summative assessment i (2011) lakdfyr ijh{kk&i...
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SUMMATIVE ASSESSMENT –I (2011)
Lakdfyr ijh{kk&I
MATHEMATICS / xf.kr
Class – X / & X
Time allowed : 3 hours Maximum Marks : 80
fu/kkZfjr le; % 3 ?k.Vs : 80
General Instructions:
(i) All questions are compulsory.
(ii) The question paper consists of 34 questions divided into four sections A,B,C and D.
Section A comprises of 10 questions of 1 mark each, section B comprises of 8
questions of 2 marks each, section C comprises of 10 questions of 3 marks each and
section D comprises 6 questions of 4 marks each.
(iii) Question numbers 1 to 10 in section A are multiple choice questions where you are
to select one correct option out of the given four.
(iv) There is no overall choice. However, internal choice have been provided in 1
question of two marks, 3 questions of three marks each and 2 questions of four
marks each. You have to attempt only one of the alternatives in all such questions.
(v) Use of calculator is not permitted.
lkekU; funsZ”k %
(i) lHkh iz”u vfuok;Z gSaA
(ii) bl iz”u i= esa 34 iz”u gSa, ftUgsa pkj [k.Mksa v, c, l rFkk n esa ckaVk x;k gSA [k.M & v esa 10 iz”u gSa
ftuesa izR;sd 1 vad dk gS, [k.M & c esa 8 iz”u gSa ftuesa izR;sd ds 2 vad gSa, [k.M & l esa 10 iz”u gSa
ftuesa izR;sd ds 3 vad gS rFkk [k.M & n esa 6 iz”u gSa ftuesa izR;sd ds 4 vad gSaA
(iii) [k.M v esa iz”u la[;k 1 ls 10 rd cgqfodYih; iz”u gSa tgka vkidks pkj fodYiksa esa ls ,d lgh fodYi
pquuk gSA
(iv) bl iz”u i= esa dksbZ Hkh loksZifj fodYi ugha g S, ysfdu vkarfjd fodYi 2 vadksa ds ,d iz”u esa, 3 vadksa ds 3
iz”uksa esa vkSj 4 vadksa ds 2 iz”uksa esa fn, x, gSaA izR;sd iz”u esa ,d fodYi dk p;u djsaA
(v) dSydqysVj dk iz;ksx oftZr gSA
Section-A
Question numbers 1 to 10 carry one mark each. For each questions, four alternative choices have been provided of which only one is correct. You have to select the correct choice.
560039
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1.Euclid’s division lemma states that if a and b are any two ve integers, then there exists
unique integers q and r such that :
(A) abqr, 0 < r < b (B) abqr, 0 r b
(C) abqr, 0 r < b (D) abqr, 0 < b < r
a b q r
(A) abqr, 0 < r < b (B) abqr, 0 r b
(C) abqr, 0 < r < b (D) abqr, 0 < b < r
2. If 1 is zero of the polynomial p(x)ax2
3(a1) x1, then the value of ‘a’ is
(A) 1 (B) 1 (C) 2 (D) 2
p(x)ax23(a1) x1 1 a
(A) 1 (B) 1 (C) 2 (D) 2
3. If PQR~XYZ, Q = 50 and R = 70, then XY is equal to :
(A) 70 (B) 50 (C) 120 (D) 110
PQR~XYZ Q = 50 R = 70 XY
(A) 70 (B) 50 (C) 120 (D) 110
4.
If tanA5
12, find the value of (sinAcosA)secA :
(A) 6
13 (B)
7
12 (C)
17
12 (D)
12
17
tanA5
12(sinAcosA)secA
(A) 6
13 (B)
7
12 (C)
17
12 (D)
12
17
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5. If sin (36) cos, where and 36 are acute angles, then value of is
(A) 36 (B) 54 (C) 27 (D) 90
sin (36) cos, 36
(A) 36 (B) 54 (C) 27 (D) 90
6.
If cosec2x and ycot2 then the value of 22
14 x
y
is :
(A) 1 (B) 1
2 (C)
1
3 (D)
1
4
cosec2x ycot2 22
14 x
y
(A) 1 (B) 1
2 (C)
1
3 (D)
1
4
7. 1192
1112 is :
(A) Prime number (B) Composite number
(C) An odd prime number (D) An odd composite number
11921112
(A) (B)
(C) (D)
8. If xa, yb is the solution of the equations xy2 and xy4 , then the values of
a and b are, respectively.
