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Syllabus

let P be the set of the first three prime numbers and R be a relation of P defined as R={(x,y) : x≥y ; x,y ∈ P} express R and R

^{-1}as a set of orderd pairs.. plzzz solve thisA=(A intersection B)U(A-B) and A U (B-A)=AUB

f(x) =px+qandf(f(f(x))) = 8x+ 21, wherepandqare real numbers, thenp + qequals(A) 3 (B) 5 (C) 7 (D) 11

44. If f(x) =x

^{2}+bx+c and f(2+t) = f(2-t) for all real numbers t, then which of the following is true ?(A) f(1) < f(2) < f(4) (B) f(2)< f(1) < f(4)

(C) f(2) < f(4) < f(1) (D) f(4)< f(2) < f(1)

- Exactly one of P,Q and R if P, Q and R are disjoint sets
- At least one of P, Q and R but not in all three of them at the same time.
- Exactly two of P, Q and R
- Exactly one of P, Q and R or in all the three of them

Q. 3) $\mathrm{if}\left(\mathrm{A}\cap \mathrm{B}\text{'}\right)\cup \mathrm{B}-\mathrm{A}\left(\mathrm{A}\cap \mathrm{C}\text{'}\right)\mathrm{uC}-\mathrm{A}\mathrm{and}\mathrm{A}\cap \mathrm{B}-\mathrm{A}\cap \mathrm{C}$, then which of the following relations is true?

A) A-B

B) B=C

C) C=A

D) None of these

atleast two types of drinks. If each of the employees prefer at least one type of drink , then how many employees are there in the office?

^{2}+3x+2. then f(x-2) =?(A) $\frac{17}{6}$ (B) $\frac{53}{6}$ (C) $\frac{31}{3}$ (D) $\frac{35}{3}$

f(x), then which of the following can beg(x).(a) $\left({\mathrm{sec}}^{2}3\mathrm{x}+{\mathrm{cosec}}^{2}3\mathrm{x}\right){\mathrm{tan}}^{2}3\mathrm{x}$ (b) $2\mathrm{sin}3\mathrm{x}+3\mathrm{cos}3\mathrm{x}$

(c) $2\sqrt{1-{\mathrm{cos}}^{2}3\mathrm{x}}+\mathrm{cosec}3\mathrm{x}$ (d) $3\mathrm{cosec}3\mathrm{x}+2\mathrm{tan}3\mathrm{x}$

A={1,4,9,16...100} Write it in set builder form.^{2}, n belongs to N, 1<_n<_10}^{2}: x belongs to N, 1<_x<_10}Which of 1. and 2. is correct way to write above set in set builder form???Arrange the chapters in different branches in physics,chemistry,maths

physics- a)Mechanics, b)eletrodynamics, c)optics, d)properties of matter, e)Heat and thermodynamics, f)Modern physics

chemistry-a)Physical, b) Inorganic, c) Organic

Maths-a)Algebra, b)Coordinate geometry, c)Vector/3D d)Calculus

8. The range of function $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{sin}}^{-1}\left[{\mathrm{x}}^{2}+\frac{1}{2}\right]+{\mathrm{cos}}^{-1}\left[{\mathrm{x}}^{2}+\frac{1}{2}\right]$, where [.] is the greatest integer function is:-

$\left(A\right)\left\{\frac{\mathrm{\pi}}{2},\mathrm{\pi}\right\}\left(B\right)\left\{0,\frac{-1}{2}\right\}\left(C\right)\left\{\mathrm{\pi}\right\}\left(D\right)\left\{0,\frac{\mathrm{\pi}}{2}\right\}$

^{p}- 2^{q}= 120 ?In the solution given what is the basis of derivation given as

n(X intersection Y) + n(Y intersection Z) + n(X intersection Z) - 2 n(X intersection Y intersection Z) = 15

^{n-1} (n-1), g(n)=n-f(n) for every n belongs to N. then (gog)(n)=?f(f(f(f(x)))) =x(A) 2 (B) 1 (C) 4 (D) 0

6. Given $f\left(x\right)=\sqrt{\frac{8}{1-x}}+\frac{8}{1+x}andg\left(x\right)\frac{4}{f\left(\mathrm{sin}x\right)}+\frac{4}{f\left(\mathrm{cos}x\right)}$ then g(x) is

(A) periodic with period$\mathrm{\pi}$/2 (B) periodic with period $\mathrm{\pi}$

(C) periodic with period 2$\mathrm{\pi}$ (D) aperiodic

7

^{x+2}- (1/7)*7^{x+1}- 14*7^{x-1}+ 2*7^{x}= 48SET A={1,2}

sir here

can {phi,1,2} {phi,1} {phi,2}

can also be subset

Sir, are {1,2,5} subsets of set A?

Are they elements (belongs to)?