(English Medium) ICSE Class 9 - CISCE Question Bank Solutions

In right-angled triangle ABC; ∠ B = 90°. Find the magnitude of angle A, if: AB is √3 times of BC.

In right-angled triangle ABC; ∠B = 90°. Find the magnitude of angle A, if:
BC is `sqrt(3)` times of AB.

A ladder is placed against a vertical tower. If the ladder makes an angle of 30° with the ground and reaches upto a height of 15 m of the tower; find length of the ladder.

A kite is attached to a 100 m long string. Find the greatest height reached by the kite when its string makes an angles of 60° with the level ground.

Find AB and BC, if:

Find AB and BC, if:

Find AB and BC, if:

Find PQ, if AB = 150 m, ∠ P = 30° and ∠ Q = 45°.

Find PQ, if AB = 150 m, ∠P = 30° and ∠Q = 45°.

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If tan x° = `(5)/(12)`,

tan y° = `(3)/(4)` and AB = 48 m; find the length of CD.

The perimeter of a rhombus is 96 cm and obtuse angle of it is 120°. Find the lengths of its diagonals.

Solve graphically the simultaneous equations given below. Take the scale as 2 cm = 1 unit on both the axes.
x - 2y - 4 = 0
2x + y = 3

The sides of a triangle are given by the equations y - 2 = 0; y + 1 = 3 (x - 2) and x + 2y = 0.
Find, graphically : 
(i) the area of a triangle;
(ii) the coordinates of the vertices of the triangle.

The cost of manufacturing x articles is Rs. (50 + 3x). The selling price of x articles is Rs. 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.

Use your graph to determine:
No. of articles to be manufactured and sold to break even (no profit and no loss).

The cost of manufacturing x articles is Rs.(50 + 3x). The selling price of x articles is Rs. 4x.

On a graph sheet, with the same axes, and taking suitable scales draw two graphs, first for the cost of manufacturing against no. of articles and the second for the selling price against the number of articles.

Use your graph to determine:
The profit or loss made when (a) 30 (b) 60 articles are manufactured and sold.

Find graphically, the vertices of the triangle whose sides have the equations 2y - x = 8; 5y - x = 14 and y - 2x = 1 respectively. Take 1 cm = 1 unit on both the axes.

Using the same axes of co-ordinates and the same unit, solve graphically :
x + y = 0 and 3x - 2y = 10.
(Take at least 3 points for each line drawn).

Solve graphically, the following equations.
x + 2y = 4; 3x - 2y = 4.
Take 2 cm = 1 unit on each axis.
Also, find the area of the triangle formed by the lines and the x-axis.

Use the graphical method to find the value of 'x' for which the expressions `(3x + 2)/(2) and (3)/(4)x - 2`

The course of an enemy submarine, as plotted on rectangular co-ordinate axes, gives the equation 2x + 3y = 4. On the same axes, a destroyer's course is indicated by the graph x - y = 7. Use the graphical method to find the point at which the paths of the submarine and the destroyer intersect?