Mathematics Question Paper for X Std.

MATRICULATION – X STD

MATHEMATICS – PAPER – I click

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Time : 2 Hr. 30 Min Max. Marks : 100

Part – I
Note : i) This Part contains two sections – Section A and Section B
ii) Section A .contain Multiple Choice Questions. Answer all the 20 questions. Each question
carries 1 mark.
iii) Section B contains 15 questions. Answer any 10 questions. Each question carries 2 marks.
Section – A
I Choose the correct answer from the given alternatives: [20 x 1 = 20]
1. The general term of a G.P is
a ( 1 – rn )
a) ------------- b) ar n – 1 c) a + ( n – 1) d d) arn
1 – r
2. The ratio of sum of n terms of an A.P. to the sum of m terms is 256 : 441 then the ratio of the
mth term to the nth term is
a) 31 : 41 b) 16 : 21 c) 21 : 16 d) 41 : 31
3. 1,1,1,1 … is __________.
a) A.P. only b) G.P. only c) A.P. & G.P. d) Neither A.P nor G.P.
4. The sum of the squares of all the elements in the set A = {x / x €N, x is even and 2 a) 216 b) 220 c) 465 d) 11220
5. The relation between the volume ‘V’ of a sphere of radius ‘ r ’ and its surface area ‘ S ’ is
2 1 4
a) V = ---- r S b) V = ---- r S c) V = ---- r S d) V = 4 S
3 3 3
6. The ratio of the volumes of three solids namely cylinder, cone and hemisphere having equal
base area and height is
a) 1 : 3 : 2 a) 3 : 1 : 2 a) 2 : 3 : 1 a) 1 : 2 : 3
7. A solid frustum of radius ‘ R ‘ and ‘ r ‘ such that R > r is kept inside a hollow cylinder radius
‘R’ .Both cylinder and frustum, have same height ‘h’ .If water is filled in it. What is the
volume of water needed?
1 1
a) ---- Π h ( r2 + R r + R2 ) b) ---- Π h ( R2 + R r ) c) (2 R2 – Rr – r2) d) Π R2 h
3 3
8. B – A is defined as
a) { x / x € A,x € B } b) { x / x € B,x € A }
c) { x / x € A,x € B} d) { x / x € B,x € A and B }
9. X – gene in a plant is responsible for red flowers and Y – gene for white flowers. If both are present
, then the flowers produced are pink .If 20 plants have X-gene, 20 plants have Y-gene and there are 30
plants in all, then the total number of plants producing pink flowers are
a) 13 b) 10 c) 20 d) 30
10. If A and B are any two sets, then A ∩ B’ =
a) A + B b) A – B c) A U B d) A ∩ B
11. Which of the following is incorrect ?
a) set of all real numbers is not a subset of rational numbers
b) set of all irrational and rational numbers are overlapping
c) N – Z = φ d) f o g = g o f when f (x) = x2,g(x) = √ x
12. A comet is heading for Jupiter with acceleration a = 50 kms -2 .The velocity of the comet at
time ‘t’ is given by f( t) = at2 – at + 1.Then the velocity at time t = 5 second is
a) 900 kms-1 a) 1001 kms-1 a) 2001 kms-1 a) 50 kms-1
13. The difference between C.I and S.I on Rs. 6000 for 2 years at 4% per annum is
a) Rs. 19.2 b) Rs. 9.6 c) Rs. 4.8 d) Rs. 12.4
14. Short term fixed deposits are accepted by the banks for a short period ranging from ____ to
a) 46 days. 1 year b) 46 days 2 years c) 40 days, 1 year d) 56 days,1 year
15. A recurring deposit of Rs. 50 per month at 10 % S.I per annum will fetch at the end of 2
years an interest of
a) Rs. 250 b) Rs.125 c) Rs. 375 d) Rs. 500
16. If the roots of 5bx2 – (5 + b) 2 x + (5 + b) 2 – 0 are 2, 2 find b
a) 4 b) 2 c) 5 d) 9
17. Which of the following is true?
a) degree of the quadratic equation ,is one
b) the solution of x2+x+5 € R
c) degree of HCF of 2 polynomials ≤ degree of the product of the polynomials
d) degree of x2+2x2+1 is 2
18. The nature of the roots of x2+ax+bx+ab = 0 is
a) real, distinct and rational b) real, distinct and irrational c) not real d) real and equal
x
19. The partial fraction representation of ------------ is of the form
(x + 1)2
A A B Ax + B Ax + B C x + D
a) -------- b) -------- + -------- c) ----------- d) ---------- + ----------
x + 1 x + 1 (x + 1)2 (x + 1)2 x + 1 (x + 1)2
α2 β2
20. If α and β are the roots of ax2 + 3x + 2 = 0; a statement is β α
a) m 1 c) m > 0 d) m > 2
Section – B
