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If A = {1, 3, 5} and B = {2, 4}, list the elements of R, if R = {$(x,y):x,yϵA\times B$ and x > y}.

Let $p\left(x\right)=x^2–5x+a$ and $q\left(x\right)=x^2–3x+b$, where a and b are positive integers. Suppose hof(p(x),q(x)) = x – 1 and k(x) = 1cm (p(x), q(x)). If the coefficient of the highest degree term of k(x) is 1, the sum of the roots of (x – 1) + k(x) is.

The point $(-2m,m+1)$ is an interior point of the smaller region bounded by the circle $x^2+y^2=4$ and the parabola $y^2=4x$. Then $m$ belongs to the intyerval

Represent to solution set of each of the following in equations graphically in two dimensional plane :

$x-2y<0$

The equation of the reflection of the hyperbola $\frac{(x-4{)}^2}{16}-\frac{(y-3{)}^2}{9}=1$ about the line $x+y-2=0$ is

Consider the relation $4l^2-5m^2+6l+1=0$, where $l,m\in R.$ If the line $lx+my+1=0$ touches a fixed circle, then the centre of that circle is:

Let $0\le x,y,z\le \frac{\pi }{2}$ such that $\sin x\cdot \sin y\cdot \cos z=\frac{1}{4\sqrt{2}},\frac{{\sin }^{2}x\cdot {\sin }^{3}y}{\cos z}=\frac{1}{4\sqrt{2}}\text{and}\frac{\sin x\cdot {\sin }^{4}y}{{\cos }^{2}z}=\frac{1}{8}$, then which of the following is/are correct?

The function $f\left(x\right)=x^2+2x-5$ is strictly increasing in the interval

If $f\left(x\right)=\frac{x^n-a^n}{x-a}$, then $f^{\prime }\left(a\right)$ is

Consider a binary operation $\ast$ on set{1,2,3,4,5} given by the following multiplication table:
(iii)Compute $(2\ast 3)\times (4\ast 5)$
$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

Integrate the rational functions.
$\int \frac{2x}{x^2+3x+2}dx.$

If $I={\int }_0^{\pi /2}{\cos }^{n}x{\sin }^{n}x\mathrm{dx}=k{\int }_0^{\pi /2}{\sin }^{n}x\mathrm{dx}$, then k equals

Solve the following system of equations in R.

$2x-7>5-x,11-5x\le 1$

An ellipse with major and minor axis length as $2a$ and $2b$ units touches coordinate axis in first quadrant. If foci are $(x_1,y_1)$ and $(x_2,y_2),$ then the value of $x_1{x}_2+y_1{y}_2$ is

The irrational number among the following is

soln of triangles practice set is not there

If the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ is the square of the other, then $\frac{a+b}{h}+\frac{8h^2}{ab}$ is equal to

Find the binary equivalent of 234.

One fourth of a herd of camel was seen in forest..Twice the square root of the herd had gone to mountain and the remaining 15 camels were seen on the banks of a river.Find the total number of camels.

Choose the word/group of words which is most similar in meaning to the word/group of underlined ​words as used in the passage:

UNKEMPT

Sin theta + sin 2theta + sin 3theta =sin alpha and cos theta + cos 2theta + cos 3theta= cos alpha, then theta is equal to

An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball does not depend on k.

3 (tan²26 - cosec²64)

Find the value of the above trigonometric ratio

Prove that : n! (n+2) = n! + (n+1)!

Minimum value of $x^2+2xy+3y^2-6x-2y$ $x,y,ϵR$ is

$si{n}^{2}1+si{n}^{2}89+co{s}^{2}7+co{s}^{2}83=?$

If the vertices of a quadrilateral are A(2, 3), B(0, 0), C(- 5, - 2) and D(- 1, 0), then the area of triangle BCD is:

Find two numbers whose sum is 24 and product is a large as possible.

The term independent of $x$ in the expansion of ${(2x+\frac{1}{x})}^{10}$ is

If $\overline{a},\overline{b},\overline{c}$ are non collinear, non coplanar vectors and $x\overline{a}+\overline{b},x\overline{b}+\overline{c},x\overline{c}+\overline{a}$ are coplanar vectors then the value of x is

The abscissae of A and B are the roots of the equation $x^2+2ax-b^2=0$ and their coordinates are the roots of the equation $y^2+2py-q^2$= 0. The equation of the circle with AB as diameter

${lim}_{x\to \sqrt{10}}\frac{\sqrt{7+2x}-(\sqrt{5}+\sqrt{2})}{x^2-10}$

If ${}^n{P}_4$ = $30{}^n{C}_5$, then n =

Tangents are drawn from the point P(1, 8) to the circle $x^2+y^2-6x-4y-11=0$ touch the circle at the point A and B, then equation of the circumcircle of the triangle PAB is

Thirteen persons are sitting in a row. Number of ways in which four persons can be selected so that no two of them are consecutive is also equal to

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0,1),(1,1)$ and $(1,0)$ is :

If $Ax+By=1$ is a normal to the curve $ay=x^2$, then

Let $T_r$ be the $r^{th}$ term of an A.P, for r=1, 2, 3,-------. If for some positive integers m,n we have $T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $T_{mn}$ equals.

Classify the following pairs of lines as coincident, parallel or intersecting: $\left(i\right)2x+y-1=0and3x+2y+5=0\left(ii\right)x-y=0and3x-3y+5=0\left(iii\right)3x+2y-4=0and6x+4y-8=0.$

The equation of the circle which touches x-axis and whose centre is (1, 2), is

The shortest distance between a circle and an external point is r. The radius of the circle is also 'r'. What is the length of tangent from that point to the circle?