Mathematics XI
Mathematics XI
Mathematics XI
12. A function f (x) = x2 is given. Answer the following question for the function f(x).
i) What is the algebraic nature of the function?
ii) Write the name of the locus of the curve.
iii) Write any one property for sketching the curve.
iv) Write the domain of the function.
13. Compare the sum of n terms of the series: 1 + 2a +3a2 +4a3 +……….and a+ 2a + 3a+ 4a
…up to n terms.
A
14. a) In any triangle, prove that: (b + c) Sin = a Sin¿)………(3)
2
b) Express r⃗ = (4, 7) as the linear combination of a⃗ = (5, - 4) and b⃗ = (-2, 5)……..(2)
15. Calculate the appropriate measure of Skewness for the data below.
16. Define different types of discontinuity of a function. Also write the condition for
increasing, decreasing and concavity of function. 2+3
x2 dx
∫
17. Evaluate: √ a2−x 2
1
dx
∫ 1+x
18. Define Trapezoidal rule. Evaluate using Trapezoidal rule for 0 n = 4.
19. State sine law and use it to prove Lami’s theorem.
OR
A decline in the price of good X by Rs. 5 causes an increase in its demand by 20 units to
50 units. The new price is X is 15.
i) Calculate elasticity of demand.
ii) The elasticity of demand is negative, what does it mean?
;d"x u(Group –C (8×3 = 24 )
20. The factor of expression w3-1 are w-1 and w2 + w +1. If w3-1 = 0
i) Find the possible values of w and write the real and imaginary roots of w. (2)
1 wn w 2n
|w2 n 1 wn |
n
ii) Prove that: w w2n 1 = 0. Where n is positive integer. (4)
iii) Verify that: |x+ y|≤|x|+|y| with x = 2 and y = -3 (2)
21. The single equation of pair of lines is 2x2 +3xy +y2 +5x +2y -3 = 0
i) Find the equation of two straight lines represented by the single equation ….(5)
ii) Find the point of intersection of the pair of lines…(2)
⃗ c are mutually perpendicular unit vectors in space then write a
iii) If three vectors a⃗ , b∧⃗
relation between them. ……(1)
22. i) Distinguish between derivative and anti-derivative of a function. Write their physical
meanings in your context. Find, the differential coefficient of logSinx with respect to x.
…(1+ 2+2)
ii) Find the area bounded by the y – axis, the curve x2 = 4 (y - 2) and the line y = 11 (3)