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$In\Delta ABC,DE||BCand\frac{AD}{DB}=\frac{3}{5}.$ If $AC=5.6cm$, then $AE=$ _____.

In the diagram, a square is drawn such that the diagonally opposite corners touch the Centre and the circumference of a circle with radius, $r.$ what is the area of the of the square?

An open box is made from a square lamina of side 12cm, by cutting equal squares at the corners and folding up the remaining flaps. The volume of this box cannot be

27, 75, 5, 99, 70, 12, 15, 20, 30, 35, 45, 80, 77, 90, 92, 72, 4, 33, 22, 15, 20, 28, 29, 14, 16, 20, 72, 81, 85, 10, 16, 9, 25, 23, 26, 46, 55, 56, 66, 67, 51, 57, 44, 43, 6, 65, 42, 36, 7, 35.

The table below classifies according to weight, the infants born during a week in a hospital:

Find the median weight.

In the given figure, find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

If E and F are mutually exclusive events, find the probability of (E’$\cup$ F’)

Find the Surface Area of : [2 MARKS]

Find the mode of the following data.
$$\begin{array}{cccccc}Classinterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Frequency& 10& 9& 8& 17& 6\end{array}$$

Using quadratic formula solve the following quadratic equation: [3 MARKS]



$p^2{x}^2+(p^2-q^2)x-q^2=0,p\ne 0$

Cards bearng numbers 2, 3, 4,..., 11 are kept in a bag. A card is drawn at random from the bag. The probability of getting a card with a prime number is
(a) $\frac{1}{2}$ (b) $\frac{2}{5}$ (c) $\frac{3}{10}$ (d) $\frac{8}{89}$

Solve the following quadric equations by factorization method only

$x^2+1=0$

Prove the following trigonometric identities:

$\frac{1+sin\theta }{cos\theta }+\frac{cos\theta }{1+sin\theta }=2sec\theta$

The area of triangle ABC with A(3,2), B(11,8) and C(8,12) in square units is

A person sells 36 oranges per rupee and incurs a loss of $4\%$. Find how many oranges are to be sold for a rupee to have a gain of $8\%$?

If the radius of a cylinder is reduced by $50\%$, then volume of the cylinder will get reduced by

Compute the mean of the following data, using direct method:
$\begin{array}{cccccc}\text{Class}& 0-100& 100-200& 200-300& 300-400& 400-500\\ \text{Frequency}& 6& 10& 8& 12& 4\end{array}$

In the given figure, $\angle A={60}^{\circ }$ and $\angle ABC={80}^{\circ }$, then $\angle DPC$ and $\angle BQC$ are respectively ___.

Sum of age of father and son is 55 years . If father was who lived in his son is equal to his present age , the total of their age woulbd be 93 years .find their present age.

In the adjoining figure, two circles with centres at A and B, and of radii 5 cm and 3 cm touch each other internally. If the perpendicular bisector of AB meets the bigger circle in P and Q, find the length of PQ.

In the given figure, a circle is circumscribing $\Delta ABC$ where $\angle A={125}^{\circ }$ and side BC=8cm. The diameter of the circumcircle is equal to

$[sin{55}^{\circ }=0.82]$

Had Anitha scored 10 more marks in her mathematics test out of 30, 9 times these marks would have been the square of her actual marks. How many marks did she get In the test?

A triangle has two of its angles ${80}^{\circ }$ and ${60}^{\circ }$. Find any two angles of a triangle which is similar to the given triangle.

A cylindrical tube open at both ends is made of metal. The internal diameter of the tube is 11.2 cm and its length is 21 cm .The metal everywhere is 0.4 cm thick. The volume of the metal used is

Write the discriminant of the following quadratic equations:
(i) $2x^2-5x+3=0$ (ii) $x^2+2x+4=0$
(iii) $(x-1)(2x-1)=0$ (iv) $x^2-2x+k=0,kϵR$
(v) $\sqrt{3}{x}^2+2\sqrt{2}x-2\sqrt{3}=0$ (vi) $x^2-x+1=0$