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If x + y + z = 0, show that x3 + y3 + z3 = 3xyz.
Concept: undefined >> undefined
Without actually calculating the cubes, find the value of the following:
(–12)3 + (7)3 + (5)3
Concept: undefined >> undefined
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Without actually calculating the cubes, find the value of the following:
(28)3 + (–15)3 + (–13)3
Concept: undefined >> undefined
Give possible expression for the length and breadth of the following rectangle, in which their area are given:
| Area : 25a2 – 35a + 12 |
Concept: undefined >> undefined
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
Concept: undefined >> undefined
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 3x2 – 12x |
Concept: undefined >> undefined
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
Concept: undefined >> undefined
Show that in a right angled triangle, the hypotenuse is the longest side.
Concept: undefined >> undefined
In the given figure sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB.
Concept: undefined >> undefined
In the given figure, ∠B < ∠A and ∠C < ∠D. Show that AD < BC.
Concept: undefined >> undefined
AB and CD are respectively the smallest and longest sides of a quadrilateral ABCD (see the given figure). Show that ∠A > ∠C and ∠B > ∠D.
Concept: undefined >> undefined
In the given figure, PR > PQ and PS bisects ∠QPR. Prove that ∠PSR >∠PSQ.
Concept: undefined >> undefined
Show that of all line segments drawn from a given point not on it, the perpendicular line segment is the shortest.
Concept: undefined >> undefined
ABC is a triangle. Locate a point in the interior of ΔABC which is equidistant from all the vertices of ΔABC.
Concept: undefined >> undefined
In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
Concept: undefined >> undefined
In a huge park people are concentrated at three points (see the given figure):
A: where there are different slides and swings for children,
B: near which a man-made lake is situated,
C: which is near to a large parking and exit.
Where should an ice-cream parlour be set up so that maximum number of persons can approach it?
(Hint: The parlor should be equidistant from A, B and C)
Concept: undefined >> undefined
Complete the hexagonal and star shaped rangolies (see the given figures) by filling them with as many equilateral triangles of side 1 cm as you can. Count the number of triangles in each case. Which has more triangles?
Concept: undefined >> undefined
In the given figure, ∠ABC = 69°, ∠ACB = 31°, find ∠BDC.
Concept: undefined >> undefined
In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130° and ∠ECD = 20°. Find ∠BAC.
Concept: undefined >> undefined
Simplify the following
`3(a^4b^3)^10xx5(a^2b^2)^3`
Concept: undefined >> undefined
