Property 7

Q.

The multiplicative inverse of 7+5i is:

1. (7+5i)/74

2. (7-5i)/ 4

3. 7-5i

4. (7-5i)/74

Q.

If f is the identity function and g is the modulus function, then find f + g is

1. 

2. 

3. 

4. 

Q.

Area bounded by the curve $y=x{e}^{x^2}$ x - axis and the ordinates x = 0, x = a

1. $\frac{e^{a^2}+1}{2}sq.unit$
2. $\frac{e^{a^2}-1}{2}sq.unit$
3. $e^{a^2}+1sq.unit$
4. $e^{a^2}-1sq.unit$

Q. consider a real valued function such that f(x+2)=-f(2-x) then prove that the value of integration of f(x) from -3 to 7 is equal to 0.

Q. 23. Prove that nth terms of an ap cannot be n²+1.Give justification

Q.

Area bounded by the curve y = log x, x - axis and the ordinates x = 1, x = 2 is [MP PET 2004]

1. log 4 sq. unit
2. (log 4 + 1)sq. unit
3. (log 4 - 1)sq. unit
   

4. None of these

Q. 15. If f(x)=x2 + ax+b be an integral funtion of the integral variable x then 1 a is an integer and b is arational fraction 2 a and b are integer 3 b is an integer and a is a rational fraction 4 a and b are rational fraction

Q. If y=X sinx² then the value of Dy/DX is

Q. If $\sin x=\frac{a^2-b^2}{a^2+b^2}$, then the values of tan x, sec x and cosec x

Q.

When sinθ + cosθ = 1, then the value of sin2θ is

1. -1

2. 2

3. 1

4. 0

Q.

sin (n+1)x cos(n+2)x-cos(n+1)x sin(n+2)x=

1. -sinx

2. sinx

3. cosx

4. -cos x

Q.

Express $(sin\theta +icos\theta {)}^5$ in Eulers form.

1. i.

2. i.

3. 

4. 

Q.

1. 2π

2. 3π

3. 4π

4. π

Q. Prove the following identities (1-16)
$\frac{{\sin }^{3}x+{\cos }^{3}x}{\sin x+\cos x}+\frac{{\sin }^{3}x-{\cos }^{3}x}{\sin x-\cos x}=2$

Q. If $x=\frac{2\sin x}{1+\cos x+\sin x}$, then prove that $\frac{1-\cos x+\sin x}{1+\sin \mathit{}x}$ is also equal to a.

Q. The number of values of satisfying the equation sin +sin5 =sin3 such that [0, , ]

Q. The value of $\tan x\sin \left(\frac{\pi }{2}+x\right)\cos \left(\frac{\pi }{2}-x\right)$
(a) 1
(b) $-1$
(c) $\frac{1}{2}\sin 2x$
(d) none of these.

Q. (1 +x²) cos x

Q. $\underset{x\to 0}{\lim }\frac{\sin 3x+7x}{4x+\sin 2x}$

Q. If sin x + sin² x = 1, then write the value of cos¹² x + 3 cos¹⁰ x + 3 cos⁸ x + cos⁶ x.

Q. Prove that:
$\frac{\sin x+\sin 2x}{1+\cos x+\cos 2x}=\tan x$

Q. sin x – i cos 2x and cos x + i sin 2x are Conjugate to each other for

Q. sin x – i cos 2x and cos x + i sin 2x are Conjugate to each other for

Q. If cot (α + β) = 0, then write the value of sin (α + 2β).

Q. If sin x= cos 11x then the value of tan9x+cot 9x is equal to

Q.

1. 1

2. 

3. (log 2) (log 5)

4. log 2 + log 5

Q. If $f\left(x\right)=\log \left(\frac{1+x}{1-x}\right)\mathrm{and}g\left(x\right)=\frac{3x+x^3}{1+3x^2}$, then f(g(x)) is equal to
(a) f(3x)
(b) {f(x)}³
(c) 3f(x)
(d) −f(x)

Q.

Area under the curve $y=\sqrt{3x+4}$between x=0 and x=4, is

1. $\frac{56}{9}sq.unit$

2. $\frac{64}{9}sq.unit$

3. 8 sq. unit

4. None of these

Q. $\underset{x\to a}{\lim }\frac{a\sin x-x\sin a}{a{x}^2-x{a}^2}$

Q. sin x cos x