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Which of the following is the graph of y = |x|

The first term of a H P whose second term is $\frac{5}{2}$ and third term is $\frac{10}{3}$, is __

If the power of (2,1) with respect to the circle $2x^2+2y^2-8x-6y+k$ = 0 is positive if

$tan{75}^{\circ }-cot{75}^{\circ }$

[MNR 1982; Pb. CET 1990, 2000]

If the set A has 3 elements and the set B = {3, 4, 5}, then find the number of elements in $(A\times B).$

If $(x-2{)}^2-5|x-2|+6=0$, then $x\in$

Evaluate the following limit:
$\underset{x\to 3}{\text{lim}}x+3$

The value of the expression $1-\frac{si{n}^{2}y}{1+cosy}+\frac{1+cosy}{siny}-\frac{siny}{1-cosy}$

Find the value of $\underset{h\to 0}{lim}[2-h]+\underset{h\to 0}{lim}[2+h]$

Square roots of - 7 - 24i are :

Let $b_i>1fori=1,2,...,101.$ Suppose $lo{g}_e{b}_1.lo{g}_e{b}_2,......,lo{g}_e{b}_{101}$ are in Arithmetic Progression (A.P) with the common diffrence $lo{g}_{e}2.$ Suppose $a_1,a_2,.....,a_{101}$ are in A.P. such that $a_1=b_1$ and $a_{51}=b_{51}.$ If $t=b_1+b_2+...+b_{51}$ and $s=a_1+a_2+......+a{5}_3.$ then

Prove the following:
sin 2x + 2 sin 4x + sin 6x = 4 ${\text{cos}}^2$ x sin 4x

A die is rolled and two events A and B are defined as follows.
A: An odd number turns up
B: A prime Number turns up

Find the value of 36 P$(A\cup B)$.

If $y^{1/m}=[x+\sqrt{1+x^2}]$ , then $(1+x^2)y_2+x{y}_1$ is equal to :

The foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{b^2}=1$ and the hyperbola $\frac{x^2}{144}+\frac{y^2}{25}=\frac{1}{13}$ are the same.

The value of $b^2$ is ___ .

(Idempotent laws) For any set A, prove that:
$\left(i\right)A\cup A=A$

$\left(ii\right)A\cap A=A$

Find equation of the line which is equidistant from parallel lines $9x+6y-7=0$ and $3x+2y+6=0$

In the expansion of $(1+ax{)}^n$, the first three terms are $1+12x+64x^2$, then n=

Find the value of

$\sum {}_{k=1}^6$ $(sin\frac{2k\pi }{7}-icos\frac{2k\pi }{7})$.

$li{m}_{x\to \infty }$ $({1+\frac{2}{x})}^x$ =

The distances of the point (1,2,3) from the coordinate area are A, B, and C respectively now consider the following equations
$\left(1\right)A^2=B^2+C^2\text{(2)}{B}^2=2C^2\text{(3)}2A^2{C}^2=13B^2$
Which of these holds true?

If sin x + cos x = t, then sin x cos x is equal to

$Let\alpha ,\beta besuchthat\pi <\alpha -\beta <3\pi .Ifsin\alpha +sin\beta =\frac{-21}{65}andcos\alpha +cos\beta =\frac{-27}{65},thenthevalueofcos\frac{\alpha -\beta }{2}is$

In $△ABC,\frac{sin(A-B)}{sin(A+B)}=$
[MP PET 1986]

Solve : $\sqrt{3}cosx-sinx=1.$

$\text{If}y=2^{2^x},then\frac{dy}{dx}=$

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid point of the base is at origin. Find the vertices of the triangle.

A man wants to cut three lengths from a single piece of cloth of length 91 cm. The second length is to be 3 cm longer than the shortest and the third length is to be twice as long as the shortest. What are the possible lengths of the shortest piece of cloth if the third piece is to be al least 5 cm longer than the second.

A standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ is drawn along with its auxiliary circle. A point P $(asec\theta ,btan\theta )$ is taken. A perpendicular is dropped from P to the x axis which meets at the axis at R. A tangent is drawn from R to auxiliary circle. Which angle is equal to θ

From the previous problem at what angle to the horizontal must be steer in order to reach a point on the opposite bank directly east from the starting point? (Assuming his speed w.r.t. to the river is 4 m/s)

Find the number of discontinuities of the given function between x = 0 and x =2.

Evaluate $\int \sqrt{1+y^2}.2ydy$

If 0 $\le$ Argz $\le \frac{\pi }{4}$, then the least value of $\sqrt{2}$ |2z - 4i| is

If the sum of the series 2 + $\frac{5}{x}$ + $\frac{25}{x^2}$ + $\frac{125}{x^3}$+....is finite, then

Circumcentre of the triangle formed by the line y = x, y = 2x and y = 3x + 4 is

If α and β are the roots of the equation $x^2-a(x+1)-b=0$, then $(\alpha +1)(\beta +1)=$

The sum of (n+1) terms of $\frac{1}{2}+\frac{1}{1+2}+\frac{1}{1+2+3}+..........$ is

If $cos(\theta -\alpha )$ = a, $sin(\theta -\beta )$ = b,

then $co{s}^2(\alpha -\beta )$ + 2ab $sin(\alpha -\beta )$ is equal to

If $\omega$ = $\frac{-1+i\sqrt{3}}{2}$ , then $Z_1$ = $\frac{-\sqrt{3}-i}{2}$ and $Z_2$ = $\frac{\sqrt{3}-i}{2}$ can be expressed in terms of $\omega$ and ${\omega }^2$ as

Find the value of 'a' so that $x^2-11x+a=0and{x}^2-14x+2a=0$ have a common root.

There are 15 students in a class, out of which a team of 9 players is to be formed. If the captain always remains the same, we have to select x players from y students. Find the value of x + y.

If the major axis is "n” times the minor axis of the ellipse, then eccentricity is

Which of the following expressions gives the de-Broglie relationship