GATE EE 2010 Question Paper (14-Feb-2010) (Shift 1)

At $t=0,f\left(t\right)=\frac{\sin t}{t}$ has

A box contains 4 white balls and 3 red balls. In succession, two balls are randomly and removed from the box. Given that the first removed ball is white, the probability that the second removed ball is red is

An eigen vector of A = ≤ft[ {*20c 1&1&0\\ 0&2&2\\ 0&0&3 } ]

For the differential equation $\frac{d^{2}x}{d{t}^2}+6\frac{dx}{dt}+8x=0$ with initial conditions x(0)=1 and ${\frac{dx}{dt}|}_{t=0}=0,$ the solution is

For the set of equations

x₁ + 2x₂ + x₃­ + 4x₄ = 2

3x₁ + 6x₂ + 3x₃ + 12x₄ = 6

Which of the following statement is true?