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The minimum value of f(x) = $|x-1|$ +$|x-2|$ + $|x-3|$

Draw the curve $\frac{2^x}{2^{\left[x\right]}}$. Where [.] denotes greatest integer function

If $ta{n}^{2}x+secx-a=0$ has alteast one solution, then $a\in$..........

$\underset{x\to 1}{lim}\frac{logx}{x-1}$

If z is a complex number of unit modulus and argument $\theta$, find arg $\left(\frac{1+z}{1+\overline{z}}\right)$

$Rangeofthefunctionf\left(x\right)=x^2+\frac{1}{x^2+1},is$

If tan $\frac{A}{2}$ = $\frac{3}{2}$, then $\frac{1+cosA}{1-cosA}$ =

The range of $x$ satisfying $3^x+2^{2x}\ge 5^x$ is

If A = {x: $x^2$ - 5x + 6 = 0}, B = {2,4} , C = {4,5}, then

A×(B $cap$ C) is

if $i^2=-1$, then the value of $\sum _{n=1}^{200}{i}^n$ is

The roots of the equation $x^{\frac{2}{3}}+x^{\frac{1}{3}}-2$ = 0 are

If A, B and C are three sets such that $A\cap B=A\cap CandA\cup B=A\cup C$, then

The term independent of x in the expansion of $(1+x+2x^3){(\frac{3x^2}{2}-\frac{1}{3x})}^{9}is$

Find the principal solution of $\frac{1+cosx}{cosx}=2$

The value of $3^{\sqrt{{\log }_{3}4}}$ is equal to

Parametric equation of the circle, $x^2+y^2-2x+4y-11=0$ is $x=$ and $y=$ .

If sinx + cosx = $\frac{1}{5}$ then find the value of sinx.cosx.

If (1+i)(1+2i)(1+3i)......(1+ni) = a+ib, then 2.5.10.....(1+$n^2$) is equal to

Q. ब्यूटी प्रॉडक्ट की एक दुकानदार ने एक कंपनी से $12,000$ रू. मूल्य के प्रॉडक्ट खरीदे। उसने $\frac{1}{4}$ हिस्सा $40\%$ की हानि पर बेचा। उसे शेष प्रोडक्ट कितने $\%$ लाभ पर बेचना चाहिए ताकि उसे लाभ या हानि न हो?

If the coefficient of $x^7$ and $x^8$ in ${(2+\frac{x}{3})}^n$ are equal, then n is:

What is the DMAS of :

$56-36÷4\times 2+7$

If p and q are chosen randomly from the set {1,2,3,4,5,6,7,8,9,10} with replacement, determine the probability that the roots of the equation $x^2+px+q=0$ are real.___

Which number should be added to the numbers 13, 15, 19 so that the resulting numbers be the consecutive terms of a H.P.

Cube root of 217 is

How many integers satisfy the relation |x - 1| $\le$ 2 ?

Find $\underset{t\to 4}{lim}\frac{t-\sqrt{3t+4}}{4-t}$

If $z$ = $(i{)}^{(i{)}^{\left(i\right)}}$, where i = $\sqrt{-1}$, then |z| is equal to:

$\underset{x\to \infty }{lim}\frac{lo{g}_{\epsilon }\left[x\right]}{x},\text{where[x]denotes the greatest integer less than or equal to x, is:}$

Which of the following illustrates the inductive step to prove a statement P(n) about natural numbers n by mathematical induction, where k is an arbitrary natural number?

If cos A = $\frac{\sqrt{3}}{2}$, then tan 3A =

Find the area of triangle formed by the points A(5,2) B (4,7) and C (7,-4).

If $se{c}^2\theta =\frac{4xy}{(x+y{)}^2}$ is true, then which of the following is true? $(x\ne -y)$

A signal which can be green or red with probability $\frac{4}{5}and\frac{1}{5}$ respectively, is received by station A and then transmitted to station B. The probability of each station receiving the signal correctly is $\frac{3}{4}$. If the signal received at station B is green, then the probability that the original signal green is

Which of the following statements is/are true?

1. If $lo{g}_{m}a<b\Rightarrow a>m^b;whenm>1$

2. If $lo{g}_{m}a<b\Rightarrow a>m^{b}when0<m<1$

3. If $lo{g}_{m}a>b\Rightarrow a<m^{b}when0<m<1$

4. If $lo{g}_{m}a>b\Rightarrow a<m^{b}whenm>1$

The sides of a triangle are in AP and its area is 3/5 x (area of an equilateral triangle of the same perimeter) Then, the ratio of the sides is

The roots of the equation $x^2+2(a-3)x+9=0$ lies between -6 and 1 then [ a ] =________ , where [.] denotes greatest integer function x.

If ∝, β are the roots of $x^2$ + px + q = 0, ${\omega }^3$ = 1, then (ω∝ + ${\omega }^2$β).( ${\omega }^2$∝ + ωβ) =

If $\frac{3+5+7+......nterms}{5+8+11+.........+10terms}$ = 7, the value of n is:

if $\omega$ is complex number such that $|$ $\omega$ $|$ $\ne 1$ then the complex number z = $\omega$ + $\frac{1}{\omega }$ describes

If $z_1,z_{2}and{z}_3$ are complex numbers such that

|$z_1$|=|$z_2$|=|$z_3$|=$|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}|=1$,

then |$z_1$+$z_2$+$z_3$|

The distance of the point (4.5,7,6) from the y-axis is ___.

If $(1+x{)}^n=C_0+C_{1}x+C_2{x}^2+........+C_n{x}^2$, then

$C_0^2+C_1^2+C_2^2+C_3^2+..........+C_n^2$ =

Find f(x) if it satisfies the relation

$2f\left(x\right)+f(1-x)=x^2$

The shortest distance of the point (a, b, c) from the x-axis is
[MP PET 1999; DCE 1999]

What is the principal solution of sin x = cos x ?

for all values of $\theta$ , the values of $3-cos\theta +cos(\theta +\frac{\pi }{3})$ lie in the interval