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A box contains 3 black balls, 4 red balls and 3 green balls. All the balls are identical in shape and size. Rohit takes out a ball from the bag without looking into it. What is the probability that the ball drawn is a black ball?

Draw a right triangle ABC is which AB = 6 cm, BC = 8 cm and $\angle B={90}^{\circ }$. Draw BD perpendicular from B on AC and draw a circle passing through the points B, C and D.
Construct tangents from A to this circle.

If the number $91876y2$ is completely divisible by $8$, then the smallest whole number in place of $y$ will be:

Which term of the A.P. 3,10,17,... will be 84 more than its 13th term?

The number of points on x-axis which are at a distance $c(c<3)$ from the points (2, 3) is

If the point $A(3,-2,4),B(1,1,1)$ and $C(-1,4,-2)$ are collinear then $(CA:AB)=$

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is a red card.

1. 36

On a graph paper, plot the triangle ABC, whose vertices are at the points A (3, 1), B(5, 0) and C (7, 4).

On the same diagram, draw the image of the triangle ABC under reflection in the origin O (0, 0).

An aeroplane takes 1 hour less for a journey of 1200km if its speed is increased by 100 km/hr from its usual speed of the plane.

If x - 2 is a factor for $x^2+ax+b$ and a + b = 1, find the values of a and b.

A die is thrown once. Find the probability of getting
(i) an even number (ii) a number less than 5
(iii) a number greater than 2 (iv) a number between 3 and 6
(v) a number other than 3 (vi) the number 5.

The $n^{th}$ term of a sequence is $3n–2$. Is the sequence an A.P. ? If so, find its ${10}^{th}$ term.

Question 1 (viii)
Without actually performing the long division, state whether $\frac{6}{15}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

A card is drawn at random from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a kind nor a queen.

Find the value of x + y in the figure given below:

Solve the following pair of equations:

$\frac{1}{x}+\frac{3}{y}=1$

$\frac{6}{x}-\frac{12}{y}=2$

(Where $x\ne 0,y\ne 0)$

If an object is dropped from a height of 39 feet, the function $h\left(t\right)=-16t^2+39$ gives the height of the object after t seconds. Choose the graph of the function.

Let ${\sin }^{-1}x+{\cos }^{-1}y=\lambda \pi ,$ where $x+\frac{1}{x}=2$ and $y+\frac{1}{y}=-2.$ Then $\lambda$ is equal to

Gopi buys a fish from a shop for his aquarium. The shopkeeper takes out one fish at random from a tank containing 5 male fish and 8 female fish (see figure). What is the probability that the fish taken out is a male fish?

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, find the distance between their tops.

A card is drawn at random from a well shuffled deck of 52 cards. Find the probability of getting a card bearing a number greater than 2 but less than 9.

Find the area of the smaller part of
the circle x² + y² = a²
cut off by the line

In $\Delta ABC$. and E are the mid-points of AB and AC respectively. Find the ratio of the areas of $\Delta AED$ and $\Delta ABC$.

Question 14
A 1.2 m tall girl spots a balloon moving with the wind in a horizontal line at a height of 88.2 m from the ground. The angle of elevation of the balloon from the eyes of the girl at any instant is ${60}^{\circ }$. After some time, the angle of elevation reduces to ${30}^{\circ }$. Find the distance travelled by the balloon during the interval.

The probability that a leap year has 53 Sundays is