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Find the value of , which satisfies the inequation:

–2 < ¹/₂ – ²/₃ < ¹¹/₆, ε N.

In the figure. What measure of the makes AP a tangent?

Which of the following may not be a polynomial if F(x) and G(x) is a polynomial?

Find the AP whose sum to n terms is 2 $n^2$ + n.

Solve

$\sqrt{3}{x}^2-\sqrt{2}x+3\sqrt{3}=0$

In $\Delta ABC$, which is circumscribed by a circle ,$\angle A={45}^{\circ }$, BC =6 cm. What is the diameter of the circumcircle?

If $\angle A$ and $\angle P$ are acute angles such that tan A = tan P, then show that $\angle A=\angle P$

If for some $\alpha \in R,$ the lines $L_1:\frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $L_2:\frac{x+2}{\alpha }=\frac{y+1}{5-\alpha }=\frac{z+1}{1}$ coplanar, then the line $L_2$ passes through the point:

1. 1620

In $\Delta ABC$, AL and CM are the perpendiculars from the vertices A and C to BC and AB respectively. If AL and CM intersect at O, prove that:
(i) $\Delta OMA\sim \Delta OLC$
(ii) $\frac{OA}{OC}=\frac{OM}{OL}$

A solid right circular cylinder of radius 60 cm and height 20 cm is melted and recast into a right circular cone of height 3 times that of the cylinder. Find the curved surface area of the cone in square cm correct up to two places of decimal. $(Use\pi =3.14)$

Find two consecutive positive odd integers whose product is 483.

In the given figure, O is the center of the circumcircle of triangle ABC. Tangents at A and B intersect at T. If $\angle ATB={80}^{\circ }$ and $\angle AOC={130}^{\circ }$, Calculate $\angle CAB$. [4 MARKS]

If D is any point on the side BC of $\Delta ABC,$ then

For a G.P, first term = 5, common ratio = 3. Find its fourth term.

To divide a line segment, the ratio of division must be _____.

In the given series, 1.5, 0.5, -0.5, -1.5, .... , -8.5 If $n^{th}$ term is -8.5, find n.

Draw a circle of radius 3.5 cm and two perpendicular diameters in it. Construct tangents at the ends of the diameters.

If $\alpha$ and $\beta$ are the zeros of the polynomial $f\left(x\right)=5x^2-7x+1$, find the value of $(\frac{1}{\alpha }+\frac{1}{\beta }).$.

Find an arithmetic sequence whose first term is 5 and common difference is 9.

The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 respectively. Find the slant height of the frustum.

Find the cost of 85 shares of Rs 60 each when quoted at Rs 63.25.

A concrete pour of $1080$ cum is planned with a $120$ cum/hr capacity. If the effeciency of the plant is assumed to $75$%, what will be approximate time taken for completing the pour?

Hello

Please help me with the following

The sides of a triangle touch a circle. Sides AB, BC, CA touch the circle at points P, Q, R respectively. Prove that:

1. AP+BQ+CR=BP+CQ+AR

2.AP +BQ+CR=1/2 *perimeter of 🔺 ABC

The first term of an AP is 2 and its last term is 12. The number of terms is given as 10. Find the sum of the terms of this AP.

Cuboids can be formed by stacking

[Stacking means placing objects on top of one another]

In each of the second degree polynomials given below, find the numbers to be taken as x to get zero:

(i) x² − 5x + 6

(ii) x² − 2x − 1

(iii) x² + 5x + 6

(iv) 2x² − 7x − 15

(v) x² + x − 6

(vi) 9x² + 12x + 4

(vii) x² − x − 6