Arithmetic Mean

Q.

A number is the reciprocal of the other. If the arithmetic mean of the two numbers be $\frac{13}{12}$, then the numbers are

1. $\frac{1}{4},\frac{4}{1}$

2. $\frac{3}{4},\frac{4}{3}$

3. $\frac{2}{5},\frac{5}{2}$

4. $\frac{3}{2},\frac{2}{3}$

Q.

If three positive real numbers a, b, c are in A.P., with abc=4, then the minimum value of b is

1. 3

2. 4^1/3

3. 2

4. 1/2

Q.

The G.M of the roots of the equation $x^2-18x+9=0$ is

1. $3$

2. $4$

3. $2$

4. $1$

Q.

If 8 arithmetic means are placed between 2 and 17 then the 5th arithmetic mean will be:

1. 61/3

2. 76/3

3. 31/3

4. 106/3

Q. If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are .

Q. y=[2x-1] = 3[x-6]. Find the possible values of [3x+y].

Q. A number is the reciprocal of the other. If the arithmetic mean of the two numbers be $\frac{13}{12},$ then the numbers are

1. $\frac{3}{2},\frac{2}{3}$
2. $\frac{1}{4},\frac{4}{1}$
3. $\frac{3}{4},\frac{4}{3}$
4. $\frac{2}{5},\frac{5}{2}$

Q. 16. If the mean of x-5y, x-3y, x-y, x+y, x+3y, x+5y is 12, then the value of x is

Q.

The arithmetic mean of a and b is $\frac{a^n+b^n}{a^{n-1}+b^{n-1}}$. The value of n is

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

Q.

The first negative term of the A.P.
62, 57, 52.... is the

1. 10 th term

2. 14 th term

3. 18 th term

4. 12 th term

Q. IF THIRD TERM OF AN HP IS 3 AND TENTH TERM IS 10, WHICH TERM OF THE HP IS NOT DEFINED A:12TH B:13TH C:15TH D:16TH

Q. If is the A.M. between a and b , then find the value of n .

Q. find the mean of first six even numbers

Q. 13. If xyz+xy+yz+xz+x+y+z=384 where x, y, z are positive integers then find value of x+y+z

Q. If $\underset{x\to a}{\lim }\frac{x^9-a^9}{x-a}=9,$ find all possible values of a.

Q. The value of ${\cos }^4\mathrm{\theta }+{\sin }^4\mathrm{\theta }-6{\cos }^2\mathrm{\theta }{\sin }^2\mathrm{\theta }$
(a) $\cos 2\mathrm{\theta }$
(b) $\sin 2\mathrm{\theta }$
(c) $\cos 4\mathrm{\theta }$
(d) none of these

Q. 120.Solve the equation :- tan mx=cot nx

Q. If $\mathrm{cosec}x+\cot x=\frac{11}{2}$, then tan x =
(a) $\frac{21}{22}$

(b) $\frac{15}{16}$

(c) $\frac{44}{117}$

(d) $\frac{117}{44}$

Q. Sum of 3 consecutive terms in AP is 12 and their product is 60, then sum of their squares is

स.श्रे. में 3 क्रमागत पदों का योगफल 12 है तथा इनका गुणनफल 60 है, तब इनके वर्गों का योगफल है

1. 55
2. 50
3. 60
4. 45

Q. If $x,|x+1|,|x-1|$ are first three terms of an A.P. then the sum of its first $20$ terms is

1. $180$
2. $190$
3. $350$
4. $360$

Q. If $\frac{1}{2(y-a)}$ is the arithmetic mean of $\frac{1}{y-x}$ and $\frac{1}{y-z}$ where $a,x,y,z\in R$, then $x-a,y-a$ and $z-a$ are in

1. A.P.
2. G.P.
3. A.G.P.
4. H.P.

Q.

The equation $a{x}^2+bx+c=0$, where a, b, c are the sides of a $△ABC$, and the equation $x^2+\sqrt{2}x+1=0$ have a common root, the measure of $\angle C$ is

1. 90°

2. 45°

3. 60°

4. None of these

Q. find †an x sec^2x dx

Q. If tan θ + sec θ = $\sqrt{3}$, 0<θ<π, then θ is equal to
(a) $\frac{5\mathrm{\pi }}{6}$
(b) $\frac{2\mathrm{\pi }}{3}$
(c) $\frac{\mathrm{\pi }}{6}$
(d) $\frac{\mathrm{\pi }}{3}$

Q. The arithmetic mean of six numbers is $\mathrm{20.5.}$ If two numbers are added to the progression, then the new arithmetic mean is $\mathrm{17.5.}$ If their difference is $3,$ then the two numbers are

1. $-7$ and $10$
2. $6$ and $10$
3. $8$ and $11$
4. $7$ and $10$

Q. Prove the following identities (1-17)

$\frac{{\tan }^3\mathrm{\theta }}{1+{\tan }^2\mathrm{\theta }}+\frac{{\cot }^3\mathrm{\theta }}{1+{\cot }^2\mathrm{\theta }}=\frac{1-2{\sin }^2\mathrm{\theta }{\cos }^2\mathrm{\theta }}{\sin \mathrm{\theta }\cos \mathrm{\theta }}$

Q. If $A_1,A_2$ be two arithmetic means between $\frac{1}{3}$ and $\frac{1}{24},$ then their values are

1. $\frac{7}{72},\frac{5}{36}$
2. $\frac{17}{72},\frac{5}{36}$
3. $\frac{7}{36},\frac{5}{72}$
4. $\frac{5}{72},\frac{17}{72}$

Q.

If a, b, c be positive, then minimum value of $\frac{b+c}{a}$ + $\frac{c+a}{b}$ + $\frac{a+b}{c}$ is __

Q. Let a, b, c be positive integers such that $\frac{b}{a}$ is an integer. If a, b, c are in geometric progression and the arithmetic mean of a, b, c is b + 2, then the value of $\frac{a^2+a-14}{a+1}$ is___

Q. If $\tan \mathrm{\theta }=t$ then $\tan 2\mathrm{\theta }+\sec 2\mathrm{\theta }=$

(a) $\frac{1+t}{1-t}$

(b) $\frac{1-t}{1+t}$

(c) $\frac{2t}{1-t}$

(d) $\frac{2t}{1+t}$