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The cost of levelling a square lawn at RS 15 per square meter is rs19935.Find the cost of fencing the lawn at rs 22 per meter

In a cyclic quadrilateral ABCD, the diagonal AC bisects the $\angle BCD$. Prove that the diagonal BD is parallel to the tangent to the circle at point A.

A ladder is placed along a wall such that its upper end is resting against a vertical wall. The foot of the ladder is 2.4 m from the wall and the ladder is making an angle of ${68}^{\circ }$ with the ground. Find the height, upto which the ladder reaches.

Simplify $\frac{x^3-27}{x^2+10x+24}\times \frac{x^2+4x-12}{x^2-5x+6}.$

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the approximate volume of the toy.

By the method of sustitution, find the solutionset of the pair of linear equations :

x + 2y = 5 and 3x + 7y = 17

Perform the following arithmetic operations. [4 MARKS]

1) 26.5 - 3.14 + 9.47 - 2.1 = ?
2) (5.3 $\times$ 2.1) - (6.2 $\times$ 1.4) = ?
3) (0.001$\times$100) + (89.3 + 10.6) = ?
4) 4.05 + 5.13 - 9 = ?

The Greenwood International School marching band sold gift wrap to earn money for a band trip to Singapore. The gift wrap in solid colors was sold for $4.00perroll,andtheprintgiftwrapwassoldfor$6.00 per roll. The total number of rolls sold is 480 and the total amount of money collected is $2340. How many rolls of solid colored gift wraps were sold?

ABCD is a parallelogram with $\angle$ABC $={90}^{\circ }$, then number of right angles in the parallelogram excluding $\angle$ABC is/are ____

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is

Consider a square S of 5 cm side. The square S is divided into squares of unit area. Each unit square is coloured with red, yellow or both. If a point is chosen at random, what is the probability that it lies in a square containing both the colours?​

Question 3
State whether the following is true or false.
A pair of tangents can be constructed from a point P to a circle of radius 3.5 cm situated at a distance of 3 cm from the centre.
[Thinking process
Let r = radius of circle and d = distance of a point from the centre.
1. If r = d, then point lie on the circle i.e only one tangent is possible
2. If r < d, then point lie outside the circle. i.e a pair of tangent is possible.
3. If r>d, then point lie inside the circle i.e no tangent is possible.
]

A man wants to buy 62 shares available at ₹ 132 (par value being 100). If the dividend is 7.5%, find his annual income

If one of the zeroes of the polynomial g(x) = $(k^2+4)x^2+13x+4k$ is reciprocal of the other then k is

In Euclids division lemma,to show thatthe cube of any positive intiger is of the form of 9m,9m+1,9m+8,why we r taking b=3

Points A and B are 70 km apart on a highway. A car starts from A and another car starts from B simultaneously. If they travel in the same direction, they meet in 7 hours. But,if they travel towards each other, they meet in 1 hour. Find the speed of the each car.

Eight metallic spheres; each of radius 2 mm, are melted and cast into a single sphere. Calculate the radius of the new sphere.

In the given figure, O is the centre of the circle. The tangent at B and D intersect each other at point P.

If AB is parallel to CD and $\angle$ ABC = ${55}^o$, find :

(i) $\angle$ BOD (ii) $\angle$ BPD

If x = 1 + a + $a^2$ .......... to $\infty$ (|a|<1), y = 1 + b + $b^2$ ......... to $\infty$(|b| < 1),

then Z = 1 + ab + $a^2$ $b^2$ + $a^3$ $b^3$..... to $\infty$ is

The sum of two triangles is 95° and their differences is 25°,find all three angles of a triangle.

A square hole of cross sectional area 4 cm² is drilled across a cube with its length parallel to a side of the cube. If an edge of the cube measures 5 units, what is the total surface area of the structure so formed?

Solve the following pair of linear equations.

$\frac{2}{\sqrt{x}}+\frac{3}{\sqrt{y}}=2$

$\frac{4}{\sqrt{x}}-\frac{9}{\sqrt{y}}=-1$

Here, x > 0 and y > 0.

Construct a cyclic quadrilateral ABCD when AB = 7.6 cm, $\angle ABD={30}^{\circ }$, AD = 5.4cm and AB || CD.

Construct a 2 $\times$ 2 matrix whose elements are $a_{ij}$=$\frac{1}{2}$ (2i – 3j)

If $3A+\left[\begin{array}{cc}4& -1\\ -27& 6\end{array}\right]=\left[\begin{array}{cc}2& 0\\ 2& 32\end{array}\right]$ then find A.

Find the missing number in the rectangles in this factor tree.

Find the number of integers that lie between the roots of the equation $x^2+7x+12=0$

If n is an even natural number, then what is the least possible factor of the expression $n(n+1)(n+2)$?

A bag contains 6 red balls & some blue balls. If probability of drawing a blue ball from the bag is thrice the probability of drawing a red ball. Find the number of blue balls in the bag.

Two tangents drawn from an external point are

Find the solution to the following system of linear equations:
2x+3y=8
x-2y+3=0

Find the roots of the equation $x^2–14x+17=0$ by the method of completing the square.

Question 2 (ii)
Write first four terms of the A.P. when the first term "a" and the common difference "d" are given as follows.
(ii) a = -2, d = 0

In fig., PA and PB are two tangents drawn from an external point P to a circle with centre C and radius 4 cm. If PA ⊥ PB, then the length of each tangent is:

If sin[${90}^{\circ }$- (A+B)] = cosx = cosy

find the value of x and y if y is the angle C of triangle ABC. (In triangle ABC, A + B = ${90}^{\circ }$)

Find the point equidistant from the points P(1,3) and Q(-5,-5), and which lies on the line $y=-1$.

Question 6
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabets in the surnames was obtained as follows:
$\begin{array}{ccccccc}Numberofletters& 1-4& 4-7& 7-10& 10-13& 13-16& 16-19\\ Numberofsurnames& 6& 30& 40& 16& 4& 4\end{array}$

Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.

In the given figure, AC = AE. Select the statements that are true.

In an A.P. the two consecutive terms are (2n+3) and (2n+5). Find the common difference of the A.P.

Which of the following options are equal to $co{s}^{2}A-si{n}^{2}A$?

In the figure, PB and QA are perpendicular to segment AB. If OA = 5 cm, PO = 7cm and area ($\Delta$QOA) = 150 $c{m}^2$, find the area of $\Delta$POB.

Use method of contradiction to show that $\sqrt{3}$ and $\sqrt{5}$ are irrational numbers.

The product of two consecutive natural numbers is 72. Frame the quadratic equation.