The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

1) 16.0
2) 15.8
3) 14.0
4) 16.8

The number of real roots of the equation |x|² – 3|x| + 2 = 0 is

1) 4

2) 3

3) 2

4) 1

The solution set of values of x satisfying equation 

1)  all real numbers  
2) (-∞ , 0]
3) [0,∞)
4) (-∞ , -1) È (1, ∞)

What must be the matrix $$X$$ if $$\displaystyle 2X+\left[ \begin{matrix} 1 \\ 3 \end{matrix}\begin{matrix} 2 \\ 4 \end{matrix} \right] =\left[ \begin{matrix} 3 \\ 7 \end{matrix}\begin{matrix} 8 \\ 2 \end{matrix} \right] $$?

1) $$\displaystyle \left[ \begin{matrix} 1 \\ 2 \end{matrix}\begin{matrix} -3 \\ -1 \end{matrix} \right] $$
2) $$\displaystyle \left[ \begin{matrix} 2 \\ 4 \end{matrix}\begin{matrix} 6 \\ -2 \end{matrix} \right] $$
3) $$\displaystyle \left[ \begin{matrix} 2 \\ 4 \end{matrix}\begin{matrix} -6 \\ -2 \end{matrix} \right] $$
4) $$\displaystyle \left[ \begin{matrix} 1 \\ 2 \end{matrix}\begin{matrix} 3 \\ -1 \end{matrix} \right] $$

$$\dfrac{dy}{dx}=e^{-2y},x=5\Rightarrow y=0,$$ then  $$y=3,find\ the\ value\ of\ 2x$$.

1) e⁵ + 9
2) e⁶ + 9
3) e⁸ + 9
4) e⁴ + 9
.

Let there exist a unique point P inside a D  ABC such that  ÐPAB= ÐPBC= ÐPCA= α . If PA = x, PB = y, PC = z, D= area of  D  ABC and a, b, c, are the sides opposite to the angle A,B,C respectively, then tan α  is equal to

If R is the set of all real numbers and f : R → R is given by f(x) = 3x²+ 1. Then, the set f ^-1 ([1, 6]) is

p: She is beautiful.
q:She is happy.
Then (∼p)⇒(∼q), means

1) If she is beautiful, then she is not happy.

2) If she is not beautiful, then she is happy.

3) If she is not beautiful, then she is not happy.

4) If she is not happy, then she is not beautiful.

If α and β are two different complex numbers with |β| = 1, then

1) ½
 2) 0
3) -1
4) 1

p: I am topper.

q: I worked hard.

The symbolic form of the statement : "I am topper or I worked hard", formed from statements p,q can be

1) P↔Q

2) P∨Q

3) P∧Q

4) P→Q