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  1.  -5
  2. 6
  3. 1
  4. -3
Volume of parallelopiped,  Here  and,  Given that V is 546, put it in the above equation. Option (4) is correct

\int_{0}^{\pi /2} \frac{1}{1+\sqrt{tanx}} dx

  1. \pi

  2. \pi/2

  3. \pi/4

  4. 3\pi/2

...............................(1) We also know that,  Using this property in equation (1) ,  .....................(2) Adding equation (1) and (2),  Option (3) is correct
  1. x2+y2-3x+1=0
  2. x2+y2-x+5=0

  3. x2+y2-8x+6y=8

  4. x2+y2-4x+8y=7

General equation of circle ,  Now find the points of intersection of the two circles. At the intersection,              Putting the value of x1 in the equation of any of the two circle to find y1. Now we have 3 points through which the circle is passing,     ,       ,     Now putting these points in general equation we will have 3...
  1. \frac{x}{\sqrt{1+x^{2}}}
  2. \frac{1}{\sqrt{1+x^{2}}}
  3. \frac{\sqrt{1+x^{2}}}{x}
  4. \sqrt{1+x^{2}}
Let  Using Pythagoras theorem,  Option (2) is correct

(1+\omega^{2}-\omega)(1-\omega^{2}+\omega) is

  1. 4

  2. \omega

  3. 2

  4. Zero

With the help of 2 properties of cube roots of unity, we can solve this question. Property 1,  Property 2,  Now we have to find the value of (1+-)(1-+) Using property 2,  Now use property 1, Option (1) is correct  
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