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Given a triangle ABC and E is mid point of median AD of ∆ABC. If ar(∆BED) = 20 cm², then ar(∆ABC) is:

1. 0.5

Find the value of
$co{t}^2{30}^{\circ }-2co{s}^2{60}^{\circ }-\frac{3}{4}se{c}^2{45}^{\circ }-4si{n}^2{30}^{\circ }.$

In the figure below, A, B, C, D are points on the circle.

Compute the angles of the quadrilateral ABCD and the angles between its diagonals.

Question 78

Solve the following:

0.16(5x-2)=0.4x+7

Prove that 1/2+√3 + 2/√5-√3 + 1/2-√5=0

Saurabh invests ₹ 1,50,000 for three years at the rate of 10% per annum. Find the sum due to Saurabh at the end of the first year.

If $e^{f\left(x\right)}=\frac{10+x}{10-x},x\in (-10,10)$ and

$f\left(x\right)=kf\left(\frac{200x}{100+x^2}\right)$ then $k=$

In th figure , AC $\perp$CE and $\angle A:\angle B:\angle C=3:2:1$, find value of

$\angle ECD.$

1. 0.099

Which of the following represents a polynomial in one variable?

A cylindrical bowl of internal diameter $18cm$ and height $15cm$ is full of liquid. The whole of the liquid is to be filled in small cylindrical bottles of diameter $3cm$ and height $4cm.$ Each bottle is sold for $Rs.5,$ then find the amount earned.

If you take '$x$' as the number of chocolates you have, and you receive the same number of chocolates from your friend, then what will be the number of chocolates you have in total?

How many planes can be made to pass through three distinct points?

There is hollow cube. Its external edge is 5 cm long and its internal edge is 3 cm long. What is its surface area in $c{m}^2$ ?

If the points A,B and C have position vectors (2,1,1), (6,-1,2) and (14,-5,P) respectively and if they are collinear, then P =

Mean marks obtained by a student in his five subjects are $15$. In English he secures $8$ marks, in Economics $12$, in Mathematics $18$, and in Commerce $9$. Find out the marks he secured in Statistics.

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector.
(Take $\pi$ = 3.14)

ABCD is a parallelogram. AE and CF are angle bisectors of ∠DAC and ∠ACB, respectively. Show that the lines AE and CF are parallel to each other.

$27$ spherical iron balls of radius $5cm$ each are melted and recasted into a big sphere. The radius of the big sphere is

The base of a prism is a right angled triangle with dimensions as follows: base =15 cm and altitude= 8 cm. If the height of the prism is 20 cm, the total surface area of the prism will be equal to:

Complete the flow
chart in the correct sequence as it happens in the story.

Hint: it begins
from the time John Pescud first saw Jessie till the time they marry.

Question 8(iv)

Using $(x+a)(x+b)=x^2+(a+b)x+ab$, find

$9.7\times 9.8$

If ABC is an arc of a circle and $\angle ABC={135}^o$, then the ratio of arc $\stackrel{⌢}{ABC}$ to the circumference is

If $\frac{x}{a}=\frac{y}{b}=\frac{z}{c}$, then

Express 2.4178 in p/q form

The pillars of a temple are cylindrically shaped. If each pillar has a circular base of radius $20cm$ and height $10m$. How much concrete mixture would be required to build $14$ such pillars?

The water in a cubical tank of side $10m$ is transferred to completely fill a cuboidal tank of length $l=5m,$ breadth $b=10m,$ and height $h.$ Then, the height of the cuboidal tank (in metres) is ___

AB & CD are two equal chords of a circle with Centre O which intersect each other at the right angle at point P. If the perpendiculars from the centre to AB and CD meet them at M and N respectively, then MONP is a_______.