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Vani, her father and her grandfather have an average age of 53. One-half of her grandfather's age plus one-third of her father's age plus one-fourth of Vani's age is 65. Four years ago if Vani's grandfather was four times as old as Vani then what are the three equations we can use to find their present ages?

Find the mean, median and mode of the following data: [CBSE 2013]

From the figure, identify:

(a) The centre of circle (e) Two points in the interior

(b) Three radii (f) a point in the exterior

(c) a diameter (g) a sector

(d) a chord (h) a segment

A game consists of tossing a ₹5 coin twice and noting down its outcomes. Jesika wins if she gets exactly one head. What is the probability that she will lose the game?

In the given figure, TAS is a tangent to the circle, with centre O, at the point A. If $\angle$OBA = ${32}^{\circ }$, find the value of x.

AB is a diameter of the circle and A, P, B, R are four points on the circle. The lines AP, RB intersect at Q. Find $\angle BPR.$

There are 8 members in a club of which A and B are two members. A committee of 5 is to be formed. How many of these will include A and exclude B?

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In the given figure, AB = 5 cm, BC = 4 cm, AC = 3 cm. The diameter of the circle is

How many term are there in the A.P.?
(i)7,10,13,...43.
(ii)-1,$-\frac{5}{6},-\frac{2}{3},-\frac{1}{2},...,\frac{10}{3}$
(iii) 7,13,19,...,205.
(iv)18,$15\frac{1}{2}$,13,...,-47.

Car A travels km for every litre of petrol, while car B travels ( + 5) km for every litre.

If car A uses 4 litres more than car B in covering the 400km, write down an equation in and solve it to determine the number of litres of petrol used by car B for the journey

A twenty storied building was observed from outside, each floor has a kite shaped figure which gets on magnifying as observed from the $1^{st}$ to ${20}^{th}$ floor. The area of first five kites on each floor was calculated and they were found to develop a pattern. These five areas are ${10m}^2$, ${15m}^2$ , ${20m}^2$, ${25m}^2$, ${30m}^2$ and so on. The area of the kite on the top floor is ____.

OABC is a rhombus, three of whose vertices A, B, C lie on a circle with center O. If the radius of the circle is 10 cm. find the area of the rhombus.

Solve the following system using Cramer’s Rule.

$5x+y=-13$

$3x-2y=0$

Question 4

In the following figure, DE||AC and DF||AE. Prove that $\frac{BF}{FE}=\frac{BE}{EC}$ .

If A =$\left[\begin{array}{cc}a& b\\ b& a\end{array}\right]$ and $A^2$ =$\left[\begin{array}{cc}x& y\\ y& x\end{array}\right]$ , then

Maurice applied for a job and got selected. She has been offered a job with a starting monthly salary Rs.10000. If annual increment in her salary is Rs.400, form a series for her monthly salary for first six years. Is this series an AP?

Find the area of the triangle formed by joining the mid points of the sides of the triangle formed with coordinates A (-4, 3), B (2, 3) and C (4, 5).

Rachel goes to a shop to buy a box costing Rs. 2376. The rate of the sales tax is $8\%$. She tells the shopkeepers to allow a discount on the price of the box to such an extent that she pays Rs. 2376 inclusive all the tax. Find the discount in the price of the box.

In $\Delta$ABC, B is a right angle, and BD is perpendicular to AC and DE is perpendicular to BC. Then AD.DC =

Form a quadratic equation for the given situation:
Vijay inherited huge wealth from his father and by establishing a soft drinks company, he squared his wealth. He started a company which manufactures airplane toys and incurred huge losses amounting to $k(>0)$ times the wealth he inherited initially. His total assets now stand at debt of Rs. 4 crores.