Higher Order Derivatives

Q. 17 Let the function f: RR be defined by fix)= 2x + sinx, x e R, then f is(2) One-one but not ontopiY One-one and onto(4) Neither one-one nor onto(3) Onto but not one-one

Q. 10. If y =log10x, than the value dy/dx is

Q.

In a $\angle ABC,$ if $\angle A={45}^{\circ },\angle B={60}^{\circ },and\angle C={75}^{\circ },$ find the ratio of its sides.

Q.

Prove that:

(sin 3x + sin x) sin x + (cos 3x-cos x) cos x = 0

Q.

Prove the following:
cot 4x ( sin 5x + sin 3x) = cot x (sin 5x- sin 3x)

Q. 40. Consider f: R → R & f(x) = x3 + x2 + ax + 4 be bijective, then interval for a is?

Q. 2x+3xy=0

Q.

Number of values of x which satisfies the relation $|x-1|$ + $|x-2|$ =1

1. 1

2. 2

3. 0

4. Infinite

Q. The sum of x and y intercepts cut off by the circle x^2+y^2+4x-8y-2=0 is:

Q. If $y={\left(x^2-1\right)}^m,$ then the value of (2m)th differential coefficient of y is

1. m
2. (2m)!
3. 2m
4. m!

Q.

$a+ar+a{r}^2+\cdots +a{r}^{n-1}=\frac{a(r^n-1)}{r-1}$

Q. if a = 1 + \sqrt3 b=2 and c=\sqrt{2 } then the measure of \angle B i

Q. 79. simply : ilog (x-i/x+i).

Q. 19. A={(x, y):x, yI , x≥0, y≥0 and 4x+5y≤40} B={(x, y):x, yI , x≥0, y≥0 and 5x+4y≤40

Q. 6.If y =log10x, than the value dy/dx is

Q. This section contains 1 Assertion-Reason type question, which has 4 choices (a), (b), (c) and (d) out of which ONLY ONE is correct.

इस खण्ड में 1 कथन-कारण प्रकार का प्रश्न है, जिसमें 4 विकल्प (a), (b), (c) तथा (d) दिये गये हैं, जिनमें से केवल एक सही है।

A : Let f(x) = e^x and g(x) = e^2x are two functions defined on R then f(x).g(x) be an increasing function on R.

A : माना f(x) = e^x तथा g(x) = e^2x दो फलन हैं, जो R पर परिभाषित हैं, तब R पर f(x).g(x) एक वर्धमान फलन है।

R : Multiplication of two increasing functions is an increasing function.

R : दो वर्धमान फलनों का गुणनफल एक वर्धमान फलन है।

1. Both (A) and (R) are true and (R) is the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं तथा (R), (A) का सही स्पष्टीकरण है
   
2. Both (A) and (R) are true but (R) is not the correct explanation of (A)
   
   (A) तथा (R) दोनों सही हैं लेकिन (R), (A) का सही स्पष्टीकरण नहीं है
3. (A) is true but (R) is false
   
   (A) सही है लेकिन (R) गलत है
4. (A) is false but (R) is true
   
   (A) गलत है लेकिन (R) सही है

Q. 23. Find range of fun ction f(x)=1/(2x-3)(x+1)

Q. if z+\sqrt2\vert z+1\vert+i=o, where i=\sqrt{-1}, then \vert Re(z)+Im(z)\vert is

Q. 3. If \sqrt3cosec x=-2, find X.

Q. if y=log x base 10 then the value ofdy/dx is

Q. If $e^y+xy=e,$ the ordered pair $(\frac{dy}{dx},\frac{d^{2}y}{d{x}^2})$ at $x=0$ is equal to :

1. $(-\frac{1}{e},\frac{1}{e^2})$
2. $(\frac{1}{e},-\frac{1}{e^2})$
   
3. $(\frac{1}{e},\frac{1}{e^2})$
4. $(-\frac{1}{e},-\frac{1}{e^2})$

Q. Find the derivative of the following function:
f(x)= $(x+secx)(x-tanx)$

Q. A polynomial $p\left(x\right)$ of second degree which will vanish at $x=3$ and $x=5$ and will have value of $4$ when $x=2$, is in the form of $a{x}^2+bx+c$. The value of $[a+b+c]$ is
(where $[\cdot ]$ deontes the greatest integer function).

Q. If $y=a\cos \left(\ln x\right)+b\sin \left(\ln x\right)$, then $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}$ is equal to

1. \N
2. $y$
3. $-y$
4. none of these

Q.

$\sqrt{2+\sqrt{2+2cos4\theta }}$ =

1. 

2. 

3. 

4. 

Q. Let $f:R\to R$ be a function such that $f\left(x\right)=x^3+x^2{f}^{\prime }\left(1\right)+x{f}^{\prime \prime }\left(2\right)+f^{\prime \prime \prime }\left(3\right),x\in R$. Then $f\left(2\right)$ equals :

1. $-4$
2. $30$
3. $8$
4. $-2$

Q. 13. If y=cos6x+6cos4x+15cos2x+10/cos5x+5cos3x+10cosx, then dy/dx is

Q.

How many roots, real or complex, does the polynomial $7+5{\mathrm{x}}^4-3{\mathrm{x}}^2$ have in all?

Q. If $y=sin\left(sinx\right),then\frac{d^{2}y}{d{x}^2}+tanx\frac{dy}{dx}+yco{s}^{2}x$ will be equal to

1. 1
2. -1
3. 2
4. \N

Q. If $f:R\to R$ and $f\left(x\right)$ is a polynomial function of degree eleven and $f\left(x\right)=0$ has all real and distinct roots. Then the equation $\left(f^{\prime }\right(x){)}^2-f(x\left)f^{\prime \prime }\right(x)=0$ has

1. no real roots
2. 10 real roots
3. 11 real roots
4. 21 real roots