \alpha \,\,\cot \beta \,\,\cot \gamma is equal to
View answer and explanation
Correct option: A
cot⁡  δ\cot \,\,\delta
Option A (cot⁡δ\cot \delta) is correct because after applying trigonometric identities and simplifying the given equation, we arrive at the relation cot⁡αcot⁡βcot⁡γ=cot⁡δ\cot \alpha \cot \beta \cot \gamma = \cot \delta.
125 Medium
125 of 165
Application +4 | -1
If cos⁡  (θ+ϕ)=m  cos⁡  (θ−ϕ)\cos \,\,\left( {\theta + \phi } \right) = m\,\,\cos \,\,\left( {\theta - \phi } \right) is equal to
View answer and explanation
Correct option: C
1−m1+m  cot⁡  ϕ\frac{{1 - m}}{{1 + m}}\,\,\cot \,\,\phi
Option C (1−m1+mcot⁡ϕ\frac{{1 - m}}{{1 + m}}\cot \phi) is correct because it is the result of applying the componendo and dividendo rule and trigonometric identities to the given equation.
126 Medium
126 of 165
Application +4 | -1
If − π≤x≤π,   − π≤y≤π   and  cos⁡  x+cos⁡  y=2- \,\pi \le x \le \pi ,\;\, - \,\pi \le y \le \pi \;\,\mathrm{and}\,\,\cos \,\,x + \cos \,\,y = 2, then the value of cos(x−y)\mathrm{cos}\left( {x - y} \right) is
View answer and explanation
Correct option: C
1
Option C (1) is correct because the maximum value of cosine is 1, so both cos(x) and cos(y) must be 1. This implies x = 0 and y = 0, therefore cos(x - y) = cos(0) = 1.
127 Easy
127 of 165
Analyzing +4 | -1
The value of sin⁡  12∘  sin⁡  24∘  sin⁡  48∘  sin⁡  84∘\sin \,\,12^\circ \,\,\sin \,\,24^\circ \,\,\sin \,\,48^\circ \,\,\sin \,\,84^\circ, is
View answer and explanation
Correct option: A
cos⁡  20∘  cos⁡  40∘  cos⁡  60∘  cos⁡   80∘\cos \,\,20^\circ \,\,\cos \,\,40^\circ \,\,\cos \,\,60^\circ \,\,\cos \,\,\,80^\circ
Option A (cos⁡ 20∘ cos⁡ 40∘ cos⁡ 60∘ cos⁡ 80∘\cos \,20^\circ \,\cos \,40^\circ \,\cos \,60^\circ \,\cos \,80^\circ) is correct because it is equal to the given expression after applying trigonometric identities.
128 Easy
128 of 165
Application +4 | -1
If sin⁡  (x+y)sin⁡  (x−y)=a+ba−b\frac{{\sin \,\,\left( {x + y} \right)}}{{\sin \,\,\left( {x - y} \right)}} = \frac{{a + b}}{{a - b}}, then tan⁡  xtan⁡  y\frac{{\tan \,\,x}}{{\tan \,\,y}} 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 applying the componendo and dividendo rule and simplifying the trigonometric ratios.
129 Easy
129 of 165
Application +4 | -1
If sin⁡A=nsin  B\sin A = nsin\;B, then n−1n+1  tan⁡  A+B2\frac{{n - 1}}{{n + 1}}\,\,\tan \,\,\frac{{A + B}}{2} is equal to
View answer and explanation
Correct option: B
tan⁡  A−B2\tan \,\,\frac{{A - B}}{2}
Option B tan⁡  A−B2\tan \,\,\frac{{A - B}}{2} is correct because applying componendo and dividendo to n1=sin⁡Asin⁡B\frac{n}{1} = \frac{{\sin A}}{{\sin B}} and simplifying leads to the given expression being equal to tan⁡  A−B2\tan \,\,\frac{{A - B}}{2}.
130 Medium
130 of 165
Application +4 | -1
The value of 1+cos⁡  56∘+cos⁡  58∘−cos⁡  66∘1 + \cos \,\,56^\circ + \cos \,\,58^\circ - \cos \,\,66^\circ is
View answer and explanation
Correct option: A
4  cos⁡  28∘  cos⁡  29∘  sin⁡33∘4\,\,\cos \,\,28^\circ \,\,\cos \,\,29^\circ \,\,\sin 33^\circ
Option A (4cos⁡28∘cos⁡29∘sin⁡33∘4\cos 28^\circ \cos 29^\circ \sin 33^\circ) is correct because it represents the simplified form of the trigonometric expression after applying the sum-to-product and other trigonometric identities.
