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What will be the condition for ($a^2$ - 9)$x^2$ + bx + c = 0 to be a quadratic equation?

Taxes which are imposed on the weight of the commodities are called

Let f(x) be a function defined on [-1, 1]. If the distance between (0,0) and (x, f(x)) is 1 unit, then find the function.

Out of $1900km$, Vishal travelled some distance by bus and some by aeroplane. Bus travels with average speed $60km/hr$ and the average speed of aeroplane is $700km/hr$. It takes $5$ hours to complete the journey. Find the distance, Vishal travelled by bus.

Question 167

In a five-digit number, digit at ten's place is 4, digit at unit's place is one - fourth of ten's place digit, digit at hundred's place is 0, digit at thousand's place is 5 times of the digit at unit's place and ten thousand's place digit is double the digit at ten's place. Write the number.

If 6 cotθ + 2 cosecθ = cotθ + 5 cosecθ, then cosθ is:

The probability of a day being rainy is 0.75, then the probability of it not being a rainy day is .

I have 2 road rollers. These road rollers are joined end to end along the flat surfaces to form a combined longer road roller. What are the surfaces present in the new road roller?

Question 4 (v)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(v) $3,3+\sqrt{2},3+2\sqrt{2},3+3\sqrt{2}$

In a circle of radius 5 cm, $AB$ and $AC$ are two chords such that $AB=AC=6cm.$ Find the length of the chord $BC$.

Choose the ogive curve for the given data.

$$\begin{array}{cc}Marks& Numberofstudents\\ >05& 48\\ >10& 45\\ >15& 39\\ >20& 30\\ >25& 18\\ >30& 10\end{array}$$

The figure above displays a circle with centre O. $\angle AOC=aand\angle ABC=b$. The relationship between a and b = _________

In $\Delta ABC$, point D and E lies on the line AB and AC respectively as shown in the figure. Find the measure of $\angle AED$.

What is the area of this trapezium?

ED and BC are perpendicular to DC. ED = a, BC = b, DC = c

The angle of elevation of the top of a tower from a point A due south of the tower is ${30}^{\circ }$ and from B due east of the tower is ${60}^{\circ }$. If AB = 10, Find the height of the tower.

Points A and B have co-ordinates (3, –1) and (1, –5) respectively. Find:

i) the slope of AB

ii) the equation of the right bisector of the segment AB.

Show that A (3,-2) is a point of trisection of the line-segment joining the points (2, 1) and (5, -8). Also, find the co-ordinates of the other point of trisection.

1. 7

In a parallelogram, one angle is $\frac{4}{5}$th of the adjacent angle. The adjacent angles of the parallelogram are

In the given figure, AB and BC are the tangents to the circle from the point B. D is the centre of the circle. BD = 5 cm and
CD = 3 cm. Find the value of AB - BC.

Which of the following is always rational?

Shriya and Vidya solved a quadratic equation. In solving it, Shriya made a mistake in the constant term and obtained the roots as 5, – 3 while Vidya made a mistake in the coefficient of x and obtained the roots as 1, –3. The correct roots of the equation are

The sum of $r$ terms of an AP is $2r^2+3r.$ The $n^{\text{th}}$​ term is ___.

The outer and inner diameters of a hemispherical bowl are $17cm$ and $15cm$ respectively. Find the cost of polishing it all over at $25$ paise per $c{m}^2$. ( Take $\pi$ $=\frac{22}{7}$).