Processing math: 22%




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21.

 On the interval [0,1] , the function x25 (1-x)75 takes its maximum value at the point


A) 0

B) 14

C) 12

D) 13



22.

 If p,q, r are  simple propositions with truth values T,F,T , then  the truth value of  (pq)r)

p is 


A) true

B) false

C) true , if r is false

D) true, if q is true



23.

If a line segment  OP makes angles of   \frac{\pi}{4} and  \frac{\pi}{3}  with X-axis and Y-axis,  respectively . Then, the direction cosines are 


A) \frac{1}{\sqrt{2}},\frac{\sqrt{3}}{2},\frac{1}{\sqrt{2}}

B) \frac{1}{\sqrt{2}},\frac{1}{2},\frac{1}{\sqrt{2}}

C) 1,\sqrt{3},1

D) 1,\frac{1}{\sqrt{3}},1



24.

 A tetrahedron  has vertices at  O  (0,0,0) , A(1,-2,1) ,B(-2,1,1)  and C  (1,-1,2). Then the angle between the faces OAB and ABC will be


A) \cos^{-1}\left(\frac{1}{2}\right)

B) \cos^{-1}\left(\frac{1}{6}\right)

C) \cos^{-1}\left(\frac{-1}{3}\right)

D) \cos^{-1}\left(\frac{1}{4}\right)



25.

The two liines x=my+n, z=py+q  and x=m'y+n', z=p'y+q' are perpendicular to each other, if


A) mm'+pp'=1

B) \frac{m}{m'}+\frac{p}{p'}=-1

C) \frac{m}{m'}+\frac{p}{p'}=1

D) mm'+pp'=-1



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