**22MATS11 Set – 2 Solved Model Question Paper 1st semester P cycle for Computer Science and Engineering (CSE) Stream** 22 Scheme

**Module – 1**

**1 b] Find the angle between the curves r=\frac{a}{1+\cos\theta} and r=\frac{b}{1-\cos\theta} **

**1 c] Find the radius of curvature of the curve y=x^{3}(x-a) at the point (a,0)**

or

**2 a] Show that the r=a(1+\cos\theta) r=a(1-\cos\theta) curves and cuts each other orthogonally.**

**2 b] Find the pedal equation of the curve r(1-\cos\theta)=2a .**

**Module -2**

**3 a] Expand \log(1+\sin x) Up to the term containing x^{4} using maclaurin’s Series.**

**3 c] Find the extreme values of the function f(x,y)=x^{2}+y^{2}+6x-12 .**

or

**4 a] Evaluate \lim_{x \to 0} \left( \frac{a^{x}+b^{x}+c^{x}}{3} \right)^{1/x} **

**Module 3**

**5 a] Solve \frac{d y}{dx}+\frac{y}{x}=y^{2}x .**

**5 b] Find the orthogonal trajectories of r=a(1+\cos\theta) , where a is parameter.**

**5 c] Solve p^{2}+2py\cot x -y^{2}=0 .**

or

**6 a] Solve y(2xy+1)dx -xdy=0 .**

**6 b] Find the orthogonal trajectories of the family r^{n}\sin n\theta=a^{n} .**

**Module – 4**

**7 a] (i) Find the remainder when 223 is divided by 47. (ii) Find the last digit in 7118 .**

**7 b] Find the solutions of the linear congruence 11x=4(mod25) .**

**7 c] Encrypt the message STOP using RSA with key (2537 . 13) using the prime number 43 and 59.**

or

**8 a] Using Fermat’s Little Theorem, show that 830 -1 is divisible by 31.**

**Module – **5

**9 a] Find the rank of the matrix**

**9 b] By Using Gauss-Jordan method.x+y+z = 92x+y-z = 02x+5y+7z= 52**

**9 c] Using power method, find the largest eigenvalue and corresponding eigenvector of the matrix**

or

**10 b] Test for consistencyx-2y+3z = 23x-y+4z= 42x+y-2z = 5 and hence solve**