(A) 3 and 5 (B) 5 and 3 (C) 3 and 1 (D) 1 and3
xa yb xy2 xy4 a b
(A) 3 5 (B) 5 3 (C) 3 1 (D) 1 3
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9. In ABC, if AB90, cot B
3
4, then the value of tan A is :
(A) 4
5 (B)
3
4 (C)
4
3 (D)
3
5
ABC AB90, cot B3
4, tan A
(A) 4
5 (B)
3
4 (C)
4
3 (D)
3
5
10. The mean and median of same data are 24 and 26 respectively. The value of mode is :
(A) 23 (B) 26 (C) 25 (D) 30
24 26
(A) 23 (B) 26 (C) 25 (D) 30
Section-B
Question numbers 11 to 18 carry two marks each.
11. Prove that 3 5 is irrational.
3 5
12. Form a quadratic polynomial whose one of the zeroes is 15 and sum of the zeroes is 42.
15 42
13. For what value of k will the following pair of linear equations has no solution :
3xy1 ; (2k1) x(k1) y2k1
k
3xy1 ; (2k1) x(k1) y2k1
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14. Evaluate :
tan2 453 sin2 60.
tan2 453 sin2 60.
OR /
Prove that :2
1
tan1 sec
sec
2
1
tan1 sec
sec
15. If figure,
EA EB
EC ED , prove that EAB~ECD.
, EA EB
EC ED
EAB~ECD
16. If the areas of two similar triangles are equal then show that triangles are congruent.
17.
Convert the following data into a more than type distribution.
Class
Intervals
5055 5560 6065 6570 7075 7580
Frequency 2 8 12 24 38 16
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5055 5560 6065 6570 7075 7580
2 8 12 24 38 16
18. Find the mode of the following distribution :
Class 010 1020 2030 3040 4050
Frequency 15 18 16 5 6
010 1020 2030 3040 4050
15 18 16 5 6
Section-C
Questions numbers 19 to 28 carry three marks each.
19. Prove that the square of any positive integer is of the form 5m, 5m1 or 5m4 for some
integer m.
5m, 5m1 5m4 m
20. Show that 3 2 is irrational.
3 2
OR /
Prove that 7 2 2 is irrational.
7 2 2
21. Eight times a two digit number is equal to three times the number obtained by reversing the
order of its digits. If the difference between the digit is 5, find the number.
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8
5
OR /
A part of monthly expenses of a family is constant and the remaining varies with the price of
rice. When the cost of rice is ` 250 per quintal, the monthly expenditure of the family is ` 1000
and when the cost of rice is ` 240 per quintal the monthly expenditure is ` 980. Find the
monthly expenditure of the family when the cost of rice is ` 300 per quintal.
` 250 ` 1000 `240
` 980 `300
22. Find the zeroes of the quadratic polynomial 6x2
7x3 and verify the relationship between the
zeroes and the coefficients.
6x27x3
23.
Prove that 1
cosecA sinA secA cosA tanA cotA
1
cosecA sinA secA cosA tanA cotA
24. Prove that :
2cot 90 cosec 90 . sin
sectan tan 90
.
2cot 90 cosec 90 . sin
sectan tan 90
25.
In the figure given below, XY AC and XY divides triangular region ABC into two parts equal in area. Find
the ratio of AX
AB
.
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XY AC XY, ABC AX
AB
26. In figure, ABC is right angled at B and D is the mid point of BC, prove that
AC24AD2
3AB2.
ABC B BC, D
AC24AD2
3AB2.
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27. The mean of the following distribution is 62.8 and the sum of all frequencies is 50. Compute the
missing frequencies f1 and f2.
Classes 020 2040 4060 6080 80100 100120 Total
Frequency 5 f1 10 f2 7 8 50
62.8 50 f1 f2
020 2040 4060 6080 80100 100120
5 f1 10 f2 7 8 50
OR /
Find the mean of the following data :
28. Find the median of the following frequency distribution :
Section-D
Questions numbers 29 to 34 carry four marks each.
29. If two zeroes of the polynomial p(x)x46x3
26x2138x35 are 2 3 , find the other
zeroes.
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p(x)x46x3
26x2138x35 2 3
30. Prove that the ratio of the areas of two similar triangles are equal to the ratio of squares of their
corresponding sides.
OR /
Prove that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of
the other two sides.
31.
Show that3
2
sin 2 sintan
2 cos cos
3
2
sin 2 sintan
2 cos cos
OR /
Evaluate : 2 2
2
3 sec 31 sin 41 sin 49 2
cosec 59 tan 30
2 2
2
3 sec 31 sin 41 sin 49 2
cosec 59 tan 30
32. Prove that:
tan cot
1 cot 1 tan
1seccosec.
tan cot
1 cot 1 tan
1sec cosec
33. Solve the following system of linear equations graphically :
2(x1)y and x3y15.
Also find the coordinates of points where lines meet the y-axis.
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2(x1)y x3y15.
y-
34. Draw less than and more than ogive for the following distribution and hence obtain the
median.