JEE Mains · Maths · STD 12 - 1. relation and function
For \(x \in \left( {0,\frac{3}{2}} \right)\), let \(f\left( x \right) = \sqrt x \), \(g\left( x \right) = \tan \,x\) and \(h\left( x \right) = \frac{{1 - {x^2}}}{{1 + {x^2}}}\). If \(\phi \left( x \right) = \left( {\left( {hof} \right)og} \right)\left( x \right)\), then \(\phi \left( {\frac{\pi }{3}} \right)\) is equal to
- A \(\tan \,\frac{{11\pi }}{{12}}\)
- B \(\tan \,\frac{\pi }{{12}}\)
- C \(\tan \,\frac{5\pi }{{12}}\)
- D \(\tan \,\frac{7\pi }{{12}}\)
Answer & Solution
Correct Answer
(A) \(\tan \,\frac{{11\pi }}{{12}}\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = \sqrt x ,g\left( x \right) = \tan \,x,h\left( x \right) = \frac{{1 - {x^2}}}{{1 + {x^2}}}\) \(fog\left( x \right) = \sqrt {\tan x} \) \(hofog\left( x \right) = h\left( {\sqrt {\tan x} } \right) = \frac{{1 - \tan x}}{{1 + \tan x}}\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\lim _{x \rightarrow 2}\left(\sum_{n=1}^{9} \frac{x}{n(n+1) x^{2}+2(2 n+1) x+4}\right)\) is equal to :JEE Mains 2021 Medium
- If the tangent to the curve \(y=x^{3}\) at the point \(P \left( t , t ^{3}\right)\) meets the curve again at \(Q ,\) then the ordinate of the point which divides \(PQ\) internally in the ratio \(1: 2\) isJEE Mains 2021 Hard
- Let \(A=\left[\begin{array}{lll}1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1\end{array}\right], a, b \in R\). If for some \(n \in N\), \(A ^{ n }=\left[\begin{array}{ccc}1 & 48 & 2160 \\ 0 & 1 & 96 \\ 0 & 0 & 1\end{array}\right]\) then \(n + a + b\) is equal to \(\dots\dots\)JEE Mains 2022 Hard
- The acute angle between two lines such that the direction cosines \(l, m, n,\) of each of them satisfy the equations \(l+ m + n = 0\) and \(l^2 + m^2 - n^2 = 0\) is ..…… \(^o\)JEE Mains 2013 Hard
- If \(a\) and \(b\) are real numbers such that \((2+\alpha)^{4}=a+b \alpha,\) where \(\alpha=\frac{-1+i \sqrt{3}}{2},\) then \(a+b\) is equal toJEE Mains 2020 Hard
- The probability of selecting integers \(a \in[-5,30]\) such that \(x^{2}+2(a+4) x-5 a+64>0\), for all \(x \in R\), is:JEE Mains 2021 Hard
More PYQs from JEE Mains
- Let a line \(L\) pass through the point of intersection of the lines \(b x+10 y-8=0\) and \(2 x-3 y=0\), \(b \in R -\left\{\frac{4}{3}\right\}\). If the line \(L\) also passes through the point \((1,1)\) and touches the circle \(17\left( x ^{2}+ y ^{2}\right)=16\), then the eccentricity of the ellipse \(\frac{x^{2}}{5}+\frac{y^{2}}{b^{2}}=1\) is.JEE Mains 2022 Hard
- If the angle of intersection at a point where the two circles with radii \(5\, cm\) and \(12\, cm\) intersect is \(90^o\), then the length (in \(cm\)) of their common chord isJEE Mains 2019 Hard
- If the vector \(\vec b = 3\hat j + 4\hat k\) is written as the sum of a vector \({\vec {b_1}}\) , parallel to \(\vec a = \hat i + \hat j\) and a vector \({\vec {b_2}}\) , perpendicular to \(\vec a\) , then \({\vec {b_1}} \times {\vec {b_2}}\) is equal toJEE Mains 2017 Hard
- A plane \(P\) meets the coordinate axes at \(A, B\) and \(C\) respectively. The centroid of \(\Delta ABC\) is given to be \((1,1,2)\) . Then the equation of the line through this centroid and perpendicular to the plane \(P\) isJEE Mains 2020 Hard
- Let \(y=y(x)\) be the solution curve of the differential equation \(\frac{d y}{d x}=\frac{y}{x}\left(1+x y^2\left(1+\log _e x\right)\right)\) \(x > 0, y(1)=3\). Then \(\frac{y^2(x)}{9}\) is equal to :JEE Mains 2023 Hard
- Let the normal at a point \(P\) on the curve \(\mathrm{y}^{2}-3 \mathrm{x}^{2}+\mathrm{y}+10=0\) intersect the \(\mathrm{y}\) -axis at \(\left(0, \frac{3}{2}\right) .\) If \(\mathrm{m}\) is the slope of the tangent at \(\mathrm{P}\) to the curve, then \(|\mathrm{m}|\) is equal toJEE Mains 2020 Hard