Model Set 3

Candidates are required to give their answers in their own words as far as practicable. The figure in the margin indicates full marks.

Subjective Test

Group B

Attempt ANY SIX questions: [6×5=30]

1 In a classroom of 200 students, 80 failed in mathematics, 140 failed in English and 40 failed in both subjects. Find

i) How many students passed in both subjects?

ii) How many students passed in English only?

iii) How many students failed in English only?

2 Find the domain and range of the function f(x) =

$\sqrt{(2-x-x^2 )}$

3 Find the Maclaurin series of the function f(x) = Sinx.

4 Define absolute value of real number. Prove that is irrational number.

5 Prove that:

$\begin{pmatrix} 1 &a &b+c \\ 1 &b &c+a \\ 1 &c &a+b \end{pmatrix} = a^2 (a+3)$

6 Find the locus, vertex, equation of directrix and length of Latus rectum of the ellipse 25x² + 4y² = 100.

7 Prove that: x² + y2 = 1 if x – iy =

$\frac{\(3-2i)}{\(3+2i)}$

Group C

Attempt ANY TWO questions: [2×10=20]

8.Define triangular a matrix. Show that B =

$\begin{pmatrix} 1 &a &b+c \\ 1 &b &c+a \\ 1 &c &a+b \end{pmatrix}$

as a sum of symmetric and skew symmetric matrix.

9 Let f : RR and g : RR be defined by f(x) = x² + 1 and g(x) = 3x – 1 then find

a. g²(x) b. f^-1og(x) c. fog(x) d. gof(x)

10 Find the equation of the circle passing through the points (5, 5), (6, 4) and (-2, 4).

*All the best*