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If the y-coordinate of the vertex of the graph of $y={\mathrm{ax}}^2+\mathrm{bx}+c,a<0$ is zero, then the zero of the quadratic polynomial is equal to

1. 463.39

Reflection of the point $(-1,15)$ in the y-axis is ____________

How many silver coins, 1.75 cm in diameter and of thickness 2 mm , must be melted to form a cuboid of dimensions 5.5 cm x 10 cm X 3.5 cm?

If 8, x, 48, and 18 are in proportion then the value of x is ___

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

Question 3

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.

$\begin{array}{cc}\text{Expenditure (in Rs)}& \text{Number of families}\\ 1000-1500& 24\\ 1500-2000& 40\\ 2000-2500& 33\\ 2500-3000& 28\\ 3000-3500& 30\\ 3500-4000& 22\\ 4000-4500& 16\\ 4500-5000& 7\end{array}$

In the figure given below, PA and PB are tangents to the circle from point P. When the centre of the circle O and the point P are joined, how are the values of x and y related?

If two dice are thrown simultaneously, then the probability that the sum of the numbers which come up on the dice to be more than 5 is ________

Question 1 (vi)

Find the square roots of each of the following numbers by Division method:

1369

The sides of a quadrilateral ABCD are tangents to the circle with centre ‘O’. If AB = 8 cm and CD = 5 cm find AD + BC.

Given
A = {$x:11x-5>7x+3,xϵR$}
B = {$x:18x-9\ge 15+12x,xϵR$}
The range of set $A\cap B$ is .

Question 2 (iii)
On comparing the ratios $\frac{a_1}{a_2}$, $\frac{b_1}{b_2}$ and $\frac{c_1}{c_2}$ , find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
6x – 3y + 10 = 0
2x – y + 9 = 0

1. 60

How many numbers lie between 10 and 300, which when divided by 4 leaves a remainder 3?

In the figure, P is hte centre of an excircle of ▲ ABC. If $\angle ABC=40°$ and $\angle BAC=80°$, find the angle measure of triangle APC.

If point P lies on the line y = 2, then what is its x-coordinate?

Find the value of x and y, if $\left[\begin{array}{cc}x+y& y\\ 2x& x-y\end{array}\right]\left[\begin{array}{c}2\\ -1\end{array}\right]=\left[\begin{array}{c}3\\ 2\end{array}\right]$

Question 1 (iii)

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following:

$p\left(x\right)=x^4-5x+6,g\left(x\right)=2-x^2$

Find the 20^th term from the last term of the A.P. 3, 8, 13, …, 253

In an acute-angled triangle, express a median in terms of its sides.

The probability of picking the letter K if you pick a random letter from the word TREKKING is $\frac{x}{4}$. x is

Which of the following numbers can form sides of a right-angled triangle?

There is a circle with centre O. P is a point from where only one tangent can be drawn to this circle. What can we say about P?

A point C divides a line segment AB in the ratio 5:6. The ratio of lengths AB: BC is:

ABC is an isosceles triangle, right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of $\Delta ABEand\Delta ACD$.

In the given figure, $\angle 1=\angle 2$ and $\frac{AC}{BD}=\frac{CB}{CE}$.

Prove that $\Delta ACB\sim \Delta DCE$.