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JEE • MATHEMATICS • TRANSFORMATIONS

Transformations practice · Medium

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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.

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Showing 1-30 of 45 questions
1 Medium
1 of 45
Application +4 | -1
If y=2x−2−x2x+2−xy=\frac{2^x-2^{-x}}{2^x+2^{-x}}, where 0<y<10 < y < 1, then the value of xx is....
View answer and explanation
Correct option: B
12log⁡2(1+y1−y)\frac{1}{2} \log _2\left(\frac{1+y}{1-y}\right)
Option B (12log⁡2(1+y1−y)\frac{1}{2} \log _2\left(\frac{1+y}{1-y}\right)) is correct because it is the result of solving the given equation for xx using algebraic manipulation and logarithms.
2 Medium
2 of 45
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 the value of cot⁡α  cot⁡β  cot⁡γ\cot \alpha \,\,\cot \beta \,\,\cot \gamma is
View answer and explanation
Correct option: C
cot⁡δ\cot \delta
Option C (cot⁡δ\cot \delta) is correct because after applying componendo and dividendo and simplifying the given equation, we arrive at the result cot⁡αcot⁡βcot⁡γ=cot⁡δ\cot \alpha \cot \beta \cot \gamma = \cot \delta.
3 Medium
3 of 45
Application +4 | -1
If angle θ\theta is divided into two parts AA and BB such that A−B=xA-B=x and tan⁡A:tan⁡B=k:1\tan A : \tan B=k: 1, then the value of sin⁡x\sin x is
View answer and explanation
Correct option: A
k−1k+1sin⁡θ\frac{k-1}{k+1} \sin \theta
Option A (k−1k+1sin⁡θ\frac{k-1}{k+1} \sin \theta) is correct because applying the componendo and dividendo rule to the given ratio of tangents leads to the correct expression for sin⁡x\sin x.
4 Medium
4 of 45
Application +4 | -1
If A+B+C=π,  n∈ZA + B + C = \pi ,\,\,n \in Z, then tan⁡  nA+tan⁡  nB+tan⁡  nC\tan \,\,nA + \tan \,\,nB + \tan \,\,nC is equal to
View answer and explanation
Correct option: C
tan⁡  nA  tan⁡  nB  tan⁡  nC\tan \,\,nA\,\,\tan \,\,nB\,\,\tan \,\,nC
Option C (tan⁡ nA tan⁡ nB tan⁡ nC\tan \,nA\,\tan \,nB\,\tan \,nC) is correct because it follows from the trigonometric identity for the tangent of the sum of three angles when the sum of the angles is a multiple of π\pi.
5 Medium
5 of 45
Application +4 | -1
If 3cos⁡x=2cos⁡(x−2y)3 \cos x=2 \cos (x-2 y), then tan⁡(x−y)tan⁡y\tan (x-y) \tan y is equal to
View answer and explanation
Correct option: C
15\frac{1}{5}
Option D (15\frac{1}{5}) is correct because applying the componendo and dividendo rule to the given equation and using trigonometric identities leads to the expression tan⁡(x−y)tan⁡y=15\tan(x-y) \tan y = \frac{1}{5}.
6 Medium
6 of 45
Analyzing +4 | -1
If   sin⁡3  x  sin⁡  3x=∑m=0n  cm  cos⁡  mx,   where   c0,  c1  ,  c2,…, cn\;{\sin ^3}\,\,x\,\,\sin \,\,3x = \sum \limits_{m = 0}^n \,\,{c_m}\;\cos \,\,mx,\;\,\mathrm{where}\;\,{c_0},\,\,{c_{1\;}},\,\,{c_2}, \ldots ,\,{c_n} are constants and cn≠0{c_n} \ne 0, then the value of nn is
View answer and explanation
Correct option: B
6\mathrm{6}
Option B (6) is correct because expanding the expression sin⁡3xsin⁡3x\sin^3 x \sin 3x results in a cosine series with the highest multiple of x being 6.
