KCET · Maths · Functions
If \(f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x\), where \([x]=\) greatest integer \(\leq x\), then which of the following is not true?
- A \(f(0)=0\)
- B \(f\left(\frac{\pi}{2}\right)=1\)
- C \(\mathrm{f}\left(\frac{\pi}{4}\right)=1+\frac{1}{\sqrt{2}}\)
- D \(f(\pi)=-1\)
Answer & Solution
Correct Answer
(D) \(f(\pi)=-1\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=\sin \left[\pi^2\right] x-\sin \left[-\pi^2\right] x \\ & =\sin 9 x-\sin (-10) x \\ & =\sin 9 x+\sin 10 x \\ & f(\pi)=\sin 9 \pi+\sin 10 \pi=0\end{aligned}\)
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
- If \(A M\) and \(G M\) of roots of a quadratic equation are 5 and 4 , respectively, then the quadratic equation isKCET 2024 Easy
- If \(\quad 2 x^{2}+2 y^{2}+4 x+5 y+1=0 \quad\) and \(3 x^{2}+3 y^{2}+6 x-7 y+3 k=0 \quad\) are orthogonal, then value of \(k\) isKCET 2011 Hard
- If \(P(n): 2^{n} < n\) ! Then the smallest positive integer for which \(P(n)\) is true ifKCET 2020 Easy
- \( \int \frac{(x+3) e^{x}}{(x+4)^{2}} d x \) is eqal toKCET 2017 Medium
- If \(\sin ^{-1} a\) is the acute angle between the curves \(x^{2}+y^{2}=4 x\) and \(x^{2}+y^{2}=8\) at \((2,2)\), then \(a\) is equal toKCET 2013 Hard
- The distance of the point \( (1,2,1) \) from the line \( \frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2} \) isKCET 2019 Easy
More PYQs from KCET
- If \(A=\left[\begin{array}{cc}\alpha & 2 \\ 2 & \alpha\end{array}\right]\) and \(\left|A^{3}\right|=125\), then \(\alpha\) is equal toKCET 2013 Easy
- A transformer works on the principle ofKCET 2011 Easy
- In a face centred cubic arrangement of \( A \) and \( B \) atoms in which 'A' atoms are at the corners of
the unit cell and 'B' atoms are at the face centers. One of the 'A' atom is missing from one
corner in unit cell.the simplest formula of the compound isKCET 2017 Easy - Which of the following is not true for oxidation?KCET 2021 Easy
- All components of the electromagnetic spectrum in vacuum have the sameKCET 2007 Easy
- The torque acting on a magnetic dipole placed in uniform magnetic field is zero, when the angle between the dipole axis and the magnetic field isKCET 2023 Easy