Mathematics (211)
Tutor Marked Assignment (2021-22)
20% Marks Of Theory
1. Answer any one of the following questions.
(b) A rectangular sheet of paper 44cm × 18cm is rolled along its length and a cylinder is formed. Find the volume of the cylinder.
Ans- Given, a rectangular sheet of paper 44 cm x 18 cm is rolled a along its length to form a cylinder.
Height of cylinder = 18 cm
Circumference = 44 cm
2πr = 44
R = 7
Volume of the cylinder = πr2h
=2772 cm³
2. Answer any one of the following questions.
(b) Determine the ratio in which the line 3x + y – 9 = 0 divides the segment joining the points (1, 3) and (2,7)
Ans- Let the given points be A(1, 3) and B(2, 7).
Let the line 3x + y -9=0 divides the line segment AB in the ratio K: 1 at point P. Then the co-ordinates of Pare given by
3. Answer any one of the following questions.
(a) The length of a rectangle is 12 m more than twice the width. The area of the rectangle is 320 Square meter. Write an equation that can be used to find the length and width of the rectangle. Also find the dimensions of the rectangle.
Ans- let
Width=xm
length=(2x+12)m
area
of the rectangle-320 lengthx
width=320
(2x+12)×X320
2×(x+6)x=320
X(X+6)=160
X²+6x-160-0
X²-10x+16x-160-0
X(x-10)+16(x-10)=0
(x-10)(x+16)=0
x-10=0
or x+16=0
x=10 or
x= -16
x should be positive
value
X=10
Therefore
Width=x=10m
Length=2x+12
=2×10+12
= 20 + 12 = 32m
4. Answer any one of the following questions.
(b) If the bisector of an angle of a triangle bisects the opposite side, prove that the triangle is isosceles.
Ans:- Given, AABC, AD bisects LA and AD bisects BC. To prove:
ABC is an Isosceles triangle In AABD and AACD
ZDAB = ZDAC (AD
Bisects ZA) AD = AD (Common)
BDCD (AD bisects BC)
Thus, AABD
AACD (SAS rule)
Thus, AB = AC (By cpct)
hence, ABC is an
Isosceles triangle.
5. Answer any one of the following questions.
(a) If 6 times the 6th term of an A.P is equal to 9 times its 9th term, then show that its 15th term is zero.
Ans-
6. Prepare any one project out of the given below:
(a) Conduct a survey of atleast 50 households from your locality/village, regarding population and family income.
(i) the data related to family members in tabular form mentioning frequencies.
Ans-
(ii) Calculate the average family size. How many families are above the average family size?
Ans-
(iii) Draw the Bar graph for top 10 earning families.
Ans-
