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Using the properties of determinant, sho...

Using the properties of determinant, show that :`|[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2`

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MODERN PUBLICATION-MOCK TEST-1-EXERCISE
  1. Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)

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  2. Show that if A = [[cos theta, sin theta],[-sin theta, cos theta]], th...

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  3. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  4. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

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  5. Evalute : int(5x+3)/sqrt(x^2+4x+10)dx

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  6. By using the properties of definite integrals, evaluate the integral: ...

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  7. Solve: dy/dx+(2x)/(x^2+1)y=1/(x^2+1)^2, y(0)=0.

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  8. Find the shortest distance between the lines: vecr=6hati+2hatj+2hatk+l...

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  9. Find the equation of the plane passing through the intersection of the...

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  10. A problem in Mathematics is given the three students whose chances of ...

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  11. A problem in Mathematics is given the three students whose chances of ...

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  12. If A and B are subsets of the universal set U, then show that A⊂ A∪ B...

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  13. Is ∗ defined on the set {1, 2, 3, 4, 5} by a * b = L.C.M. of a and b ...

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  14. If X= {1, 2, 3}, if n represents any member of X, write the following ...

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  15. Find the area of the smaller region bounded by the ellipse x^2/a^2 + y...

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  16. Simplify : [veca-vecb,vecb-vecc,vecc-veca].

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  17. If veca,vecb,vecc are three vectors such that vecaxxvecb=vecc,vecbxxve...

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  18. Convert the following measurements into mL. 0.75 liters

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  19. A class has 15 students whose ages are 14, 17, 15, 14, 21, 17, 19, 20,...

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  20. Find the variance of the number obtained on a throw of an unbiased die...

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