Two different dice are tossed together. Find the probability that the product of the two numbers on the top of the dice is 6.

Concept: Concept of Probability - Random Experiment, Outcome, Equally Likely Outcomes.

The angle of elevation of an aeroplane from point A on the ground is 60˚. After flight of 15 seconds, the angle of elevation changes to 30˚. If the aeroplane is flying at a constant height of 1500√3 m, find the speed of the plane in km/hr.

Concept: Heights and Distances

The 13^{th} term of an A.P. is four times its 3^{rd} term. If its 5^{th} term is 16, then find the sum of its first ten terms.

Concept: Arithmetic Progression

A bag contains, white, black and red balls only. A ball is drawn at random from the bag.If the probability of getting a white ball is 3/10 and that of a black ball is 2/5 then find the

probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.

Concept: Concept of Probability - Random Experiment, Outcome, Equally Likely Outcomes.

At a point A, 20 metres above the level of water in a lake, the angle of elevation of a cloud is 30˚. The angle of depression of the reflection of the cloud in the lake, at A is 60˚.

Find the distance of the cloud from A.

Concept: Heights and Distances

A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is a card of spade or an ace.

Concept: Concept of Probability - Random Experiment, Outcome, Equally Likely Outcomes.

In the figure given below, PQRS is square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the intersections of its

diagonals. Find the total area of the two flower beds (shaded parts).

Concept: Circumference of a Circle

Prove that the tangent drawn at the mid-point of an arc of a circle is parallel to the chord joining the end points of the arc.

Concept: Concept of Circle - Centre, Radius, Diameter, Arc, Sector, Chord, Segment, Semicircle, Circumference, Interior and Exterior.

A truck covers a distance of 150 km at a certain average speed and then covers another 200 km at an average speed which is 20 km per hour more than the first speed. If the truck covers the total distance in 5 hours, find the first speed of the truck.

Concept: Heights and Distances

An arithmetic progression 5, 12, 19, …. has 50 terms. Find its last term. Hence find the sum of its last 15 terms.

Concept: Arithmetic Progression

Construct a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60˚. Now construct another triangle whose sides are 5/7 times the corresponding sides of ΔABC.

Concept: Division of a Line Segment

The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.

Concept: Concept of Probability - Random Experiment, Outcome, Equally Likely Outcomes.

If the coordinates of points A and B are (-2, -2) and (2, -4) respectively, find the coordinates of P such that AP =(3/7)AB, where P lies on the line segment AB.

Concept: Division of a Line Segment

All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm^{2}. [Use p = 3.14]

Concept: Circumference of a Circle

The 16^{th} term of an A.P. is five times its third term. If its 10^{th} term is 41, then find the sum of its first fifteen terms.

Concept: Arithmetic Progression

Find the 60^{th} term of the A.P. 8, 10, 12, ……., if it has a total of 60 terms and hence find the sum of its last 10 terms.

Concept: Arithmetic Progression

A bus travels at a certain average speed for a distance of 75 km and then travels a distance of 90 km at an average speed of 10 km/h more than the first speed. If it takes 3 hours to complete the total journey, find its first speed?

Concept: Heights and Distances

The 14^{th} term of an A.P. is twice its 8^{th} term. If its 6^{th} term is -8, then find the sum of its first 20 terms.

Concept: Arithmetic Progression

Construct a Δ ABC in which AB = 6 cm, ∠A = 30° and ∠B = 60°, Construct another ΔAB’C’ similar to ΔABC with base AB’ = 8 cm.

Concept: Division of a Line Segment

The probability that a number selected at random from the numbers 1, 2, 3, ..., 15 is a multiple of 4, is

`(A)4/15`

`(B)2/15`

`(C)1/5`

`(D)1/3`

Concept: Concept of Probability - Random Experiment, Outcome, Equally Likely Outcomes.