1500 families with 2 children were selected randomly and the following data was recorded.
Number of girls in a family : 0 1 2
Number of families : 475 804 221
Compute the probability of a family, chosen at random having
i) 2 girls
ii) 1 girl
iii) No girl.
Also check whether the sum of these probabilities is 1.
Express the following statement as linear equation in two variables :‘The cost of 2 oranges and 3 apples is 45. From the equation find the cost of an apple if the cost of an orange is 7.50 OR
Find two solutions for each of the following equations
(i) 2x + y = 8
ii) x – 3y = 18
In a parallelogram ABCD, P & Q are the mid points of sides DC & AB respectively. Show that the diagonal BD is trisected by line segments AP&CQ.
The relative humidity (in %) of a certain city for a month of 30 days was as follows :
98.1
98.6
99.2
90.3
86.5
95.3
92.9
96.3
94.2
95.1
89.2
92.3
97.1
93.5
92.7
95.1
97.2
91.3
95.2
97.3
96.2
92.1
84.9
90.2
95.7
98.3
97.3
96.1
92.1
89
Construct a grouped frequency distribution table with classes 84–86, 86–88 etc.
SECTION – D
Questions Number 29 to 34 carry 4 marks each.
P is any point on the chord BC of a circle such that AB=AP. Prove that CP=CQ. OR
In a circle with centre O, chord SR=chord SM. Radius OS intersects the chord RM at P. Prove that RP = PM.
The following is the distribution of weights (in kg) of 50 persons :
Weight (in kg) : 55 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 85
Number of persons : 10 10 8 6 9 5
Draw a histogram for the above data.
A closed cylindrical petro storage tank is made up of steel sheet, find
i. the lateral or curved surface area of the tank that is 4.2 m in diameter and 4.5 m high.
ii. how much steel was actually used, if (1/12) of the steel actually used was wasted in making the tank.
ABCD is a trapezium with AB║DC. If AD=BC then prove that ∟BCD=∟ADC. OR
ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD. Show that
(i) ΔAPB ~ ΔCQD
(ii) AP = CQ
Draw the graph of the linear equation 2x – y = 4. From the graph, find the co-ordinates of the point where the line intersects y – axis.
Prove that the parallelograms on the same base and between the same parallels are equal in area.
Draw histogram and frequency polygon on the same graph for the following data :
Weight (in kg) :
124–128
128–132
132–136
136–140
140–144
144–148
Number of Students :
5
8
17
24
16
12
Two circles of radii 10 cm and 17 cm intersect at two points and distance between their centres is 21 cm. Find length of common chord.
A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Solve for Solve for
Submitted By: Mr. Ajai Kumar Shukla, Rachna Tutorials