7 Medium
7 of 45
Analyzing +4 | -1
If   cos A=m  cos⁡  B   and  cot⁡  A+B2=λ  tan⁡  B−A2\mathrm{\;cos}\,A = m\,\,\cos \,\,B\,\;\mathrm{and}\,\,\cot \,\,\frac{{A + B}}{2} = \lambda \,\,\tan \,\,\frac{{B - A}}{2} then λ\lambda is

View answer and explanation
Correct option: C
m+1m−1\frac{{m + 1}}{{m - 1}}
Option C ((m+1)/(m-1)) is correct because by applying componendo and dividendo and trigonometric identities, λ is found to be (m+1)/(m-1).
8 Medium
8 of 45
Analyzing +4 | -1
The value of sin⁡  π14  sin⁡  3 π14  sin⁡  5 π14  sin⁡  7π14  sin⁡  9 π14  sin⁡  11 π14  sin⁡  13  π14\sin \,\,\frac{\pi }{{14}}\,\,\sin \,\,\frac{{3\,\pi }}{{14}}\,\,\sin \,\,\frac{{5\,\pi }}{{14}}\,\,\sin \,\,\frac{{7\pi }}{{14}}\,\,\sin \,\,\frac{{9\,\pi }}{{14}}\,\,\sin \,\,\frac{{11\,\pi }}{{14}}\,\,\sin \,\,\frac{{13\;\pi }}{{14}} is
View answer and explanation
Correct option: B
1 / 64\mathrm{1}\,\mathrm{/}\,\mathrm{64}
Option B (1 \/ 64\mathrm{1}\,{\/}\,\mathrm{64}) is correct because by using trigonometric identities and simplification, the expression reduces to 1/64.
9 Medium
9 of 45
Analyzing +4 | -1
The value of cos⁡  2 π15  cos⁡  4 π15  cos⁡  815  cos⁡  14 π15\cos \,\,\frac{{2\,\pi }}{{15}}\,\,\cos \,\,\frac{{4\,\pi }}{{15}}\,\,\cos \,\,\frac{8}{{15}}\,\,\cos \,\,\frac{{14\,\pi }}{{15}} is
View answer and explanation
Correct option: D
1/161/16
Option D (1/161/16) is correct because by applying the product-to-sum trigonometric identity repeatedly, the expression simplifies to 1/16.
10 Medium
10 of 45
Application +4 | -1
The value of cos⁡  2π15  cos⁡  4π15  cos⁡  8π15  cos⁡  14π15\cos \,\,\frac{{2\pi }}{{15}}\,\,\cos \,\,\frac{{4\pi }}{{15}}\,\,\cos \,\,\frac{{8\pi }}{{15}}\,\,\cos \,\,\frac{{14\pi }}{{15}} is
View answer and explanation
Correct option: A
116\frac{1}{{16}}
Option A (116\frac{1}{{16}}) is correct because by repeatedly using the identity 2sin⁡xcos⁡x=sin⁡2x2 \sin x \cos x = \sin 2x, the expression simplifies to 116\frac{1}{{16}}.
11 Medium
11 of 45
Application +4 | -1
If 3sin⁡(A+B)=4sin⁡(A−B)3 \sin (A+B)=4 \sin (A-B) and If tan⁡A=ktan⁡B\tan A=k \tan B, then value of kk is
View answer and explanation
Correct option: C
7
Option C (7) is correct because it is derived by using the componendo and dividendo rule on the given trigonometric equation.
12 Medium
12 of 45
Application +4 | -1
The maximum value of   sin⁡  (x+π6)+cos⁡  (x+π6)  \mathrm{\;}\sin \,\,\left( {x + \frac{\pi }{6}} \right) + \cos \,\,\left( {x + \frac{\pi }{6}} \right)\mathrm{\;} in the interval (0,  π2)\left( {0,\,\,\frac{\pi }{2}} \right) is attained at
View answer and explanation
Correct option: A
x=π12x = \frac{\pi }{{12}}
Option A (x=π12x = \frac{\pi }{{12}}) is correct because it is the value of x where the given trigonometric function attains its maximum value in the specified interval.
