Sets, Relations & Functions · NDA previous year questions

2024 29 questions

1. Q932024 · 21 Apr 2024

   Let $f(x)=|x-1|,g(x)=[x]$ and $h(x)=f(x)g(x)$ where [.] is greatest integer function. What is ${\int }_{-1}^{0}h(x)dx$ equal to?

   1. A.$-\frac{3}{2}$
   2. B.-1
   3. C.0
   4. D.$\frac{1}{2}$
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   Answer: A

2. Q942024 · 21 Apr 2024

   Let $f(x)=|x-1|,g(x)=[x]$ and $h(x)=f(x)g(x)$ where [.] is greatest integer function. What is ${\int }_0^{2}h(x)dx$ equal to?

   1. A.$-\frac{3}{2}$
   2. B.-1
   3. C.0
   4. D.$\frac{1}{2}$
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   Answer: D

3. Q952024 · 21 Apr 2024

   Let $\int \frac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha (x+1{)}^{\frac{3}{2}}+\beta (x-1{)}^{\frac{3}{2}}+c$ What is the value of $\alpha$?

   1. A.$\frac{1}{3}$
   2. B.$\frac{2}{3}$
   3. C.1
   4. D.$\frac{4}{3}$
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   Answer: A

4. Q962024 · 21 Apr 2024

   Let $\int \frac{dx}{\sqrt{x+1}-\sqrt{x-1}}=\alpha (x+1{)}^{\frac{3}{2}}+\beta (x-1{)}^{\frac{3}{2}}+c$ What is the value of $\beta$?

   1. A.$-\frac{2}{3}$
   2. B.$-\frac{1}{3}$
   3. C.$\frac{1}{3}$
   4. D.$\frac{2}{3}$
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   Answer: C