Local Maxima

Q.

If $\frac{si{n}^{4}x}{2}+\frac{co{s}^{4}x}{3}=\frac{1}{5}$ , prove that $ta{n}^{2}x=\frac{2}{3}$

Q. ∫_{}^{}root x dx( upper limit=4 and lower limit=1)

Q.

Find the value of other five trigonometric functions in cos x = - $\frac{1}{2}$, x lies in third quadrant.

Q. If z1, z2, z3 are three non-zero complex number such that z3=(1-x)z1 + x z2, where x belong to R-{0}, then determine the curve on which the points z1, z2.z3 lies.

Q. 23. Find value of tan(π/16)=(\sqrt{}4+2\sqrt{}2)-(\sqrt{}2+1)

Q. How many non zero value of x and y for which the unit vectors 9^(x) i + α j + β k and 45^(y) i + γ j + δ k makes equal angle with x axis

Q. If }5\operatorname{cos}x+12\operatorname{sin}x=k, then number of integra } values of }k is } (1) 13 (2) 14 (3) 27 (4) 26

Q. The lateral edge of a regular hexagonal pyramid is 1 cm. If the volume is maximum, then its height is

1. $\frac{1}{\sqrt{3}}$
2. $\frac{6}{\sqrt{3}}$
3. $\frac{1}{6}$
4. $\frac{1}{3}$

Q. f, g, h are three function defined from R to R as follows:

(i) f(x) = x²
(ii) g(x) = sin x
(iii) h(x) = x² + 1

Find the range of each function.

Q. If $f\left(x\right)=max(y^2-2xy+1)$ for $0\le y\le 2,$ then the minimum value of $f\left(x\right)$ $\forall x\in R$ is

1. $1$
2. $2$
3. $0$
4. Can not be determined.

Q. 7. Range of f(x)=xsinx?

Q. Why is sq. Root sin square x always +ve but square root 25 is +5 or -5?

Q. Range of f(x)=(3)/(2-x^(2)) is (1) (-oo (3)/(2) (2) (-oo 0)uu (3)/(2) oo) (3) (-oo 0 uu (3)/(2) oo) (4) (-oo (2)/(3)

Q. The maximum value of the function $f\left(x\right)=3x^3-18x^2+27x-40$ on the set $S=\{x\in R:x^2+30\le 11x\}$ is :

1. $122$
2. $-122$
3. $222$
4. $-222$

Q. If $y=f\left(x\right)$ is a polynomial function and graph of $y=f^{\prime }\left(x\right)$ in interval $(1,8)$ is shown in figure below, then consider the following data in interval $(1,8)$

If $a$ = number of point(s) where $y=f\left(x\right)$ has maxima
$b$ = number of point(s) where $y=f\left(x\right)$ has minima
longest interval of $y=f\left(x\right)$ is decreasing is $(m,n)$ then value of $(m+n+a+b)$ is

Q. Find the cube root of -27 and show that the sum of cube toots is equal to zero

Q. A covered box of volume $72{\text{cm}}^3$ and the base sides in a ratio of $1:2$ is to be made. The length of all sides so that the total surface area is the least possible is

1. $6,3,4$
2. $8,4,3$
3. $2,4,9$
4. $3,6,2$

Q. The intervals of concavity for $f\left(x\right)=\frac{x}{(x-1)}$ is :

1. Concave up for $x\in (1,\infty )$
2. Convex : $(-\infty ,0)$
3. Concave down: $(0,1)\cup (1,\infty )$
   
4. Concave down for : $x\in (-\infty ,1)$

Q. 43. find the domainand range f(x)=-|x|

Q. Find the range of f(x) = 2-\vert x+2

Q. If $f\left(x\right)={\left({\sin }^{2}x-1\right)}^n,\mathrm{then}x=\frac{\pi }{2}$ is a point of

1. local maximum, if n is odd
2. local minimum, if n is odd
3. local maximum, if n is even
4. local minimum, if n is even

Q. ntRange of f(x) =cos (ksinx) is [-1, 1] then least positive integral value of k isn

Q.

Write the numerical coefficient of $a^3-8a^{2}b+6a{b}^2-4$