Summative Assesment-II
MATHEMATICS
CLASS X
M.M: 80 Time :3 Hrs.
GENERAL INSTRUCTIONS :
1. All questions are compulsory.
2. The question paper is divided into four sections
Section A : 10 qusetions ( 1 mark each)
Section B : 8 questions ( 2marks each)
Section C : 10 questions (3 marks each)
Section D : 6 questions (4 marks each)
3. There is no overall choice. However, internal choice has been provided in
1 question of two marks, 3 questions of three marks and 2 questions of four marks each.
1 question of two marks, 3 questions of three marks and 2 questions of four marks each.
4. Use of calculators is not allowed.
SECTION A
Q1. Which of the following equations has the sum of its roots as 3?
(a) 2x2-3x+6=0
(b)-x2+3x-3=0
(c) x2+5x+6=0
(d) 3x2-3x+3=0
(a) 26th (b) 27th (c) 28th (d) 29th
Q3. In the given figure, PA & PB are tangents to the circle drawn from an
external point P. CD is a third tangent touching the circle at Q. If PB=10cm
and CQ=2cm, then the length of PC is
external point P. CD is a third tangent touching the circle at Q. If PB=10cm
and CQ=2cm, then the length of PC is
(a) 8 cm (b) 10 cm (c) 12 cm (d) 14 cm
Q4. A vertical tower is 20 m high. A man at some distance from the tower knows
that the cosine of the angle of the elevation of the top of tower is 0.5. He is standing
from the foot of the tower at a distance of
that the cosine of the angle of the elevation of the top of tower is 0.5. He is standing
from the foot of the tower at a distance of
Q5. From a well-shuffled pack of 52 cards, a card is drawn at random. Theprobability
that it is a face card is
that it is a face card is
Q6. The area of a quadrant of a circle whose circumference is 22 cm is
Q7. The radii of the ends of a frustum of a cone of height h cm are r1 cm and r2 cm.
The volume in cm3 of the frustum of the cone is
The volume in cm3 of the frustum of the cone is
Q8. The radii of two circles are 19 cm and 9 cm respectively. The radius of the circle
which has its circumference equal to the sum of the circumferences
which has its circumference equal to the sum of the circumferences
of the two circles is
(a) 28 cm (b) 30 cm (c) 26 cm (d) 32 cm
Q9. The coordinates of a point A, where AB is diameter of a circle whose
centre is (2,-3) and B is (1,4), are
(a) (3,0) (b) (0,-10) (c) (3,4) (d) (3,- 10)
Q10. The distance between the points (3,4) and (8,-6) is
(a) 5 units (b) 2 5 units (c) 3 5 units (d) 5 5 units
SECTION B
Q11. Solve:
Q12. Show that a-b,a and a+b form consecutive terms of an AP.
Q13. PA and PB are tangents from P to the circle with centre O. At point M, a
tangent is drawn cutting PA at K and PB at N. prove that KN=AK+BN.
Q14. ABCD is a quadrilateral such that LD=90°. A circle C(o,r) touches the
sides AB,BC,CD and DA at P,Q,R and S respectively. If
BC=38cm,CD=25cm and BP=27cm, then find r.
Q15. A bag contains 5 red balls and some blue balls. If the probability of
drawing a blue ball is double that of a red ball, find the number of blue
balls in the bag.
OR
Savita and Hamida are friends. What is the probability that both will have
(i) the same birthday? (ii) different birthdays?
Q16.The points (4,-1),(6,0),(7,2) and (5,1) are the vertices of a rhombus. Is it also a square?
Q17. The length of the minute hand of a clock is 14cm. Find the area swept by the
minute hand in 5 minutes.
minute hand in 5 minutes.
Q18. In the given figure, ABC is an equilateral triangle inscribed in a circle of
radius 4cm with centre O. find the area of the shaded region.
SECTION C
Q19. For what value(s) of p does the equation px2+(p-1)x+(p-1)=0 have a
repeated root?
