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1.

If  $f(a+b-x) =f(x)$ then   $\int_{a}^{b} x f(x) dx$ is  equal to

A) $\frac{a+b}{2}\int_{a}^{b} f(b-x) dx$

B) $\frac{a+b}{2}\int_{a}^{b} f(b+x) dx$

C) $\frac{b-a}{2}\int_{a}^{b} f(x) dx$

D) $\frac{a+b}{2}\int_{a}^{b} f(x) dx$

2.

The number of surjective  functions from A to B where A= {1,2,3,4} and B= {a,b} is

A) 14

B) 12

C) 2

D) 15

3.

The domain and range of the function f given by f(x)= 2-|x-5| is

A) Domain = $R^{+}$ , range = (-$\infty$,1]

B) Domain =R, Range =(-$\infty$,2]

C) Domain =R , Range =(-$\infty$,2]

D) Domain =$R^{+}$, Range = (-$\infty$ ,2]

4.

The shortest distance between  the lines x=y+2=6z-6 and x+1=2y=-12z is

A) $\frac{1}{2}$

B) 2

C) 1

D) $\frac{3}{2}$

5.

If the letters of the word KRISNA are arranged in all possible  ways  and these words are written out as in a dictionary, then the rank of the work 'KRISNA' is

A) 324

B) 341

C) 369

D) none of these

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