Important Questions
Mathematics
Std: 10
Max. Marks : 80
MCQ - One Mark
4 * 1 = 4
1. Two players Ranvir and Ranjit play table tennis. The
probability of Ranjit winning the match is 0.58. What is the probability of
Ranvir winning the match ?
(a) 0.58
(b) 0.36
(c) 0.42
(d) 0.18
2.
3. How many cubes of 3cm edge can be cut out of a cube of 18 cm edge ?
(a)36
(b) 72
(c) 180
(d) 216
4. If 4 men and 6 women earn Rs.1600 in 5 days and 3 men
and 7 women earn Rs.1740 in 6 days then in what time will 7 men and 6 women
earn Rs.3760 ?
(a) 6
(b) 7
(c) 8
(d) 9
Very Short Answer Questions - One Mark
5 * 1 = 5
1. Solve the quadratic equation : (3x - 4) (3x - 2) = 0.
2. Which of the following sequences are in AP.
(i) 1,2,3,4,5,6, ......
(ii) 3,6,9, 12, ......
(iii) 2,4,8, 16, 32,.....
(iv) 22, 24, 26, 28, ......
(v) 22, 32, 42, 52, ......
(vi) a0, a2, a4, a6.......
(vii) 95, 90, 85, 80,......
3. A dice is tossed once. What is the probability of the
dice coming up with a number < 8 ? What is the probability of the dice
coming up with the number 8?
4. Find the point on the x-axis which is equidistant from the points (-2,
5) and (2, -3).
5. In ΔABC ÐB = ÐC and D and E
are points on AB and AC such that BD = CE. Prove that DE||BC.
Short Answer Questions - Two Marks
10 * 2 = 20
1. Find the whole number which when decreased by 20 is
equal to 69 times the reciprocal of the number.
2. Without using trigonometric tables, evaluate :
3. A solid sphere of radius 3 cm is melted and then cast into small
spherical balls, each of diameter 0.6 cm. Find the number of balls thus
obtained.
4. The denominator of a fraction exceeds its numerator by
3. If 1 is added to both the numerator and the denominator, the difference
between the new and the original fraction is 
. Find the original fraction.
. Find the original fraction.
5. Find a30 - a20 for the AP -9,
-14, -19, -24, ......
6.
7. If two triangles are equiangular, prove that the ratio of their
corresponding sides is the same as the ratio of the corresponding
angle-bisector segments.
8.
9. Show that only one of every three consecutive positive integers is
divisible by 3.
10. If two triangles are equiangular, prove that the ratio of their
corresponding, sides is the same as the ratio of the corresponding altitudes.
Short Answer Questions - Three Mark
5 * 3 = 15
1.
2.
3. Draw a triangle ABC with sides BC = 5 cm, AB= 4 cm and ΔABC = 55°. Then
construct a triangle whose sides are 
of the
corresponding sides of the triangle ABC.
of the
corresponding sides of the triangle ABC.
4. Solve the following pair of equation by reducing them to a pair of
linear equation
5. Find the mode of the following data:
|
Xi
|
10
|
12
|
14
|
16
|
18
|
20
|
|
fi
|
5
|
3
|
10
|
3
|
2
|
1
|
Long Answer Questions - Six Marks
6 * 6 = 36
1.
2. Water flows out through a circular pipe, whose internal diameter is 2
cm, at the rate of 0.7 m per second into a cylindrical tank, the radius of
whose base is 40 cm. By how much will the level of water in the cylindrical
tank rise in half an hour ?
3.
4. Draw a circle of radius 3 cm. Take two points P and Q
on one of its extended diameters each at a distance of 5 cm from its centre.
Draw tangents to the circle from these two points P and Q.
5. Prove that the line segments joining the mid-points of
the sides of a triangle form four triangles, each of which is similar to the
original triangle.
6. A solid toy is in the form of a right circular cylinder with
hemispherical shape at one end and a cone at the other end Their common
diameter is 4.2 cm and the height of the cylindrical and conical portions are
12 cm and 7 cm respectively. Find the volume of the solid toy.
