Mathematics - I
Attempt any Six question
2. In a class of 100 students 40 students failed in Mathematics, 70 failed in English and 20 failed in both subject. Find
a. How many students passed in both subject ?
b. How many students passed in Mathematics only?
c. How many student failed in mathematics only?
3. Find the domain and range of the function4. Find the Maclurin series of the function
5. Prove that = (x - y)(y - z)(z - x)
6. Find a unit vector perpendicular to the plane containing points p(1,-1,0),Q(2,1,-1) and R(-1,1,2)
7. In how many ways can be letter of words "Sunday" be arraged? How many of these arrangement begin with S? How many begin with S and don't end with y?
8. If x + iy = then show that x2 + y2 = 1
Attempt any Two question
9.a) Define conic section. Find the coordinates of vertices, eccentricity and foci of the ellipse
9x2 + 4y2 - 18x - 16y - 11 = 0
b) If T : R2 ⟶ R3 defined by T(x1, x2) = (x1 + x2, x2,x1) be the linear transformation. then find matrix associated with linear map T.
10. Define irrational number. Prove that √2 is an irrational number.
If function f: R ⟶ R defined by f(x) = 2x + 1 and g:R ⟶ R defined by g(x) = x2 - 2. Find the formulae for composite function f * g and g * f and also verify that f * g ≠ g* g.
11. a) If arithmetic mean, geometic mean