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A circus artist is climbing a 30 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the distance of the pole to the peg in the ground, if the angle made by the rope with the ground level is ${30}^{\circ }$.

$\text{In the given figure, line l is the bisector of an angle}\angle A\text{and B is any point on l.}\text{If BP and BQ are perpendiculars from B to the arms of}\angle A,\text{show that}\left(i\right)\Delta APB\cong \Delta AQB\text{(ii) BP = BQ, i.e., B is equidistant from the armos of}\angle A.$

A rectangular park has length and breadth of 2 km and 1 km respectively. Due to the metro construction, the authority reduces the length and breadth of the park by $x$ km. Find the new area of the park in terms of $x$.

Question 18

P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA=AR and CW =QR.

The graph of x = 4 is a line

(a) making an intercept 4 on the x-axis

(b) making an intercept 4 on the y-axis

(c) parallel to the x-axis at a distance of 4 units from the origin

(d) parallel to the y-axis at a distance of 4 units from the origin

There are 2 cubes A and B each of volume $Xc{m}^3$. Cube B is cut into smaller cubes each of volume $Yc{m}^3$. The surface area and volumes of the resulting cubes are compared.

S1: The ratio of volumes of A and B = 1:1

S2: The ratio of surface areas of A and B = 1:1

Number of zeroes of the polynomial shown in the figure?

If each side of a triangle is tripled then find its percentage increased in area?

$(x-y)(x+y)(x^2+y^2)(x^4+y^4)\text{is equal to}$

A, B, C, D are mid points of sides of parallelogram PQRS. IF $ar\left(PQRS\right)=36c{m}^2$, then ar (ABCD) =

The marks of 15 students in an examination are
25, 19, 17, 24, 23, 29, 31, 40, 19, 20, 22, 26, 17, 35, 21.
Find the median score.

If the lines $3x-4y+4=0$ amd $6x-8y-7=0$ are tangents to a circle, find the radius of the circle.

Convert the given fraction to its decimal form :
$\frac{448}{2500}$

If A has 3 elements and P(A) denotes the power set of A, then the number of elements in P(P(A)) is

In Fig. PQR is a triangle and S is any point in its interior, show that SQ + SR < PQ + PR. [3 MARKS]

In the given figure, ABCD and ABPD are two cyclic quadrilaterals.

If $\angle BOD={160}^{\circ }$, find the difference of $\angle BPDand\angle BCD.$

In the given right angle triangle, if Sin$\theta$ =$\frac{3}{5}$

The value of 3tan$\alpha$ is :

The distance between points $A(10,-8)$ and $B(-6,4)$ is:

If $lo{g}_{12}27=a,thenlo{g}_{6}16=$

If $x^{100}+2x^{99}+k$ is divisible by $(x+1)$, then the value of $k$ is

The lateral surface area of a right circular cylinder with base diameter $28cm$ and height $20cm$ is

On a semi circle with $AB$ as diameter, a point $C$ is taken so that $\angle CAB={30}^{\circ }$. Find $\angle ACB\text{and}\angle ABC.$

Kamal started a business investing $\text{Rs.}9000.$ After five months, Sameer joined with a capital of $\text{Rs.}8000.$ If at the end of the year, they earn a profit of $\text{Rs.}4100,$ then what will be the share of Sameer in the profit?

Cardinal number of the set $G=\{x:x\in N,5<x<9\}$ is __.

Question 69
In the following question, state whether the given statement is true (T) or false (F).
There is a whole number which when added to a whole number, gives the number itself.

If $x=0.\overline{18}$, which of the following statements are true?

(i) $100x=18.\overline{18}$

(ii) $100x-x=17.\overline{18}$

(iii) $99x=18$

1. 84

In the given circle, chords AB and CD intersect each other at P. CP = (x − 4) cm, DP = (y + 10) cm, AP = (x − 1) cm, and BP = (y + 1) cm.

If x + 2y = 23, then what is the sum of the lengths of chords AB and CD?

The point whose abscissa and ordinate have same sign will lie in.

Choose the appropriate conjunction for the blank.

Share the chocolates with your little brother ____ he will start crying.

If we roll a die, there are total six possible outcomes (1,2,3,4,5,6). What is the probability of getting 2?

The initial level of water in a measuring cylinder was $12ml$. When an iron piece of irregular shape is completely immersed, the water level changed to $30ml$. Find the volume of iron in $m^3$.

An equilateral triangle ABC is inscribed in a circle centered at O, as shown below. OE is a radius such that it is perpendicular to BC and cuts BC at point D. If OD = 5 cm, then the radius of this circle is