The augmented matrix of a system of linear equations is \(\left[\begin{array}{cccc} 1 & 2 & 7 & 3 \\ 0 & 1 & 4 & 6 \\ 0 & 0 & \lambda-7 & \mu+5 \end{array}\right]\). The system has infinitely many solutions if

(a)

\(\lambda=7, \mu \neq-5\)

(b)

\(\lambda=-7, \mu=5\)

(c)

\(\lambda \neq 7, \mu \neq-5\)

(d)

\(\lambda=7, \mu=-5\)

If |z₁| = 1, |z₂| = 2, |z₃| = 3 and |9z₁z₂ + 4z₁z₃ + z₂z₃| = 12, then the value of |z₁+z₂+z₃| is 

(a)

1

(b)

2

(c)

3

(d)

4

When the eccentricity of a ellipse becomes zero, then it becomes a __________

(a)

straight line

(b)

circle

(c)

point

(d)

parabola

The angle between the lines \(\frac{x-2}{3}=\frac{y+1}{-2}, z=2 \text { and } \frac{x-1}{1}=\frac{2 y+3}{3}=\frac{z+5}{2}\) is

(a)

\(\frac{\pi}{6}\)

(b)

\(\frac{\pi}{4}\)

(c)

\(\frac{\pi}{3}\)

(d)

\(\frac{\pi}{2}\)

The number given by the Mean value theorem for the function \(\frac { 1 }{ x } \), x ∈ [1, 9] is

(a)

2

(b)

2.5

(c)

3

(d)

3.5

Linear approximation for g(x) = cos x at \(x=\frac{\pi}{2}\) is

(a)

\(x+\frac{\pi}{2}\)

(b)

\(-x +\frac{\pi}{2}\)

(c)

\(x - \frac{\pi}{2}\)

(d)

\(-x - \frac{\pi}{2}\)

The degree of the differential equation \(y(x)=1+\frac { dy }{ dx } +\frac { 1 }{ 1.2 } { \left( \frac { dy }{ dx } \right) }^{ 2 }+\frac { 1 }{ 1.2.3 } { \left( \frac { dy }{ dx } \right) }^{ 3 }+....\) is

(a)

2

(b)

3

(c)

1

(d)

4

The solution of \(\frac{dy}{dx}+y\) cot x = sin 2x is ___________

(a)

y sin x = \(\frac{2}{3}\)sin³x+c

(b)

y sec x = \(\frac{x^2}{2}+c\)

(c)

y sin x = c+x

(d)

2y sin x = sin x - \(\frac{sin\ 3x}{3}+c\)

In the set Q define a⊙b = a+b+ab. For what value of y, 3⊙(y⊙5) = 7?

(a)

y = \(\frac{2}{3}\)

(b)

y = \(\frac{-2}{3}\)

(c)

y = \(\frac{-3}{2}\)

(d)

y = 4

Which of the following is a contradiction?

(a)

p v q

(b)

p ∧ q

(c)

q v ~ q

(d)

q ∧ ~ q