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What should be added to each of the numbers $13,17$ and $22$ so that, the resulting numbers are in continued proportion?

Locus of the image of the point $(2,3)$ in the line $(2x-3y+4)+k(x-2y+3)=0,kϵR$ is a

If $x+y=x^y,$ then $\frac{dy}{dx}=$

A sweet seller has 420 kaju barfis and 130 badam barfis. She wants to stack them in such a way that each stack has the same number of sweets, and they take up the least area of the tray. What is the maximum number of barfis that can be placed in each stack for this purpose?

If the sides of a quadrilateral touch a circle, prove that the sum of a pair of opposite sides is equal to the sum of the other pair.

Question 3(v)
Find the value of:

${\left\{{\left(\frac{-2}{3}\right)}^{-2}\right\}}^2$

What can be inferred from the inequality below?

$x\ge y<5$

If $X+Y=\left[\begin{array}{cc}5& 2\\ 0& 9\end{array}\right]$ and $X-Y=\left[\begin{array}{cc}3& 6\\ 0& -1\end{array}\right],$ then

Question 12

A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

The price of a T.V set inclusive of sales tax is Rs. 13,530. If the rate of sales tax is $10\%$, find its basic (marked) price.

If the base area of a hemisphere is 10 sq.cm and its curved surface are is____.

Harikiran purchased a house for Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual installments of Rs. 1000 with 10% per annum interest. How much money is to be paid by him in total?

Two poles of equal heights are standing opposite each other on either side of the road, which is 90 m wide. From a point between them on the road, the angles of elevation of the top of the poles are ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the poles.

___ $\times$ (-13) = -143

The set of domain for $f\left(x\right)={\cos }^{-1}\left(\sec x\right)$ is

$\frac{\text{cos}\theta }{1-\text{tan}\theta }+\frac{\text{sin}\theta }{1-\text{cot}\theta }=$ ___

In $△ABC$ , medians AD ,BE and CF are drawn on sides BC , AC and AB respectively and $△ADC\sim △BEC$ . What can you say about $△ABC$ ?

In the given figure, O is the centre of the circumcircle ABC. Tangents at A and C intersect at P. Given angle $AOB={140}^{\circ }$ and angle $APC={80}^{\circ }$; find the angle BAC.

Eesha walks 4 km due north and then 3 km due east to reach Anu's place. From Anu's place, both of them walk 4 km due north and then 3 km due east. How far are both Eesha and Anu from their respective starting points?

In a $△ABC$, Let P and Q be points on AB and AC respectively such that PQ || BC. Prove that median AD bisects PQ.

The product of two consecutive positive integers is 306. Find the integers.

Find the point that divides the line joining A(2, 4) and B(6, 8) in the ratio a : 1.

Solve the following systems of equations graphically:

x - 2y = 6

3x - 6y = 0

Evaluate each of the following

sin ${45}^o$ sin ${30}^o$ + cos ${45}^o$ cos ${30}^o$

Solve the given inequality and show the graph of the solution on number line: 5x – 3 ≥ 3x – 5