Sets, Relations & Functions · NDA previous year questions

2016 39 questions

1. Q642016 · 17 Apr 2016

   For the next four (4) items that follow : Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $$f(x)=x^3+x^2{f}^{\prime }(1)+x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$$ for $x\in \mathbb{R}$. What is $f(1)$ equal to?

   1. A.-2
   2. B.-1
   3. C.0
   4. D.4
   Show answer

   Answer: D

2. Q652016 · 17 Apr 2016

   For the next four (4) items that follow : Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $$f(x)=x^3+x^2{f}^{\prime }(1)+x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$$ for $x\in \mathbb{R}$. What is $f^{\prime }(1)$ equal to?

   1. A.-6
   2. B.-5
   3. C.1
   4. D.0
   Show answer

   Answer: B

3. Q662016 · 17 Apr 2016

   For the next four (4) items that follow : Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $$f(x)=x^3+x^2{f}^{\prime }(1)+x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$$ for $x\in \mathbb{R}$. What is $f^{\prime \prime \prime }(10)$ equal to?

   1. A.1
   2. B.5
   3. C.6
   4. D.8
   Show answer

   Answer: C

4. Q672016 · 17 Apr 2016

   For the next two (2) items that follow: Consider the function $$f(x)=|x^2-5x+6|$$ What is $f^{\prime }(4)$ equal to?

   1. A.$-4$
   2. B.$-3$
   3. C.3
   4. D.2
   Show answer

   Answer: C

5. Q682016 · 17 Apr 2016

   For the next two (2) items that follow: Consider the function $$f(x)=|x^2-5x+6|$$ What is $f^{\prime \prime }(2.5)$ equal to?

   1. A.$-3$
   2. B.$-2$
   3. C.0
   4. D.2
   Show answer

   Answer: B

6. Q712016 · 17 Apr 2016

   For the next two (2) items that follow : Consider the functions $f(x)=xg(x)$ and $g(x)=\left[\frac{1}{x}\right]$ where $[\cdot ]$ is the greatest integer function. What is ${\int }_{1/3}^{1/2}g(x)dx$ equal to?

   1. A.$\frac{1}{6}$
   2. B.$\frac{1}{3}$
   3. C.$\frac{5}{18}$
   4. D.$\frac{5}{36}$
   Show answer

   Answer: B

7. Q722016 · 17 Apr 2016

   For the next two (2) items that follow : Consider the functions $f(x)=xg(x)$ and $g(x)=\left[\frac{1}{x}\right]$ where $[\cdot ]$ is the greatest integer function. What is ${\int }_{1/3}^{1}f(x)dx$ equal to?

   1. A.$\frac{37}{72}$
   2. B.$\frac{2}{3}$
   3. C.$\frac{17}{72}$
   4. D.$\frac{37}{144}$
   Show answer

   Answer: A

8. Q752016 · 17 Apr 2016

   What is $${\int }_{-2}^{2}xdx-{\int }_{-2}^2[x]dx$$ equal to, where $[\cdot ]$ is the greatest integer function?

   1. A.0
   2. B.1
   3. C.2
   4. D.4
   Show answer

   Answer: C

9. Q762016 · 17 Apr 2016

   If $${\int }_{-2}^{5}f(x)dx=4\text{and}{\int }_0^5\{1+f(x)\}dx=7$$ then what is ${\int }_{-2}^{0}f(x)dx$ equal to?

   1. A.$-3$
   2. B.2
   3. C.3
   4. D.5
   Show answer

   Answer: B

10. Q772016 · 17 Apr 2016

    What is ${\int }_0^{4\pi }|\cos x|dx$ equal to?

    1. A.0
    2. B.2
    3. C.4
    4. D.8
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    Answer: D

11. Q1082016 · 17 Apr 2016
    Passage

    For the next two (2) items that follow : Consider the function

    What is the number of points of local minima of the function $f(x)$?

    1. A.None
    2. B.One
    3. C.Two
    4. D.Three
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    Answer: C

12. Q1092016 · 17 Apr 2016
    Passage

    For the next two (2) items that follow : Consider the function

    What is the number of points of local maxima of the function $f(x)$?

    1. A.None
    2. B.One
    3. C.Two
    4. D.Three
    Show answer

    Answer: B

13. Q1112016 · 17 Apr 2016

    For the next two (2) items that follow : Consider the curves $y=|x-1|$ and $|x|=2$ What is/are the point(s) of intersection of the curves?

    1. A.$(-2,3)$ only
    2. B.$(2,1)$ only
    3. C.$(-2,3)$ and $(2,1)$
    4. D.Neither $(-2,3)$ nor $(2,1)$
    Show answer

    Answer: C

14. Q1152016 · 17 Apr 2016

    For the next four (4) items that follow: Let $f:\mathbb{R}\to \mathbb{R}$ be a function such that $f(x)=x^3+x^2{f}^{\prime }(1)+x{f}^{\prime \prime }(2)+f^{\prime \prime \prime }(3)$ for $x\in \mathbb{R}$. Consider the following: 1. $f(2)=f(1)-f(0)$ 2. $f^{\prime \prime }(2)-2f^{\prime }(1)=12$ Which of the above is/are correct?

    1. A.1 only
    2. B.2 only
    3. C.Both 1 and 2
    4. D.Neither 1 nor 2
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    Answer: C