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A bag contains 18 balls out of which x balls are red.
(i) If one ball is drawn at random from the bag, what is the probability that it is not red?
(ii) If two more red balls are put in the bag, the probability of drawing a red ball will be $\frac{9}{8}$ times the probability of drawing a red ball in the first case. Find the value of x.

Question 27

Fill in the blanks to make each statement true:

When 9 is substracted from the product of p and 4, the result is 11. The value of p is .................

A container made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of the milk which can completely fill the container at the rate of ₹ 15 per litre. (Take $\pi$= 3·14)

The number of ways in which n different things can arrange in a circle if clockwise and anti-clock-wise orders are different is ______.

Three cubes of a metal whose edges are in the ratio 3 : 4 : 5 are melted and converted into a single cube whose diagonal is 12$\sqrt{3}$ cm. Find the edges of the three cubes.

In the given figure, $\angle A={60}^{\circ }$ and $\angle ABC={80}^{\circ }$, then $\angle DPC$ and $\angle BQC$ are respectively ___.

The two equal sides of an isosceles triangle with fixed base $2\sqrt{3}\text{cm}$ are decreasing at the rate of $0.3\text{cm/sec}.$ The rate (in $\text{sq.cm/sec}$) of decrease in its area, when the two equal sides are equal to base, is equal to

The slope of the median passing through vertex A of $\Delta ABC$ whose vertices are $A(1,-3),B(-2,5)$ and $C(-3,4)$ is

A bag contains 3 blue balls and 5 green balls. What is the probability of drawing a blue ball?Give the answer up to 3 decimal places

__

The angle of elevation of the sun when the length of the shadow of the tree is √3 times the height of the tree is

Question 5

Which of the following equations has the sum of its roots as 3?

(a) $2x^2-3x+6=0$

(b) $-x^2+3x-3=0$

(c) $\sqrt{2}{x}^2-\frac{3}{\sqrt{2}}x+1=0$

(d) $3x^2-3x+3=0$​​​​​​​

$cos{1}^{\circ }\times cos{2}^{\circ }\times cos{3}^{\circ }\times \dots$$\dots ..\times cos{180}^{\circ }$
is equal to:

Evaluate $\int \frac{7x+2}{\sqrt{2x^2+5x}}dx$

(where $C$ is constant of integration)

From two points A and B on the same side of a building, the angles of elevation of the top of the building are 30° and 60° respectively. If the height of the building is 10m, find the distance between A and B correct to two decimal places.

A metallic right circular cone 20 cm high and whose vertical angle is 90° is cut into two parts at the middle point of its axis by a plane parallel to the base. If the frustum so obtained be drawn into a wire of diameter (1/16) cm, find the length of the wire.

Question 5

The class X students of a secondary school in Krishinagar have been allotted a rectangular plot of land for their gardening activity. Saplings of Gulmohar are planted on the boundary at a distance of 1 m from each other. There is a triangular lawn in the plot as shown in the figure. The students are to sow the seeds of flowering plants on the remaining area of the plot.

(a) Taking A as origin, find the coordinates of the vertices of the triangle.

(b) What will be the coordinates of the vertices of triangle PQR if C is the origin.

(c) Also calculate the areas of the triangles in these cases. What do you observe?

Explain why 0.15015001500015... is an irrational number.

If matrix $A=[a_{ij}{]}_{3\times 3}$ is defined such that $a_{ij}=\{\begin{array}{cc}2,& i=j\\ 0,& i\ne j\end{array},$ then the value of ${\ln }_{1/2}(det\left(adj\right(adj\left(A\right)\left)\right))$ is equal to

In drawing triangle ABC, it is given that AB = 3 cm, BC = 2 cm and AC = 6 cm. It is not possible to draw the triangle as:

We are given a set of first 100 naturals numbers. If the probability of the product of two numbers selected from this set be divisible by 7 is given by $\frac{p}{q}$ in it's simplest form. Then $\frac{p+q+1}{p-9}$ is ___

for what value of k 3k+2, 4k+5 and 6k-4 are in ap

Solve each of the following systems of eqautions by the method of cross-multiplication:

$\frac{2}{x}+\frac{3}{y}=13$

$\frac{5}{x}-\frac{4}{y}=-2$

Question 1 (vi)
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$3x^2-x-4$