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ICSE/ISC / Mathematics Questions

Total Questions 141
A solid consisting of a right circular cone,standing on a hemisphere,is placed upright,in a right circular cylinder,full of water,and touches the bottom. Find the volume of water left in the cylinder,having given that the radius of the cylinder is 3 cm and its height is 6 cm; the radius of the hemisphere is 2 cm and the height of the cone is 4 cm. Give your answer correct to the nearest centimetre. (Take pie=3 1/7).
A motor boat, whose speed is 15 km/hour in still water,goes 30 km downstream and comes back in a total of 4 hours 30 minutes. Find the speed of the stream.
Prove that the locus of a point equidistant from two given points in the perpendicular bisector of the line joining two points.
The line segment joining the points (5,-4) and (2,2) is divided by the point P in the ratio 1:2.Does the line x-2y=0 contain P?
Show that any four vertices of a regular pentagon form a cyclic quadilateral.
Prove that: tan A/1-cot A + cot A/1-tan A =1+tan A+ cot A
What is the sum of all positive integers less than or equal to 81 that are divisible by 3 or 5? If this question is given to us suddenly, then how can we calculate it.
what is the differnce between basic praportionality therom and midpoint therom?
Prove that the points A(-5,4),B(-1,-2) and C(5,2) are vertices of an isosceles right-angled triangle.Find the co-ordinates of the point D so that ABCD is a square.
The arithmetic mean of following distribution is 118 marks.Find the missing number x. Marks Frequencies 40 16 80 20 x 40 160 30 200 14
If angle x is acute i.e.00 <x<900 and sin 520 cosec (900-x)=1; find the measure of angle x.
Divide 1260 among A,B, and C so that the ratio between the shares of A and B is 2:3 and the ratio between the shares of B and C is 4:5.
how to construct a triangle?
who is the father of mathematics?
what is an angle?
At the rate of 10 per dozen 12 dozen eggs are bought 2 dozen eggs are broken . The rest were sold at 15 per dozen . Find his gain percnt .
WHAT is a colineary angles ?
A straight line passes through the points A(-5,2) and B(3,-6). It intersects the co-ordinate axes at points C and D. M is a point on AB which divides CD in the ratio 1:2. Find: (i) the equation of AB. (ii) the co-ordinates of points C and D. (iii) the co-ordinates of point M.
A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone is mounted on a hemisphere. If the radius of the base of the cone is 3.5 cm which is the radius of the hemisphere also and the height of the cone is 5 cm,find the volume of the water left in the tub when this solid is lowered into the water in the tub.
If 7a+8b:7c+8d = 7a-8b:7c-8d , prove that: (i) a:b = c:d (ii) 4a-5b:4c-5d = 3a+4b:3c+4d