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Find the equation of the circle passing through (0,0) and making intercepts a and b on the coordinates axes.

Let $r$ and $R$ be the inradius and the circumradius of a $△ABC$. Let $\theta$ be the angle between the line joining the incentre and the circumcentre of the $△ABC$ and $BC$. Then $\theta$ is equal to

Five different objects 1, 2, 3, 4, 5 are distributed randomly in 5 places marked 1, 2, 3, 4, 5. One arrangement is picked at random. The probability that in the selected arrangement, none of the object occupies the place corresponding to its number is:

If $e^{sinx}-e^{-sinx}=a$ has alteast one real solution, then

Find the mean deviation about the mean for the following data:

$\begin{array}{ccccccc}{x}_i& 3& 5& 7& 9& 11& 13\\ f_i& 6& 8& 15& 25& 8& 4\end{array}$

In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is $25.$ Then, the sum of $4^{\text{th}},6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to :

Let n $\in$N, $n>25$. Let A, G, H denote the arithmetic mean. Geometric mean and harmonic mean of 25 and n. The least value of n for which A, G, H $\in${25, 26,...... n} is

Find the equation of the set of points P, the sum of whose distance from $A(4,0,0)$ and $B(-4,0,0)$ is equal to 10.

If $sin6\theta =32co{s}^5\theta sin\theta -32co{s}^3\theta sin\theta +3x,$ then x=

Given sinx + cosx = $\frac{5}{4}$. If 1 + 2sinxcosx = a, find the value of 32 a.

A circle of radius ‘r’ is concentric with the Ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ Then inclination of common tangent with major axis is _______(b<r<a)

Find the maximum value of 5 + $(sinx-4{)}^2$

For the function
f(x) = $\frac{x^{100}}{100}+\frac{x^{99}}{99}+...+\frac{x^2}{2}+x+1$ prove that f'(1) = 100 f'(0).

$\frac{1}{3}$ and $\frac{1}{5}$ are first 2 terms of H.P. the 15th term of H.P is

Domain of the function $f\left(x\right)=\sqrt{2-2x-x^2}$ is

Find the principal solutions of sin 2x + cos x = 0

If the last term in the binomial expansion of ${(2^{\frac{1}{3}}-\frac{1}{\sqrt{2}})}^{n}is{\left(\frac{1}{3^{5/3}}\right)}^{lo{g}_{3}8}$, then the 5th term from the beginning is

Find the values of $\theta$ and p, if the equation $xcos\theta +ysin\theta =p$ is the normal form of the line $\sqrt{3}x+y+2=0$

The end points of the latus rectum of a parabola having vertex at origin are $(4,8)$ and $(4,-8)$ then the equation of the parabola is

A polygon has 44 diagonals, then the number of its sides are

If a, b and c are distinct positive real numbers and $a^2+b^2+c^2$ = 1, then ab + bc + ca is

If $|u|<1,|v|<1$, and $z=\frac{u-v}{1+\overline{u}v}$, then least value of $|z|$ is

The points (3, 3), (h, 0) and (0, k) are collinear if

The length of the perpendicular from the origin to a line is 7 and the perpendicular makes an angle of ${150}^{\circ }$ with the positive direction of the x-axis. Find the equation of the line.

Let the positive numbers a, b, c, d be in A.P. Then abc, abd, acd, bcd are in

If set A = {1, 2, 3} and set B = {2, 3, 5, 7}. Find the number of elements in A $\times$ B.

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If $A_n=\underset{0}{\overset{\pi /2}{\int }}\frac{\sin (2n-1)x}{\sin x}dx,B_n=\underset{0}{\overset{\pi /2}{\int }}{\left(\frac{\sin nx}{\sin x}\right)}^{2}dx,$ for $n\in N,$ then

Write the first five terms of the sequences whose $n^{th}$ term is:

$a_n=\frac{2n-3}{6}$

If h denote the A.M, k denote G.M of the intercepts made on axes by the lines passing through (1, 1) then (h, k) lies on

Mean deviation of the series a, a + d, a + 2d, a + 2nd from its mean is

In a class of $5$ students, average weight of the $4$ lightest students is $40$ kg, average weight of the $4$ heaviest students is $45$ kg. Then the difference between the maximum and minimum possible average weight is

Let $P$ be the point $(1,0)$ and $Q$ be a point on the curve $y^2=8x$. Then the locus of the mid-point of $PQ$ is

The degree of is not well defined.

Let A = {1, 2, 3, 4, 6}. Let R be the relation on A defined by $\left\{\right(a,b):a,bϵA,b$ is exactly divisible by a}.

(i) Write R in roster form.

(ii) Find the domain of R.

(iii) Find the range of R.

$\underset{x\to \infty }{lim}\frac{\sqrt{x^2+1}-\sqrt[3]{3x^2+1}}{\sqrt[4]{4x^4+1}-\sqrt[5]{5x^4-1}}isequalto$

Find the coefficient of $x^4$ in the product $(1+2x{)}^4\times (2-x{)}^5$

The equation of the circle passing through the foci of the ellipse

$\frac{x^2}{16}+\frac{y^2}{9}=1$ and having centre at (0,3) is

If $a^2(1-\sin \theta )+b^2(1+\sin \theta )=2ab\cos \theta$, then the value of $\tan \theta$ is

The equation of the directrix of the ellipse $\frac{x^2}{25}+\frac{y^2}{9}=1$ is/are