II Answer any 10 questions : 10 x 2 = 20
21. Find the middle term of an A.P. 3, 5, 7…71.
1 2
22. Which term of the A.P. 19, 18 -----, 17 ------ is the first negative term?
5 5
23. Evaluate the following : 1 + 4 + 9 + … + 225.
24. Find the radius of the cylinder if the area of its curved surface is 352 cm2 and its height 16
cm.
25. Two cones have their height in the ration 5 : 3 and the radii of their bases in the ratio 2 : 1
, find the ratio of their volumes.
26. How many litres of water will a hemispherical tank hold, whose diameter is 4.2 m?
27. If f(x) = ± √ x , x € N and f(x) € R.Check whether f is a function or not and give reason.
28. Given U = { 1,2,3,…10} , A = {3,4,6,10} , B = {1,2,4,5,6,8} Verify De Margan’s laws of
complementation. (i) (AUB)’ = A’ ∩ B’.
29. Given : f (x) = 3x – 2, g(x) = kx + 3, find k so that f o g = g o f.
30. Chezhian wants to invest Rs.10000 in a bank which pays 6 % interest per annum for 2 years
.He is not able to decide whether to invest in compound interest or simple interest kindly
advise him.
31. Ebi deposits Rs.100 every month in a bank paying 8% p.a.S.I. on R.D. How much will she
pay at the end of 60 months ?
32. If the remainder when a – 2x + 5x2 divided by x – 2 is 7, then find a.
33. Find the LCM of the following: x2 – 10x + 24, x2-11x+30
34. If M(x+ 3) + N(x – 2) ≡ 8x + 9 , find the values of M and N.
35. If one root of the equation x2 – 3x + q = 0 is twice the other, find the value of q.
Part – II
Note : (i) This Part contains four sections – Section C,Section D,Section E, and Section F.
(ii) Section C and Section E contain 3 questions. Answer any 2 questions in each section.
(iii) Section D and Section F contain 4 questions. Answer any 3 questions in each section,
(iv) Each question carries 5 marks.
Section – C
III Answer any 2 questions : 2 x 5 = 10
36. If S1,S2,S3 be the sum of n terms of three arithmetic series, the first term of each being 1 and
the respective common differences are 1, 2,3, prove that S1, + S3 = 2 S2 .
37. If p = 3 √ 3 x 3 √ 32 x 3 √ 33 … ∞ ,then find 3 √ p
38. Find 5 numbers in G.P whose product is 32 and the product of the last two numbers is 108.
Section – D
IV Answer any 3 questions : 3 x 5 = 15
39. Using Venn Diagram verify : A – ( B U C ) = (A – B) ∩ (A – C)
40. Given f(x) = 5x + 2,g(x) = 2x – 3,h(x) = 3x + 1,verify f o (g o h) = (f o g) o h.
41. Radha borrowed Rs.6000 at 6% S.I.per annum and immediately lent it to Nargis at 6 % .C.I.
per annum .How much did she gain at the end of 3 years?
42. Ramya invested Rs.500 every month for 2 years in a bank and collects Rs.12500 at the end of
2 years .Find the rate of simple interest paid by the bank on recurring deposit?
Section – E
V Answer any 2 questions: 2 x 5 = 10
43. Through a pipe of diameter 14 cm water flows uniformly at the rate of 3 km per hour. How
much water will flow through it in 10 minutes?
44. A hollow spherical shell has an inner radius of 8 cm.If the volume of the material is
1952 Π
------------ c.c, find the thickness of the shell.
3
45. A sector containing an angle of 90o is cut from a circle of radius 20 cm and folded into a
cone. Find the curved surface area of the cone.
Section – F
VI Answer any 3 questions: 3 x 5 = 15
46. Given that px2 + qx + 6 = 0 leaves a remainder 1 on division by 2x + 1 and 2 qx2 + 6x + p
leaves a remainder 2 on division by 3x – 1.Find p and q.
47. Find the values of a and b if the following polynomial to be a perfect square
3
x4 – 2x3 – (-----) x2 + ax + b
2
x2+x+1
48. Decomposite into partial fractions : ------------------
(x – 2)2 (x+2)
49. Solve : 4x – 3(2) x+3 + 128 = 0
Part – III
Note : (i) This section contains 2 questions .Answer any 1 question.
(ii) Each question carries 10 marks.
Section – G
VII Answer any 1 question: 1 x 10 = 10
50. Draw the graph of y = 2x2 – 5x+2 and hence solve the equation 2x2 – 5x + 3 = 0
51. Solve graphically the equation x2 – x – 12 = 0