ISC 2020-21 MATHEMATICS POST TEST, ZIET BBSR

If A = {1,2,3,4,5} and B = {2,3,6,7} then the number of elements in

 $\left(A\times B\right)\ \cap\left(B\times A\right)$  is

• 4

• 10

• 20

• NONE OF THESE

Let f :  $R_+\longrightarrow\left[-5,\infty\right)$ defined by

 $f\left(x\right)\ =\ 9x^2+6x-5$ , then   f   is

• one one onto

• one one into

• many one onto

• none of these

Let A, B and C are 2 x 2 matrices with entries from the set of real numbers. The operation 

* is defined as  A * B = 

 $\ \ \frac{1}{2}\left(AB\ +\ BA\right)$ , then

• A * A =  $A^2$  

• A * B = B * A

• A * ( B + c )=A * B + A * C

• all the above

If the rate of change of surface area of a sphere is

   $2m^2$ /s  , then the rate of change of its volume at r = 2 metre is 

• 1 cubic meter per second

• 2 cubic meter per second

• 5 cubic meter per second

• none of these

The distance s of the particle in time t is $s\ =\ t^3-6t^2-4t-8$ . Its acceleration vanishes at 

• t = 1

• t = 2

• t = 3

• none of these

Equation of the normal line to the curve y = x log x parallel to 2x - 2y + 3 = 0 is

• $x-y=3e^{-2}$

• $x-y=6e^{-2}$

• $x-y=3e^2$

• none of these

On the ellipse  $4x^2+9y^2=1$  , the points at which the tangents are parallel to the line 8x = 9y are 

•  $\left(\frac{2}{5},\frac{1}{5}\right),\ \left(\frac{1}{5},\frac{2}{5}\right)$  

•  $\left(-\frac{2}{5},\frac{1}{5}\right),\ \left(\frac{2}{5},-\frac{1}{5}\right)$  

• no such point exist 

• none of these

If $A^2-A+I\ =\ 0$  , then inverse of A is 

•  $A+I$  

• A

•  $A-I$  

•  $I-A$   

If n(U) = 50, n(A) = 28 and n(B)=30 then greatest value of  $n\left(A\cup B\right)$  is

• 30

• 28

• 50

• 58

If  $f\left(x\right)\ =\ \frac{\left|x\right|-x}{2x}$  then the range of f is 

• {0 , -1}

• [ 0 , -1]

• ( 0 , -1 )

• none of these