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

CBSE CLASS XII

SECTION A

Q1. If A and B are non – singular matrices of the same order, then write the relationship between AdjAB, AdjA and AdjB.

Q2. If A, B, C are three non zero square matrices of same order, find the condition on A such that AB = AC then B = C.

Q3. Prove that modulus function is continuous everywhere.

Q4. Show that the function f(x) = 2x² – 1 is continuous at x = 3.

Q5. Find the derivative of y = sin(2x) w.r.t. x.

Q6. Find the derivative of y = loge sinx  w.r.t. x

Q7. Find the principal value of cos^-1 (-1).

Q8. Find the value of

Q9. Find the value of cos{cos ^-1 (1/4) + sin ^-1 (1/4)}.

Q10. Evaluate :

SECTION B

Q11. Prove that (x/a)ⁿ  + (y/b)ⁿ = 2 touches the straight line x/a + y/b = 2 for all n €N, at the point (a,b).

Q12. Find the intervals in which the function 2x³ + 9x² + 12x – 1 are increasing or decreasing?
Or
Find the approximate value of √25.3(using differentials)

Q13. Prove that cos^-1 (12/13) + sin-1 (3/5) = sin^-1 (56/65)

Q14. Express as a sum of symmetric and skew symmetric matrices.

Q15. For what value of a and b such that the function defined by

 
Or
For what value of k such that the function defined by

Q16. Show that all positive integral powers of a symmetric matrix are symmetric.

Q17. A trust fund Rs 30000 that must be invested in two types of different types of bonds. The first bond pays 5% interest per year, and the second bond pays 7% interest per year. Using matrix multiplication, determine how to divide Rs. 30000 among the two types of bonds. If the trust fund must obtain an annual total interest of

1.  Rs 1800
2.  Rs 2000

Q18. Find dy/dx if x √(y + 1) + y √(x + 1) = 0

Paper By Mr. Neeraj Arora
Email Id : [email protected]
Ph No.: 9811242411