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This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\left|2x-1\right|sinx\\ Clearly,f\left(x\right)isnotdifferentiableatx=\frac{1}{2}\\ R.H.L.=f^{\text{'}}\left(\frac{1}{2}\right)=\underset{h\to 0}{lim}\frac{f\left(\frac{1}{2}+h\right)-f\left(\frac{1}{2}\right)}{h}\\ =\underset{h\to 0}{lim}\frac{\left|2\left(\frac{1}{2}+h\right)-1\right|sin\left(\frac{1}{2}+h\right)-0}{h}\\ =\underset{h\to 0}{lim}\frac{\left|2h\right|sin\left(\frac{1+2h}{2}\right)}{h}=2sin\left(\frac{1}{2}\right)\\ Also,L.H.L.=f^{\text{'}}\left(\frac{1}{2}\right)=\underset{h\to 0}{lim}\frac{f\left(\frac{1}{2}-h\right)-f\left(\frac{1}{2}\right)}{-h}\\ =\underset{h\to 0}{lim}\frac{\left|2\left(\frac{1}{2}-h\right)-1\right|\left[-sin\left(\frac{1}{2}-h\right)\right]-0}{-h}\\ =\underset{h\to 0}{lim}\frac{\left|-2h\right|\left[-sin\left(\frac{1}{2}-h\right)\right]}{-h}=-2sin\left(\frac{1}{2}\right)\\ \therefore L.H.L.\ne R.H.L.\\ So,thegivenfunctionf\left(x\right)isnotdifferentiableatx=\frac{1}{2}.\\ \therefore f\left(x\right)isdifferentiableinR-\left\{\frac{1}{2}\right\}\\ Hence,thecorrectoptionis\left(b\right)\end{array}$

Yes,  BCom is offered at Takshashila University for students enthusiastic about the field of Commerce. Students who are willing to take admission can check the table below to know the key highlights:

Note: The above information has been sourced from various sources. Hence, it is indicative.

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhatf\left(x\right)=\frac{4-x^2}{4x-x^3}\\ Fordiscontinuousfunction\\ \Rightarrow 4x-x^3=0\\ \Rightarrow 4\left(x-x^2\right)=0\\ \Rightarrow x\left(2-x\right)\left(2+x\right)=0\\ \Rightarrow x=0,x=2,x=-2\\ Hence,thegivenfuctionisdiscontinuousexactlyatthreepoints.\\ Hence,thecorrectoptionis\left(c\right)\end{array}$

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Weknowthatthealgebraicpolynomialsarecontinuousfunctionseverywhere.\\ \therefore f\left(x\right)+g\left(x\right)iscontinuous\left[\begin{array}{l}?Sum,differenceandproductoftwocontinuous\\ functionsisalsocontinuous\end{array}\right]\\ f\left(x\right)-g\left(x\right)iscontinuous\\ f\left(x\right).g\left(x\right)iscontinuous\\ \frac{g\left(x\right)}{f\left(x\right)}isonlycontinuousifg\left(x\right)\ne 0\\ \therefore \frac{f\left(x\right)}{g\left(x\right)}=\frac{2x}{\frac{x^2}{2}+1}=\frac{4x}{x^2+2}\\ Here,\frac{g\left(x\right)}{f\left(x\right)}=\frac{\frac{x^2}{2}+1}{2x}=\frac{x^2+2}{4x}whichisdiscontinuousatx=0.\\ Hence,thecorrectoptionis\left(d\right)\end{array}$

The total tuition fee for the BS-MS course at IISER Kolkata is INR 4.4 lakh. On the other hand, the total tuition fee for the BS-MS course at IISER Pune is INR 3.6 lakh. Therefore, it can be clearly seen that the tuition fee for IISER Pune is more affordable than IISER Kolkata. Moreover, fees are one of the components that candidates can consider while comparing the IISERs. other components can also be counted while comparing the institutions, such as placement packages, seats, accreditation, affiliation, etc. 

ASU has four campuses located throughout metropolitan Phoenix, as well as locations around the state, country, and world. The four Metro Phoenix campuses are Tempe Campus, West Valley Campus, Downtown Phoenix Campus, and Polytechnic Campus. The Tempe Campus is the original campus of ASU. It is also the largest campus of ASU. The campus size of this university is 2,030 acres.

For international students, ASU base tuition fee for UG courses is INR 35.8 lakh. Students working towards the ASU BS is Computer Science Course will learn to solve technical problems requiring creative and critical thinking in traditional and innovative Computer Science applications. The other fees that an UG student has to pay are given below:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l}Giventhaty=2x^2-5x+3\\ Letf\left(x\right)=2x^2-5x+3\\ \left(i\right)Beinganpolynomial,f\left(x\right)iscontinuousin\left[1,2\right].\\ \left(ii\right)f^{\text{'}}\left(x\right)=4x-5whichexistsin\left(1,2\right).\\ Hence,bymeanvaluetheorem,theremustexista\in \left(1,2\right)\\ A\left(1,0\right)andB\left(2,1\right)\\ \therefore f^{\text{'}}\left(c\right)=\frac{f\left(b\right)-f\left(a\right)}{b-a}\\ \Rightarrow 4c-5=\frac{\left(8-10+3\right)-\left(2-5+3\right)}{2-1}\\ \Rightarrow 4c-5=\frac{1-0}{1}=1\Rightarrow 4c=5+1=6\\ \therefore c=\frac{6}{4}=\frac{3}{2}\\ \therefore y=2{\left(\frac{3}{2}\right)}^2-5\left(\frac{3}{2}\right)+3\\ \Rightarrow =2\times \frac{9}{4}-\frac{15}{2}+3=\frac{9}{2}-\frac{15}{2}+3\\ \Rightarrow =\frac{9-15+6}{2}=0\\ Hence,\left(\frac{3}{2},0\right)isthe\\ A\left(1,0\right)andB\left(2,1\right).\end{array}$

ASU MS in Engineering is a STEM-designated course. To take admission to this course, the requirements are given below:

• Bachelor's degree with a minimum of 3.0 GPA
• An English language proficiency score: IELTS score (6.5) / PTE score (60) / TOEFL score (80) / Duolingo (105)
• An online application
• Academic transcripts
• No GRE requirement
• A professional resume
• Personal statement

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol:

This is a Short Answer Type Questions as classified in NCERT Exemplar

Sol: