Mathematics Tes...

The equation of line \(\frac{x-1}{1}=\frac{y+2}{-1}=\frac{z-3}{-3}\) and equation of plane is \(4 x+13 y-3 z+1=\) 0. Then find the distance between given point and plane.

Consider the following statements for the two non-empty sets A and B:

1. (A ∩ B) ∪ (A ∩ B̅) ∪ (A̅ ∩ B) = A ∪ B

2. (A ∪ (A̅ ∩ B̅)) = A ∪ B

Which of the above statements is/are correct?

Two cards from a pack of 52 cards are lost. One card is drawn from the remaining cards. If the drawn card is diamond then the probability that the lost cards were both hearts is:

Consider a triangle \(\Delta\) whose two sides lie on the \(x\)-axis and the line \(x+y+1=0\). If the orthocentre of \(\Delta\) is \((1,1)\), then the equation of the circle passing through the vertices of the triangle \(\Delta\) is:

Let \(\alpha\) and \(\beta(\alpha>\beta)\) be the roots of the equation \(x^2-8 x+q=0\). If \(\alpha^2-\beta^2=16\), then what is the value of \(q\) ?

What is the n^th term of the sequence 25, -125, 625, -3125, …….?

From eighty cards numbered 1 to 80 , two cards are selected randomly. The probability that both the cards have the numbers divisible by 4 is given by:

Find the angle between the line \(\frac{x+1}{2}=\frac{y}{3}=\frac{z-3}{6}\) and the plane \(10 x+2 y-11 z=3\).

If \(A=\left[\begin{array}{ccc}1 & 3+x & 2 \\ 1-x & 2 & y+1 \\ 2 & 5-y & 3\end{array}\right]\) is a symmetric matrix, then \(3 x+y\) is equal to: