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If $\frac{1120}{\sqrt{a}}=80$, then what is the value of $a$?

IF P is any point in the interior of a parallelogram ABCD, then prove that area of the triangle APB is less than half the area of parallelogram.

In the following figure, OA =OC and AB =BC.

Prove that :

(i) $\angle$ AOB = ${90}^0$

(ii) $\Delta$ AOD $\cong \Delta$ COD

(iii) AD =CD

Factorise $9z^3–27z^2-100z+300$ if it is given that $3z+10$ is a factor of it?

Explain the reading and interpretation of bar graphs.

Which of the following properties/methods is not used in the construction method of Triangle Construction 3?

Consider the equation $y=x^2$. Which of the following is/are true?

In the following figure, OB and OC are the angle bisectors. Find $\angle BOC$

(a) A florist has certain number of garlands. 110 of them have champak, 50 have jasmine flowers and 30 garlands have both the flowers. Find the total number of garlands with him.

(b) In a class of 60 students everyone should select either Mathematics or Science or both. If 45 students select Mathematics, 30 students select Science, how many students do select both the subjects?

(c) In a survey of 1000 families of T.V. viewers in a city, it was found that 750 families view Kannada programmes, 400 families view Hindi programmes and 300 families view both the programme. Find how many families do view (i) Kannada programmes only (ii) Hindi programmes only (iii) neither of the programmes.

The distance between any two parallel tangents is equal to the ___ of the circle.

Find the value of $\angle$COB.

Question 128

In $\Delta ABC$, $DE\parallel BC$ (figure). Find the values of x, y and z.

What is the radius of the circle shown below?

Find the value of $x$, if $8^{x-3}={16}^{4-x}.$

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = ${70}^{\circ }$, Angle Q = ${100}^{\circ }$, Angle R = ${80}^{\circ }$ and Angle S =${110}^{\circ }$.

Find the greatest fraction among the following.

If the height of a cylinder is doubled and radius remains the same, then volume will be

(a) doubled (b) halved

(c) same (d) four times

If $x=7+4\sqrt{3}$ and xy = 1, then $\frac{1}{x^2}+\frac{1}{y^2}=$

A line segment CD has two points R and S such that CR:RD=2:3 and CS:SD=5:6.

Sort in ascending order of lengths.

In the diagram, select the major arc and the minor arc of the circle, with respect to the chord AB.

Thinking process



Firstly, use the property that sum of cointeritor angles is ${180}^{\circ }$.Secondly use the property that sum of all angles in a triangle Is ${180}^{\circ }$ and then prove the required result.

If g = $t^{\frac{2}{3}}+4t^{\frac{-1}{2}}$, what is the value of g when t = 64?

In the given figure find the value of x.

In triangle ABC, right angled at B, if $\angle$A is increased till it becomes ${90}^{\circ }$, what can you say about AC and AB if BC = 1 unit

In the figure below, 2 vertices of a parallelogram are joined to the midpoints of two sides. If AP = 5 cm, PQ = ___