131 Easy
131 of 165
Analyzing +4 | -1
If A+B+C=180∘A + B + C = 180^\circ, then ∑  tan⁡  A2  tan⁡  B2\sum \,\,\tan \,\,\frac{A}{2}\,\,\tan \,\,\frac{B}{2} is
View answer and explanation
Correct option: B
1
Option B (1) is correct because the given condition A+B+C=180∘A + B + C = 180^\circ leads to the trigonometric identity ∑tan⁡A2tan⁡B2=1\sum \tan \frac{A}{2} \tan \frac{B}{2} = 1.
132 Easy
132 of 165
Application +4 | -1
If 5  cos⁡x+12  cos⁡y=135\,\,\cos x + 12\,\,\cos y = 13, then the maximum value of 5  sin⁡x+12  sin⁡y5\,\,\sin x + 12\,\,\sin y is
View answer and explanation
Correct option: B
120\sqrt {120}
Option B is correct because it represents the maximum value obtained by using the given equation and trigonometric identities.
133 Hard
133 of 165
Analyzing +4 | -1
The value of cosec2  π2+cosec2  2π7  +  cosec2  3π7\mathrm{cose}{\mathrm{c}^2}\,\,\frac{\pi }{2} + \mathrm{cose}{\mathrm{c}^2}\,\,\frac{{2\pi }}{7}\,\, + \,\,\mathrm{cose}{\mathrm{c}^2}\,\,\frac{{3\pi }}{7} is
View answer and explanation
Correct option: D
23{2^3}
Option D (23{2^3}) is correct because the sum of the squares of the cosecant terms simplifies to 8 using trigonometric identities and properties of roots of trigonometric equations.
134 Easy
134 of 165
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.
135 Easy
135 of 165
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).

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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
136 Medium
136 of 165
Analyzing +4 | -1
Which of the following functions have period 2π2\mathrm{\pi }?
View answer and explanation
Correct option: C
y=sin⁡t+cos⁡2ty = \sin t + \cos 2t
Option C is correct. The period of sin⁡t\sin t is 2π2\pi and the period of cos⁡2t\cos 2t is π\pi. The least common multiple of 2π2\pi and π\pi is 2π2\pi.
137 Easy
137 of 165
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.
138 Easy
138 of 165
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.
139 Medium
139 of 165
Application +4 | -1
The value of sin⁡  (B+A)+  cos  (B−A)sin⁡  (B−A)+cos⁡  (B+A)\frac{{\sin \,\,\left( {B + A} \right) + \;\mathrm{cos}\,\,\left( {B - A} \right)}}{{\sin \,\,\left( {B - A} \right) + \cos \,\,\left( {B + A} \right)}} is equal to
View answer and explanation
Correct option: B
cos⁡  A+sin⁡  Acos⁡  A−sin⁡  A\frac{{\cos \,\,A + \sin \,\,A}}{{\cos \,\,A - \sin \,\,A}}
Option B (cos⁡,A+sin⁡,Acos⁡,A−sin⁡,A\frac{{\cos \\,A + \sin \\,A}}{{\cos \\,A - \sin \\,A}}) is correct because simplifying the given expression using trigonometric identities leads to the result cos⁡,A+sin⁡,Acos⁡,A−sin⁡,A\frac{{\cos \\,A + \sin \\,A}}{{\cos \\,A - \sin \\,A}}.
140 Easy
140 of 165
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}.
141 Easy
141 of 165
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.
142 Easy
142 of 165
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}.
143 Hard
143 of 165
Analyzing +4 | -1
If tan⁡  3Atan⁡A  =k\frac{{\tan \,\,3A}}{{\tan A}}\,\, = k, then sin⁡  3Asin⁡A\frac{{\sin \,\,3A}}{{\sin A}} is equal to
View answer and explanation
Correct option: C
2kk−1,   k∉[1/3,   3]\frac{{2k}}{{k - 1}},\;\,k \notin \left[ {1/3,\,\;3} \right]
Option C (2kk−1,  k∉[1/3,  3]\frac{{2k}}{{k - 1}},\;k \notin \left[ {1/3,\;3} \right]) is correct because by using trigonometric identities and the given condition, we can express sin⁡ 3Asin⁡A\frac{{\sin \,3A}}{{\sin A}} in terms of k, and determine the range of k.
144 Easy
144 of 165
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}.
145 Medium
145 of 165
Analyzing +4 | -1
In a △ABC,a,b\triangle A B C, a, b and cc are the sides of the triangle opposite to the angles 2222222222 dA,B,C2222222222 \mathrm{~d} A, B, C, respectively. Then, the value of a3sin⁡(B−C)+b3sin⁡(C−A)+c3sin⁡(A−B)a^3 \sin (B-C)+b^3 \sin (C-A)+c^3 \sin (A-B) is
View answer and explanation
Correct option: A
0
Option A (0) is correct because the expression simplifies to zero using trigonometric identities and the sine rule.
146 Easy
146 of 165
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.
147 Easy
147 of 165
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.
148 Easy
148 of 165
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.
149 Easy
149 of 165
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.
150 Easy
150 of 165
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.
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