Case study (4 Marks)

Question 14 Marks

Read the text carefully and answer the questions
Five friends Mohit, Sachin, Rohit, Mohan and kapil were playing in a ground, where they sit in a row in a straight line.

(a) In how many ways these five students can sit in a row?
(b) Total number of sitting arrangements if Mohit and Sachin sit together:
(c) What are the possible arrangements if Rohit and Mohan sits at the extrement positions?
(d) What are the possible orders if Kapil is sitting in the middle?

Answer

Five friends Mohit, Sachin, Rohit, Mohan and kapil were playing in a ground, where they sit in a row in a straight line.

(i) Total number of ways $=5$ ! $=120$
(ii) Two position are fixed for Mohit and Sachin therefore considering it as one unit, total students left $=3+1=4$ Total possible arrangement $=4!\times 2!=48$
(iii)Total possible arrangements $=3!\times 2!=12$
(iv)Total possible arrangements $=4$ ! $=24$

View full question & answer→

Question 24 Marks

Read the text carefully and answer the questions
In a library 25 students read physics, chemistry and mathematics books. It was found that 15 students read mathematics, 12 students read physics while 11 students read chemistry. 5 students read both mathematics and chemistry, 9 students read physics and mathematics. 4 students read physics and chemistry and 3 students read all three subject books.

(a) Find the number of students who read none of the subject.
(b) Find the number of students who read atleast one of the subject.
(c) Find the number of students who read only one of the subjects.
(d) Find the number of students who read only mathematics.

Answer

In a library 25 students read physics, chemistry and mathematics books. It was found that 15 students read mathematics, 12 students read physics while 11 students read chemistry. 5 students read both mathematics and chemistry, 9 students read physics and mathematics. 4 students read physics and chemistry and 3 students read all three subject books.

(i) Atleast one $=11+9+5+4-2(3)$
$
=29-6=23
$
$
\Rightarrow \text { None }=25-23=2
$
(ii) The number of students who reading atleast one of the subject is 23 .
(iii)Only maths $=15-9-5+3=4$
Only physics $=12-9-4+3=2$
Only chemistry $=5 \Rightarrow$ Total $=11$
(iv)The number of students who reading only mathematics is 4 .

View full question & answer→

Question 34 Marks

Read the text carefully and answer the questions
Sachin is playing with long string, he hang the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

(a) What is the standard equation of parabola in this case?
(b) Parabola passes through the which point?
(c) Find the value of a in the standard equation?
(d) What is particular equation of parabol?

Answer

Sachin is playing with long string, he hang the ends of the string at two points on the wall. Now, it is in the form of parabola with its vertical axis and is 10 m high and 5 m wide at its base as shown in the following figure:

(i) the Equation of the parabola is of the form $\mathrm{x}^{2}=4 \mathrm{ay}$ (as it opening Upwards).
(ii) It can be clearly seen from the given figure that parabola passes through point $\left(\frac{5}{2}, 10\right)$.
(iii)It can be clearly seen that the parabola passes through point $\left(\frac{5}{2}, 10\right)$.
$
\begin{aligned}
& \left(\frac{5}{2}\right)^{2}=4 \mathrm{a}(10) \\
& \Rightarrow \mathrm{a}=\frac{25}{4 \times 4 \times 10} \\
& =\frac{5}{32}
\end{aligned}
$
(iv)The equation of parabola is
$
x^{2}=4 a y
$
$
\mathrm{x}^{2}=4\left(\frac{5}{32}\right) y=\left(\frac{5}{8}\right) y
$

View full question & answer→

Applied Maths Case study (4 Marks)

Test yourself on this topic