Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
JEE Main 201325 AprilOnline
Exam
JEE Main
Year
2013
Date
25 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2013 · 25 April · Online · Mathematics · Straight Lines

Let x ∈(0,1) . The set of all x such that ^ -1 x> ^ -1 x , is the...

Let x∈(0,1)x \in(0,1). The set of all xx such that sin⁡−1x>cos⁡−1x\sin ^{-1} x>\cos ^{-1} x, is the interval:

Options

  1. A(12,12)\left(\frac{1}{2}, \frac{1}{\sqrt{2}}\right)
  2. B(12,1)\left(\frac{1}{\sqrt{2}}, 1\right)
  3. C(0,1)(0,1)
  4. D(0,32)\left(0, \frac{\sqrt{3}}{2}\right)

Correct answer

B. (12,1)\left(\frac{1}{\sqrt{2}}, 1\right)

Step-by-step solution

Given sin⁡−1x>cos⁡−1x\sin ^{-1} x \gt \cos ^{-1} x where x∈(0,1)x \in(0,1)⇒sin⁡−1x>π2−sin⁡−1x⇒2sin⁡−1x>π2⇒sin⁡−1x>π4⇒x>sin⁡π4\Rightarrowx>12\begin{aligned}&\Rightarrow \sin ^{-1} x>\frac{\pi}{2}-\sin ^{-1}x \\ &\Rightarrow 2 \sin ^{-1} x>\frac{\pi}{2} \Rightarrow \sin ^{-1}x>\frac{\pi}{4}\\ &\Rightarrow x>\sin \frac{\pi}{4} \Rightarrowx>\frac{1}{\sqrt{2}} \end{aligned}$MaximumvalueofMaximum value of\sin ^{-1} xisis\frac{\pi}{2}So,maximumvalueofSo, maximum value ofxis1.So,is 1 . So,x \in \left(\frac{1}{\sqrt{2}},$1\right)
Practice Straight Lines on Quantrex Academy →

More from Straight Lines

If a straight line drawn through the point of intersection of the lines 4x+3y-1=0 and… JEE Main 2026From the point (-1, -1) , two rays are sent making angles of 45° with the line x + y = 0… JEE Main 2026In an equilateral triangle PQR , let the vertex P be at (3, 5) and the side QR be along… JEE Main 2026Let P(3 α, 2 α) , α ≠ 0 , be a point on the ellipse (x^2)/(9)+(y^2)/(4)=1 , Q be a point… JEE Main 2026Let A,B be points on the two half-lines x- 3 |y|=α , α>0 at a distance of α from their… JEE Main 2026Let the line L_1 : x + 3 = 0 intersect the lines L_2 : x - y = 0 and L_3 : 3x + y = 0 at… JEE Main 2026Let the vertex A of a triangle ABC be (1, 2) , and the mid-point of the side AB be (5… JEE Main 2026Let the mid points of the sides of a triangle ABC be ((5)/(2), 7) , ((5)/(2), 3) and (4… JEE Main 2026Let ABC be an equilateral triangle with orthocenter at the origin and the side BC on the… JEE Main 2026Let the angles made with the positive x -axis by two straight lines drawn from the point… JEE Main 2026Let A(1,0), B(2,-1) and C((7)/(3), (4)/(3)) be three points. If the equation of the… JEE Main 2026Let A(1,2) and C(-3,-6) be two diagonally opposite vertices of a rhombus, whose sides AD… JEE Main 2026A rectangle is formed by the lines x=0, y=0, x=3 and y=4 . Let the line L be… JEE Main 2026Among the statements (S 1) : If A(5,-1) and B(-2,3) are two vertices of a triangle, whose… JEE Main 2026Let a point A lie between the parallel lines L_ 1 and L_ 2 such that its distances from… JEE Main 2026A line passing through the point P(a, θ) makes an acute angle α with the positive x… JEE Main 2025 Full Straight Lines list Straight Lines JEE Maths PYQsJEE Mathematics PYQs All JEE Main PYQs