CUET UG 2022 | NTA | Maxima and Minima | Example and Solutions

Hi, friends today we are conducting a Mock Test on CUET 2022 - Mathematics preparation for Common University Entrance Test.

CUET (UG) 2022

Maxima and Minima 

Example and Solution  

1. $\small f(x)=x^2+xsinx+4cosx$ this function has it's minima at 

(a) $\small x=0$ (Ans) 

(b) $\small x=1$

(c)  $\small x>1$

(d)  $\small x-1$

2. $\small (x-a_1)^2+(x-a_2)^2+.....+(x-a_n)^2$ it has minima at x = ?

(a) A.M of $\small a_1,a_2,a_3,....a_n$ (Ans)

(b) G.M of $\small a_1,a_2,a_3,....a_n$

(c)  H.M of $\small a_1,a_2,a_3,....a_n$

(d)  None of these

3. Find the minima of this function $\small 4e^{2x}+9e^{-2x}$

(a) $\small 14$

(b) $\small 12$ (Ans)

(c)  $\small 10$

(d)  $\small 8$

4. If the function $\small f(x)$ is $\small x^3+\frac{1}{x^3}$,The maxima of this function is ___________ than/to minima.

(a) greater 

(b) lesser (Ans)

(c)  equal

(d)  None of this 

5. If $\small xy=4$, then the maxima and minima of $\small 4x+9y$ is (a,b).

(a) a=-34,b=34

(b) a=-b

(c)  a= 24, b=-24

(d)  (a) and (b) (Ans)

6. $\small a+(x-b)^{\frac{4}{3}}+(x-b)^{\frac{4}{3}}$ has minima at 

(a) $\small x=b$

(b) $\small x=0$

(c)  $\small x=0,b$

(d)  None of these 

7. $\small x^m(a-x)^n$ has maxima 

(a) $\small \frac{m^mn^na^{m+n}}{(m+n)^{m+n}}$

(b) 

$\small \frac{m^mn^na^{m-n}}{(m+n)^{m-n}}$

(c)  

$\small \frac{m^mn^na^{m\times n}}{(m+n)^{m\times n}}$

(d)  None of these

8. $\small sin(x)+cos(x)$ has maxima 

(a) $\small \frac{1}{\sqrt{2}}$

(b) $\small 1$

(c)  $\small 2$

(d)  $\small \sqrt{2}$

9. $\small f(x)=cos(x)$ has maxima at 

(a) $\small x=(2n+1)\pi$

(b) 

$\small x=2n\pi$

(c)  $\small x=(2n+\frac{1}{2})\pi$

(d)  $\small x=(2n-\frac{1}{2})\pi$

10. $\small y=5+|x-1|$ has minima at 

(a) 0

(b) 10

(c)  5

(d)  -5

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