CBSE Guess > Papers > Important Questions > Class XII > 2010 > Maths > Mathematics By Mr. Neeraj Arora

CBSE CLASS XII

Q19. If x² + y² = t – 1/t, and x⁴ + y⁴ = t² + 1/t², then prove that dy/dx = I / x³y

or

if y = sin(logx), prove that x²y² + xy¹ + y = 0

20.

Q21. If x,y,z€[-1,1] such that sin^-1 x+sin^-1 y+sin^-1 z = 3π/2,

Find the value of: x²⁰⁰⁶+y²⁰⁰⁷+z^{2008- 9}/(x²⁰⁰⁶+y²⁰⁰⁷+z²⁰⁰⁸)

Q22.       

SECTION C

Q23. Using the properties of determinants proves that:

or
prove that (using the properties of determinants):

Q24.  Find the inverse of the matrix A by using elementary row transformation.

Q25. The sum of three numbers is 2. If twice the second number is added to the sum of the first and third, the sum is1. By adding second and third number to five times the first number, we get 6. Find the three numbers by using matrix method.

Q26. Find the equations of the tangent and normal to the curve at the indicated point
y = x⁴ – 6x³ + 13x² – 10x + 5 at (1, 3) 

Q27.  Find dy/dx if, y = x ^sinx + (sinx)^x

Q28. Show that of all the rectangles inscribed in a given circle, the square has the maximum area.
or
Show that of all the rectangles with the given perimeter, the square has the maximum area.

Q29.   

Paper By Mr. Neeraj Arora
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Ph No.: 9811242411