13 Medium
13 of 45
Application +4 | -1
If in △ABC,cos⁡B+cos⁡C=2−2cos⁡A\triangle A B C, \cos B+\cos C=2-2 \cos A, then
View answer and explanation
Correct option: B
b,a,cb, a, c are in AP
Option B (b,a,cb, a, c are in AP) is correct because the given condition leads to the relationship sin⁡B+sin⁡C=2sin⁡A\sin B + \sin C = 2 \sin A, which implies that b,a,cb, a, c are in arithmetic progression.
14 Medium
14 of 45
Analyzing +4 | -1
The values of α\alpha for which the equation sin⁡4x+cos⁡4x+sin⁡  2x+α=0{\sin ^4}x + {\cos ^4}x + \sin \,\,2x + \alpha = 0 may be valid, are
View answer and explanation
Correct option: B
0≤α≤120 \le \alpha \le \frac{1}{2}
Option C (−32≤α≤12-\frac{3}{2} \le \alpha \le \frac{1}{2}) is incorrect. The correct answer is B (0≤α≤120 \le \alpha \le \frac{1}{2}) because the equation is valid only when 0≤3+2α≤40 \le 3 + 2\alpha \le 4.
15 Medium
15 of 45
Application +4 | -1
If A+B+C=πA + B + C = \pi, then sin⁡  2A+sin⁡  2B+sin⁡  2C=\sin \,\,2A + \sin \,\,2B + \sin \,\,2C =
View answer and explanation
Correct option: A
4  sin⁡  A  sin⁡ B  sin⁡  C4\,\,\sin \,\,A\,\,\sin \,B\,\,\sin \,\,C
Option A (4sin⁡Asin⁡Bsin⁡C4 \sin A \sin B \sin C) is correct because by using the sum-to-product trigonometric identities and the fact that A+B+C=πA + B + C = \pi, the expression sin⁡2A+sin⁡2B+sin⁡2C\sin 2A + \sin 2B + \sin 2C simplifies to 4sin⁡Asin⁡Bsin⁡C4 \sin A \sin B \sin C.

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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
16 Medium
16 of 45
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.
17 Medium
17 of 45
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.
18 Medium
18 of 45
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.
19 Medium
19 of 45
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.
20 Medium
20 of 45
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.
21 Medium
21 of 45
Application +4 | -1
The maximum value of 3 cos⁡ θ+5 sin⁡(θ−π6)3\,\cos \,\theta + 5\,\sin \left( {\theta - \frac{\pi }{6}} \right) for any real value of θ\theta is
View answer and explanation
Correct option: D
19\sqrt {19}
Option C (19\sqrt {19}) is correct. The maximum value is found by converting the expression into the form a*cos(theta) + b*sin(theta) and then using the formula sqrt(a2 + b2).
22 Medium
22 of 45
Application +4 | -1
Minimum value of 13  sin⁡  θ−4  cos⁡  θ+7\frac{1}{{3\,\,\sin \,\,\theta - 4\,\,\cos \,\,\theta + 7}} is
View answer and explanation
Correct option: A
112\frac{1}{{12}}
Option A, 112\frac{1}{{12}}, is correct because it is the minimum value of the given expression, which occurs when the denominator is maximized.
23 Medium
23 of 45
Analyzing +4 | -1
If an+1=12  (1+an){a_{n + 1}} = \sqrt {\frac{1}{2}\,\,\left( {1 + {a_n}} \right)}, then cos⁡  (1−a02a1 a2 a3…to    ∞)=\cos \,\,\left( {\frac{{\sqrt {1 - a_0^2} }}{{{a_1}\,{a_2}\,{a_3} \ldots \mathrm{to\;}\,\,\infty }}} \right) =
View answer and explanation
Correct option: C
a0{a_0}
Option C (a0{a_0}) is correct because the infinite product simplifies to a value that allows the cosine to be evaluated, resulting in a0{a_0}.
