CBSE 2010 CLASS X MATHS SET NO2 

An iron pillar has lower part in the form of a right circular cylinder and the upperpart in the form of a right circular cone. The radius of the base of each of the cone and cylinder is 8 cm. The cylindrical part is 240 cm high and the conical part is 36 cm high. Find the weight
of the pillar if 1cm3 of iron weighs 7.5 grams. (Take π=22/7 )
 
A container (open at the top) made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with radii of its lower and upper ends as 8 cm and 20 cm
respectively. Find
(i) the cost of milk when it is completely filled with milk at the rate of Rs 15 per litre. (ii) the cost of metal sheet used, if it costs Rs 5 per 100 cm2 ( Take π= 3.14)  
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the
squares of the other two sides.
Use the above theorem, in the following.
If ABC is an equilateral triangle with AD perpendicular to BC, then AD^{ 2} = 3 DC^{ 2}
 
Prove that the ratio of areas of two similar triangles is equal to the square of the ratio of
their corresponding sides.
Use the above theorem, in the following.
The areas of two similar triangles are 81 cm^{ 2} and 144 cm^{ 2}. If the largest side of the smaller
triangle is 27 cm, find the largest side of the larger triangle.
 
There are two poles, one each on either bank of a river, just opposite to each other. One
pole is 60m high. From the top of this pole, the angles of depression of the top and the
foot of the other pole are 30° and 60° respectively. Find the width of the river and the
height of the other pole.
 
Solve the following system of linear equations graphically:
3x + y  12 = 0 x  3y + 6 = 0 Shade the region bounded by these lines and the xaxis. Also find the ratio of areas of triangles formed by given lines with xaxis and the yaxis.  
Construct a triangle similar to given ABC in which AB = 4 cm, BC = 6 cm and ABC =
60°, such that each side of the new triangle is ¾ of given δABC.
 
In what ratio does the point P(2,5) divide the line segment joining A(3,5) and B(4,9)?
 
For what value of ‘K’ the points A (1,5), B (K,1) and C (4,11) are collinear?
 
Prove that the points A(3,0), B(1,3) and C(4,1) are the vertices of an isoscles right triangle.
 
Find the sum of all three digit numbers which leave the remainder 3 when divided by 5.
 
Determine an A.P. whose 3rd term is 16 and when 5th term is subtracted from 7th term,
we get 12.
 
For what value or ‘k’ will the following pair of linear equations have infinitely many solutions
kx + 3y = k3 12x + ky = k  
Prove that 5 + √2is irrational.
 
Find the zeroes of the quadratic polynomial x^{ 2} + 5x + 6 and verify the relationship between
the zeroes and the coefficients.
 
All cards of ace, jack and queen are removed from a deck of playing cards. One card is
drawn at random from the remaining cards. find the probability that the card drawn is
a) a face card b) not a face card  
Find the values of x for which the distance between the point P (2,3) and Q (x,5) is 10
units.
 
Express sin67°+ Cos75o in terms of trigonometric ratios of angles between 0° and 45°
 
From your pocket money, you save Rs.1 on day 1, Rs. 2 on day 2, Rs. 3 on day 3 and so
on. How much money will you save in the month of March 2008 ?
 
The height of a tower is 10m. Calculate the height of its shadow when Sun’s altitude is
45°.
 
What is the distance between two parallel tangents of a circle of the radius 4 cm?
 
A bag contains 5 red and 4 black balls. A ball is drawn at random from the bag. What is the
probability of getting a black ball?
 
Which measure of central tendency is given by the xcoordinate of the point of intersection
of the ‘more than’ ogive and ‘less than’ ogive?
 
The length of tangent from a point A at a distance of 5 cm from the centre of the circle is 4
cm. What will be the radius of the circle?
 
What is the nature of roots of the quadratic equation
4x^{2}  12x  9 = 0?
 
Give an example of polynomials f(x), g(x), q(x), and r(x) satisfying
f(x) = g(x) • q(x) + r(x) where deg r(x) = 0.
 
State the Fundamental Theorem of Arithmetic.
 
The interior of building is in the form of a right circular cylinder of radius 7m and height 6m,
surmounted by a right circular cone of same radius and of vertical angle 60°. Find the
cost of painting the building from inside at the rate of Rs 30/m^{ 2}
 
 
CBSE 2010 CLASS X MATHS sample paper guess paper model question important questions cbse board Central Board for Secondary Education

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