Factorization Method Form to Remove Indeterminate Form

Q. If G(x) = - $\sqrt{25-x^2}$ then $\underset{x\to 1}{lim}\frac{G\left(x\right)-G\left(1\right)}{x-1}$ has the value

1. 
2. 
3. 
4. 

Q.

If $A+B+C=\pi ,$then$\cos 2A+\cos 2B+\cos 2C$ is

1. $1+4\cos A\cos B\sin C$

2. $-1+4\sin A\sin B\cos C$

3. $-1–4\cos A\cos B\cos C$

4. None of these

Q. 79. Sin A=3/5 and cos B=9/41, A is greater than 0 and less than 90 , then b is greater than -90 and less than 0 findsin A-B

Q.

ABC is an isosceles triangle inscribed in a circle of radius r. If AB=AC and h is altitude from A to BC, then $\underset{h\to 0}{lim}\frac{△}{p^3}$ is equal to (where $△$ is the area and P is the perimeter of the triangle ABC)

1. 1/32r

2. 1/64r

3. 1/128r

4. 1/216r

Q.

$li{m}_{x\to a}$$\frac{\left(\sqrt{3x-a}\right)-\left(\sqrt{x+a}\right)}{x-a}$ =

1. 

2. 

3. 2a

4. 

Q.

$\underset{x\to \infty }{lim}(\sqrt{(x^2+8x+3)}-\sqrt{(x^2+4x+3)})=$

Q. 47 Find minimum value of sinA+sinB+sinC if A+B+C=

Q.

If x is very large compared to y, then the value of k if $\sqrt{\frac{x}{x+y}}\sqrt{\frac{x}{x-y}}$ = $1+\frac{y^2}{k{x}^2}$

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Q.

If $f\left(x\right)=3-x$, where $-4\le x\le 4$, then the domain of $lo{g}_e\left[f\right(x\left)\right]$ is:

1. $\left[-4,4\right]$

2. $(-\infty ,3]$

3. $\left(-\infty ,3\right)$

4. $[-4,3)$

Q. If $z=(\sqrt{2}-\sqrt{-3})$, find Re(z), Im(z), $\overline{z}$ and |z|.

Q.

Evaluate $\underset{x\to 0}{lim}\frac{(\sqrt{1+3x}-\sqrt{1-3x})}{x}$

Q. Let $[A{]}_{2\times 2}$ and $[B{]}_{3\times 3}$ be the two matrices such that $det\left(A\right)=2$ and $det\left(B\right)=3.$ Then the value of $det(det(A)\cdot B)+det(det(B)\cdot A)$ is

1. $48$
2. $24$
3. $42$
4. $20$

Q. 2.If tax=(siny-cosy)/(siny+cosy), then prove that: siny+cosy=2cosx

Q. lim x->0 sin(alpha x)-sin(beta x)/e^(alpha x)-e^ (beta x)

Q.

If $f\left(0\right)=1,f\left(1\right)=5$ and $f\left(2\right)=11$$4a+2b+1=11$, then the equation of polynomial of degree two is

1. $x^2+1=0$

2. $x^2+3x+1=0$

3. $x^2-2x+1=0$

4. None of these

Q.

Evaluate the following limit:
$\underset{x\to 1}{\text{lim}}\frac{a{x}^2+bx+c}{c{x}^2+bx+a},a+b+c\ne 0$

Q. Sin 36 degrees + cos 36 degrees = square root of 2 cos 9 degrees?

Q. 133.If A+B+C= Pi, cotx = cotA + cotB + cotC. Then prove that sin (x-A) sin (x-B) sin (x-C) = sin(cube)

Q. 29.Sin2 (51-x) +sin (39 + x) =

Q. $\underset{x\to \frac{\pi }{4}}{lim}\frac{{\cot }^{3}x-\tan x}{\cos (x+\frac{\pi }{4})}$ is:

1. $4\sqrt{2}$
2. $4$
3. $8\sqrt{2}$
4. $8$

Q. If $\sin \mathrm{A}=\frac{4}{5}$and $\cos \mathrm{B}=\frac{5}{13}$, where 0 < A, $\mathrm{B}<\frac{\mathrm{\pi }}{2}$, find the values of the following:

(i) sin (A + B)
(ii) cos (A + B)
(iii) sin (A − B)
(iv) cos (A − B)

Q.

$\underset{x\to \infty }{lim}(\sqrt{x^2+x}-x)$ equals

1. 

2. 

3. 

4. 

Q.

Evaluate $\underset{x\to 2}{lim}\left\{\frac{(x^2-4)}{\sqrt{3x-2}-\sqrt{x+2}}\right\}$

Q. The value of ${\sin }^2\frac{5\mathrm{\pi }}{12}-{\sin }^2\frac{\mathrm{\pi }}{12}$ is
(a) $\frac{1}{2}$
(b) $\frac{\sqrt{3}}{2}$
(c) 1
(d) 0

Q. $\underset{x\to 0}{\lim }\frac{8}{x^8}\left\{1-\cos \frac{x^2}{2}-\cos \frac{x^2}{4}+\cos \frac{x^2}{2}\cos \frac{x^2}{4}\right\}$ is equal to

(a) $\frac{1}{16}$

(b) $-\frac{1}{16}$

(c) $\frac{1}{32}$

(d) $-\frac{1}{32}$

Q.

Find the domain of $f\left(x\right)=\frac{1}{\sqrt{\frac{1}{\sqrt{x+|x|}}}}$

Q.

The value of $\underset{x\to \infty }{lim}\sqrt{x}(\sqrt{x+c}-\sqrt{x})is:$

1. c/3

2. c/4

3. c

4. c/2

Q. Sin(17π/3) is equal to

Q. In ∆ABC, if a = 18, b = 24 and c = 30 and ∠c = 90°, find sin A, sin B and sin C.

Q. $\underset{x\to 0}{\lim }\frac{2\sin x^{\circ }-\sin 2x^{\circ }}{x^3}$