24 Medium
24 of 45
Analyzing +4 | -1
In a triangle ABC,  sin⁡A−cos⁡  B=cos⁡  CABC,\,\,\sin A - \cos \,\,B = \cos \,\,C, then angle BB is
View answer and explanation
Correct option: A
π2\frac{\pi }{2}
Option A (π2\frac{\pi }{2}) is correct because substituting sin⁡A=cos⁡B+cos⁡C\sin A = \cos B + \cos C and using trigonometric identities leads to B=π2B = \frac{\pi}{2}.
25 Medium
25 of 45
Application +4 | -1
If A+B+C=πA+B+C=\pi, then the 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
1−2cos⁡Acos⁡Bcos⁡C1-2 \cos A \cos B \cos C
Option D (1−2cos⁡Acos⁡Bcos⁡C1-2 \cos A \cos B \cos C) is correct because by using trigonometric identities and the given condition A+B+C=πA+B+C=\pi, we can simplify the expression.
26 Medium
26 of 45
Application +4 | -1
The value of cos⁡4  (π8)+cos⁡4  (3 π8)+cos⁡4  (5 π8)+cos⁡4  (7π8){\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}\,\,\left( {\frac{{7\pi }}{8}} \right) is
View answer and explanation
Correct option: C
32\frac{3}{2}
Option C (32\frac{3}{2}) is correct because it is the result of simplifying the given trigonometric expression using trigonometric identities and angle transformations.
27 Medium
27 of 45
Analyzing +4 | -1
If the equation cos⁡  3x+cos⁡  2x=sin⁡  3x2+sin⁡  x2,   0≤x≤2π\cos \,\,3x + \cos \,\,2x = \sin \,\,\frac{{3x}}{2} + \sin \,\,\frac{x}{2},\,\;0 \le x \le 2\pi, then the number of values of xx is
View answer and explanation
Correct option: D
5
Option D is correct because solving the trigonometric equation yields 5 distinct solutions within the given interval 0 ≤ x ≤ 2π.
28 Medium
28 of 45
Application +4 | -1
The minimum value of f(x)=sin⁡4  x+cos⁡4  x,  0≤  x≤π2f\left( x \right) = {\sin ^4}\,\,x + {\cos ^4}\,\,x,\;0 \le \,\,x \le \frac{\pi }{2} is

View answer and explanation
Correct option: D
12\frac{1}{2}
Option D (12\frac{1}{2}) is correct because the minimum value of the function sin⁡4 x+cos⁡4 x{\sin ^4}\,x + {\cos ^4}\,x in the given range is 12\frac{1}{2}.
29 Medium
29 of 45
Analyzing +4 | -1
The expression 2cos⁡  π13cos⁡  9 π13+cos⁡  3 π13+cos⁡  5 π132\cos \,\,\frac{\pi }{{13}}\cos \,\,\frac{{9\,\pi }}{{13}} + \cos \,\,\frac{{3\,\pi }}{{13}} + \cos \,\,\frac{{5\,\pi }}{{13}} is equal to
View answer and explanation
Correct option: B
0
Option B (0) is correct because by applying trigonometric identities and simplification, the expression reduces to 0.
30 Medium
30 of 45
Analyzing +4 | -1
If A=cos⁡2θ+sin⁡4θA = {\cos ^2}\theta + {\sin ^4}\theta, then for all values of θ,
View answer and explanation
Correct option: D
34≤A≤1\frac{3}{4} \le A \le 1
Option D (34≤A≤1\frac{3}{4} \le A \le 1) is correct because the given expression can be bounded between these values by using trigonometric identities and properties.
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