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Prove that in a regular pentagon, the perpendicular from any vertex to the opposite side bisects that side.

Solve $\frac{1}{3}-(\frac{5}{6}\times \frac{9}{18})+\frac{2}{9}$.

In the figure below, the angle a = 150^o. The other angle in the figure which is also 150^o is:

1. 50

In the figure, ABCD is a cyclic quadrilateral, If $\angle BCD={100}^{\circ }and\angle ABD={70}^{\circ },find\angle ADB$

Use factor theorem to find whether polynomial g(x) is a factor of polynomial f(x)

f(x) = $x^5+3x^4-x^3-3x^2$ + 5x + 15, g(x) = x + 3

Diagonal AC and BD of trapezium ABCD, in which AB ||DC, intersect each other at O. The triangle which is equal in area of $△AOD$ is

A point B on the level ground is x m away from the foot of a h meter tall tower. If the angle of elevation of the top of the tower from the point B is B°, then the height of the tower is ______ m.

If one of the pair of complementary angles is 30º, what is the other angle?

Question 1 (v)

Write$\frac{2}{11}$ in decimal form and say what kind of decimal expansion it has.

The cost of a room in a hotel is partially fixed and partially varying with the hours stayed. A person staying for 10 hours paid ₹ 600 and a person staying for 15 hours paid ₹ 840. Find the algebraic expression representing this situation.

Question 3(f)

Pick out the solution from the values given in the bracket next to each equation. Show that the other values do not satisfy the equation.

x +4 = 2 (-2, 0, 2, 4)

2.142678 is a ………

Every rational number is

(a) a natural number (b) a whole number (c) an integer (d) a real number

If $x^2$ + $y^2$ = $z^2$. Then which of the following is/are true?

$x-y=0$ is a line which is ______________.

What do you infer, if S-t graphs of two cyclists meet at a point?

In a particular section of Class IX, $40$ students were asked about the months of their birth and the following graph was prepared for the data so obtained:

Find the probability that a student of the class was born in August.

The abscissa or x-coordinate of any point on Y- axis is:

If $x=3+\sqrt{8},$ find the value of $x^2+\frac{1}{x^2}$.

Question 85 (vi)

Expand the following, using suitable identities.

$(x+3)(x+7)$

Using the remainder theorem, find the remainder, when p(x) is divided by g(x), where
$p\left(x\right)=2x^3-7x^2+9x-13,g\left(x\right)=x-3$

What's the relation between the curved surface area of a hemisphere and the total surface area of hemisphere?

Given the matrices

$A=\left[\begin{array}{cc}1& -1\\ 4& -1\end{array}\right]$ and $B=\left[\begin{array}{cc}1& -1\\ 2& -2\end{array}\right]$. The two matrices $X$ and $Y$ are such that $X=B{A}^{-1}$ and $Y=A^{-1}B,$ then the matrix $3(X+Y)$ is: