Comprehension
Consider an obtuse-angled triangle ABC in which the difference between the largest and the smallest angle is \(\frac{\pi}{2}\) and whose sides are in arithmetic progression. Suppose that the vertices of this triangle lie on a circle of radius 1.
Question: 1
Let a be the area of the triangle ABC. Then the value of (64a)2 is
Let a be the area of the triangle ABC. Then the value of (64a)2 is
Updated On: Mar 30, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 1007.99 - 1008.01
Solution and Explanation
Correct value is 1008.00
Was this answer helpful?
0
0
Question: 2
Then the inradius of the triangle ABC is ______.
Then the inradius of the triangle ABC is ______.
Updated On: Mar 30, 2024
Hide Solution
Verified By Collegedunia
Correct Answer: 0.24 - 0.26
Solution and Explanation
The inradius of the triangle ABC is 0.25.
Was this answer helpful?
0
0
Top Questions on introduction to three dimensional geometry
- Let
\[ f(x) = \begin{cases} x\left( \frac{\pi}{2} + x \right), & \text{if } x \geq 0 \\ x\left( \frac{\pi}{2} - x \right), & \text{if } x < 0 \end{cases} \]
Then \( f'(-4) \) is equal to:- KEAM - 2024
- Mathematics
- introduction to three dimensional geometry
If \( f'(x) = 4x\cos^2(x) \sin\left(\frac{x}{4}\right) \), then \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:
- KEAM - 2024
- Mathematics
- introduction to three dimensional geometry
- Let \[ f(x) = \frac{|5 - x|(x + 5)}{\tan(x - 5)} \quad {for} \quad x \neq 5. \] Then \[ \lim_{x \to 5} f(x) { is equal to:} \]
- KEAM - 2024
- Mathematics
- introduction to three dimensional geometry
Let \( f(x) = x \sin(x^4) \). Then \( f'(x) \) at \( x = \sqrt[4]{\pi} \) is equal to:
- KEAM - 2024
- Mathematics
- introduction to three dimensional geometry
- Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors. The angle between \( \vec{a} \) and \( \vec{b} \) is \( 30^\circ \), the angle between \( \vec{a} \) and \( \vec{b} + \vec{c} \) is \( 45^\circ \). If \( |\vec{b}| = \sqrt{6} \) and \( |\vec{c}| = 2\sqrt{2} \), then \( |\vec{b} + \vec{c}| \) is:
- KEAM - 2024
- Mathematics
- introduction to three dimensional geometry
View More Questions
Questions Asked in JEE Advanced exam
- A positive, singly ionized atom of mass number \( A_M \) is accelerated from rest by the voltage \( 192 \, \text{V} \). Thereafter, it enters a rectangular region of width \( w \) with magnetic field \( \vec{B}_0 = 0.1\hat{k} \, \text{T} \). The ion finally hits a detector at the distance \( x \) below its starting trajectory. Which of the following option(s) is(are) correct? \[ \text{(Given: Mass of neutron/proton = } \frac{5}{3} \times 10^{-27} \, \text{kg, charge of the electron = } 1.6 \times 10^{-19} \, \text{C).} \]
- JEE Advanced - 2024
- Electromagnetic Field (EMF)
- A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass \( m \) and radius \( r \) and is in a uniform vertical magnetic field \( B_0 \). When a current \( I \) is passed through the loop, the loop turns about the line PQ by an angle \( \theta \). The angle \( \theta \) is given by:
- JEE Advanced - 2024
- Electromagnetic Field (EMF)
- A region in the form of an equilateral triangle (in x-y plane) of height \( L \) has a uniform magnetic field \( \mathbf{B} \) pointing in the \( +z \)-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height \( L \), is placed in the x-y plane with its vertex \( P \) at \( x = 0 \) in the orientation shown in the figure. At \( t = 0 \), the loop starts entering the region of the magnetic field with a uniform velocity \( \mathbf{v} \) along the \( +x \)-direction. The plane of the loop and its orientation remain unchanged throughout its motion.
Which of the following graphs best depicts the variation of the induced emf (\( \mathcal{E} \)) in the loop as a function of the distance (\( x \)) starting from \( x = 0 \)?- JEE Advanced - 2024
- Radioactivity
- A table tennis ball has radius \( \frac{3}{2} \times 10^{-2} \, \text{m} \) and mass \( \frac{22}{7} \times 10^{-3} \, \text{kg} \). It is slowly pushed down into a swimming pool to a depth \( d = 0.7 \, \text{m} \) below the water surface and then released from rest. It emerges from the water surface at speed \( v \), without getting wet, and rises to a height \( H \). Which of the following option(s) is(are) correct?\(\text{(Given: } \pi = \frac{22}{7}, g = 10 \, \text{m/s}^2, \text{density of water} = 1 \times 10^3 \, \text{kg/m}^3, \text{viscosity of water} = 1 \times 10^{-3} \, \text{Pa.s).}\)
- JEE Advanced - 2024
- Radioactivity
- An infinitely long thin wire, having a uniform charge density per unit length of \(5 \, \text{nC/m}\), is passing through a spherical shell of radius \(1 \, \text{m}\), as shown in the figure. A \(10 \, \text{nC}\) charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points \(P\) and \(R\), in Volt, is ______. \[ \text{(Given: In SI units } \frac{1}{4\pi\epsilon_0} = 9 \times 10^9, \ln 2 = 0.7). \] Ignore the area pierced by the wire.
- JEE Advanced - 2024
- Radioactivity
View More Questions