Q20. If m times the mth term of an AP is equal to n times its nth term,
show that the (m+n)th term of the AP is zero
show that the (m+n)th term of the AP is zero
OR
Solve the equation:
1+4+7+10+…..+ x =287
Q21. Prove that the area of triangle whose vertices are (t,t-2),(t+2,t+2) and
(t+3,t) is independent of t.
Q22. Construct a triangle similar to a given triangle ABC, with sides measuring
5cm, 6cm and 8cm, such that its sides are 6/5 of the corresponding sides of
Q23. Two pillars of equal height and on either side of a road, which is 100m
wide. The angles of elevation of the top of the pillars are 60o and 30o at a
point on the road between the pillars. Find the height of the pillars.
OR
A person, standing on the bank of a river, observes that the angle of
elevation subtended by a tree on the opposite bank to be 60o. When he
moves 20m away from the bank, he finds the angle to be 30o. Find the
width of the river.
Q24.
What is the probability of having 53 Thursdays in a leap year?
Q25.
Prove that the points (-2,5), (3,-4) and (7,10) are the vertices of an
isosceles right triangle.
OR
Prove that the points (a,b+c), (b,c+a) and (c,a+b) are collinear.
Q26. A bucket is raised from a well by means of a rope which is wound round
a wheel of radius 38.5 cm. Given that the bucket ascends in 1 min. 28
a wheel of radius 38.5 cm. Given that the bucket ascends in 1 min. 28
seconds with a uniform speed of 1.1 m/sec calculate the number of complete
revolutions the wheel makes in raising the bucket.
revolutions the wheel makes in raising the bucket.
Q27. Three cubes of metal whose edges are in the ratio 3:4:5 are melted
and converted into a single cube whose diagonal is 12 3 cm. Find the edges
and converted into a single cube whose diagonal is 12 3 cm. Find the edges
of the three cubes.
Q28. An iron pole consisting of a cylindrical portion 110cm high and of base
diameter 12cm is surmounted by a cone which is 9cm high. Find the mass
of the pole, given that 1 cu cm of iron has 8gm mass(approx.)
SECTION D
Q29. The diagonal of a rectangular field is 60 metres more than the shorter
side. If the longer side is 30 metres more than the shorter side, find the
length of the sides of the field.
OR
A peacock is sitting on the top of a pillar, which is 9m high. From a point
27m away from the bottom of the pillar, a snake is coming to its hole, at
the base of the pillar. Seeing the snake the peacock pounces on it. If their
speeds are equal, then at what distance from the hole is the snake caught?
the base of the pillar. Seeing the snake the peacock pounces on it. If their
speeds are equal, then at what distance from the hole is the snake caught?
Q30. Find the number of natural numbers which lie between 101 and 304 and
are divisible by 3 or 5. Also, find their sum.
are divisible by 3 or 5. Also, find their sum.
OR
The gate receipts at the show of a film amounted to Rs. 6500 on the first night
and showed a drop of Rs. 110 every succeeding night. If the operational expenses
of the show are Rs. 1000 a day, then find on which night the show ceases to be profitable.
and showed a drop of Rs. 110 every succeeding night. If the operational expenses
of the show are Rs. 1000 a day, then find on which night the show ceases to be profitable.
Q31. Prove that the radius of a circle is perpendicular to the tangent at the point of contact.
Q32. From the top of a lighthouse, the angles of depression of two ships on the
opposite side of it are observed to be a and ß. If the height of the lighthouse is
h metres and the line joining the ships passes through the
opposite side of it are observed to be a and ß. If the height of the lighthouse is
h metres and the line joining the ships passes through the
foot of the lighthouse, show that the distance between the ships is
Q33. Two tangents TP and TQ are drawn to a circle with centre O from an
external point T.
Q34. The height of a cone is 30cm. A small cone is cut off from the top by a
pane parallel to the base. If its volume is 1/27 of the volume of the given cone, at what
height above the base is the section made?
pane parallel to the base. If its volume is 1/27 of the volume of the given cone, at what
height above the base is the section made?