Deemed University 2010 B.C.A Computer Application University: Lingayas University Term: I Title of the : Mathematics-I - Question Paper

Roll No. ..

 

Lingayas University, Faridabad

BCA 1^st Year (Term I)

Examination Nov 2010

Mathematics-I (MA - 1104)

[Time: 3 Hours] [Max. Marks: 100]

 

Before answering the question, candidate should ensure that they have been supplied the correct and complete question paper. No complaint in this regard, will be entertained after examination.

 

Note: All questions carry equal marks. Attempt five questions. Question No. 1 is compulsory. Select two questions from section B, & two questions from section C.

Section A

Q-1. Part A

Select the correct answer of the following multiple choice questions: (10x1=10)

(i) If A = B = and (A + B)² = A² + B²

then values of a and b are

(a) a = 4, b = 1 (b) a = 1, b = 4
(c) a = 0, b = 4 (d) a = 2, b = 4

(ii) If A² A + I = 0, then the inverse of A is

(a) A^-2 (b) A+I (c) I-A (d) A-I

(iii) If A & B are symmetric matrix the ABA is

(a) symmetric matrix (b) skew symmetric
(c) diagonal matrix (d) scalar matrix

(iv)

(a) log_e (x + sin x) + c (b) log (sin x + cos x) + c

(c) 2 sec² x/2 + c (d) [x + log (sin x + cos x) + c]

(v) The general solution of differential equation =is

(a) log y = kx (b) y = kx (c) xy = k (d) y = k log x

(vi) A matrix whose all elements are zero is called

(a) unit matrix (b) null matrix
(c) scalar matrix (d) diagonal matrix

(vii) Find x, y such that

(a) x = 2, y = 4 (b) x = 3, y = 4
(c) x = 1, y = 0 (d) x = 4, y = 1

(viii) If A & B are two matrix such that AB is defined then (AB)^T is

(a) A^TB^T (b) AB^T (c) B^T A^T (d) A^T B

(ix) If then find A+B.

(a) (b)

(c) (c)

(x) A matrix in which number of rows is equal to the number of columns is called

(a) Diagonal matrix (b) Null Matrix
(c) Rows Matrix (d) Square Matrix

 

 

 

Part B

(i) Show that

=

(ii) If A = and I = then find K so that

A² = 8 A + KI (5x2=10)

Section B

Q-2. (a) Solve the following equation using matrix method:

x + 2y + z = 7, x + 3z = 11, 2x 3y = 1

(b) If A = , find Adj A. (10x2=20)

Q-3. (a) If x^y = y^x find

(b) Evaluate (10x2=20)

Q-4. (a) If y = find .

(b) Evaluate the following:

(10x2=20)

 

Section C

Q-5. (a) Evaluate

 

(b) Differentiate the following function with respect to x.

(10x2=20)

Q-6. (a) Express the matrix A = as the sum of symmetric and skew symmetric matrix.

(b) Evaluate (10x2=20)

Q-7. (a) Verify Langrages Mean Value Theorem for function if

f(x) = (x-3) (x-6) (x-9) on interval [3, 5].

(b) Verify Rolles Theorem for the function f (x) = x² 5x + 6 on interval [2, 3]. (10x2=20)

Q-8. (a) Find the local maximum & local minimum values of the function f (x) = 3x⁴ + 8x³ + 6x²

(b) Test the continuity of the function f (x) at origin:

f (x) = (10x2=20)