Find the simplified form of \(f(x)=|x-2|+|2+x|,\quad if-3\le x\le 3.\)

6

(a)

Find the value of the expression
\({ cos }^{ 4 }\frac { \pi }{ 8 } +{ cos }^{ 4 }\frac { 3\pi }{ 8 } +{ cos }^{ 4 }\frac { 5\pi }{ 8 } +{ cos }^{ 4 }\frac { 7\pi }{ 8 } .\)

6

(a)

If \({ \left( \frac { 1+i }{ 1-i } \right) }^{ 3 }-{ \left( \frac { 1-i }{ 1+i } \right) }^{ 3 }=x+iy\), then find (x,y).

6

(a)

Find the complex number satisfying the equation \(z+\sqrt { 2 } \left| (z+1) \right| +i=0\)

6

(a)

Solve \(1\le |x-2|\le 3\).

6

(a)

Solve for \(x,|x+1|+|x|>3\)

6

(a)

Solve for \(x,\frac { |x-2|-1 }{ |x-2|-2 } \le 0\)

6

(a)

Find the number of combinations , whwn some or all of n objects are taken at a time.

6

(a)

How many automobile lincene plates can be made, if each plate contains two different letters followed by three different digits?

6

(a)

Using the digits 1,2,3,4,5,6,7,a number of different digit is formed . Find how many numbers are formed ? Further , Find how many of these are
(i) exactly divisible by 2 ?
(ii) exactly divisible by 25 ?
(iii) exactly divisible by 4 ?

6

(a)

Using binomial theorem, determine which number is larger (1.2)⁴⁰⁰⁰ or 800?

6

(a)

Show that 2⁴ⁿ⁺⁴ - 15n - 16, where n\(\in\) N, is divisible by 225.

6

(a)

If a₁, a₂, a₃, ....,a_n are in AP, where a_i > 0 for all i, Show that \(\frac { 1 }{ \sqrt { { a }_{ 1 } } +\sqrt { { a }_{ 2 } } } \) + \(\frac { 1 }{ \sqrt { { a }_{ 2 } } +\sqrt { { a }_{ 3 } } } \) + .....+ \(\frac { 1 }{ \sqrt { { a }_{ n-1 } } +\sqrt { { a }_{ n } } } \)  = \(\frac { n-1 }{ \sqrt { { a }_{ 1 } } +\sqrt { { a }_{ n } } } \)

6

(a)

A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
routine or complex

6

(a)

A team of medical students doing their internship have to assist during surgeries at a city hospital.The probabilities of surgeries rated as very complex,routine,simple rated as very complex,complex,complex, routine,simple or very simple respectively 0.15,0.20,0.31,0.26 and 0.08.Find the probabilities that a particular surgery will be rated
routine or simple

6

(a)

One of the four persons John, Rita, Aslam or Gurpreet will be promoted next month.Consequently, the sample space consists of four elementary outcomes S={Johnpromoted, Rita promoted, Gurpreet promoted} You are told that the chances of John's promotion is same as that of Gurpreet, Rita's Chances of promotion are twice as likely as Johns.Aslam's chances are four times that of John.
If A={John promoted or Gurpreet promoted}, then find P(A)

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A')

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(B')

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cup \)B)

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cap \)B)

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A\(\cap \)B')

6

(a)

If A and B are mutually exclusive events, such that P(A)=0.35 and P(B)=0.45, then find P(A'\(\cap \)B')

6

(a)

Draw the Venn diagrams to illustrate the following relationship among sets, E, M and U, where E is the set of students studying English in a school, M is the set of students studying Mathematics in the same school, U is the set of all students in that school.
There is no student who studies both Mathematics and English.
 

6

(a)

Find the angle in degrees and radians between minutes hand and hour hand of a clock at 7 : 20.

6

(a)

Find the value of \([1+cos{\pi\over 8}][1+cos{3\pi\over 8}][1+cos{5\pi\over 8}][1+cos{{7\pi\over8}}]\)

6

(a)