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Class 12th CBSE Mathematics 29 Questions 100 Marks

Class 12th CBSE Mathematics 29 Questions 100 Marks

**Sample Paper – 2012
Class – XII
Subject – Mathematics**

- Let A = {3, 5} and B = {7, 11}. And R = {(a, b): a , a – b is odd}, then show that R is an empty relation.
- Prove that sin{tan-1(1)} =
- If A = and B = find A + B.
- If A = verify that AA‑1 = I
- Prove that (a + b + c) is a factor of :
- Evaluate :
- Evaluate :
- Find the unit vector in the direction of the vector: =
- Find λ so that . A: 3
- Find the magnitude of , if . A:

__Section – B__

- Prove that a relation
**R**on the set**Z**of all integers defined by: (x, y) ó x – y is divisible by 4 is an equivalence relation on Z. - Solve : . A: 1/
- Show that x = 2 is a root of the equation: and solve it completely. Ans: -3,1,2
**The**function define d as : f(x) = is continuous in [ 0,8] find ‘a’ and ‘b’.**Ans a=3 b=-2**- Find when: x = and y = .
- Find a point on the curve y = x3 – 3x , where the tangent is parallel to the chord joining the points (1, -2) and (2,2).
- Evaluate :
dx .*Or* - If with reference to the right handed system of mutually perpendicular unit vectors , , , then express in the form of , where is parallel to and is perpendicular to
- If
- If show that
- Show that a closed right circular cylinder of given total surface area and maximum volume is such that its height is equal to the diameter of its base.
- Obtain the differential equation representing the family of parabolas having vertices at the origin and axis along the positive direction of X-axis. Ans: y2 – 2xyy’=0

__SECTION – C__

- Find the shortest distance between the lines and
**Or**Find the image of the point (3,5,3) in the line: A: (-1,1,7) - Find the area of the region { }
- Evaluate the integrals from the first Principal
- Solve the system of equation using matrix method 2x + 3y + 3z = 5, x – 2y + z = - 4, 3x –y – 2z = 3
- Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius r is.
- A Cooperative society of farmers has 50 hectares of land to grow two crops X and Y. The profit from crops X and Y per hectare are estimated as Rs 10,500 and Rs 9,000 respectively. To control weeds, a liquid herbicide has to be used for crops X and Y at rates of 20 liters and 10 liters per hectares. Further, not more than 800 liters of herbicide should be used in order to protect fish and wild life using a pond which collects drainage from this land. How much land should be allocated to each crop so as to maximize the total profit of the society?
- A husband and a wife appeared for an interview for two posts. The probability of their selection is 1/7 and 1/5 respectively. What is the probability that: (i) both of them will be selected A:1/35 (ii) only one of them will be selected A:2/7 (iii) at least of them will be selected A:11/35 (iv) none of them will be selected. A:24/35
A discrete random variable X has mean score equal to ‘6’ and variance equal to ‘2’. Assuming that the underline distribution is binomial, what is the probability when Ans:3136/6561*Or*

Paper Submitted By:

Name Chetan Jain

Email jainchetan2004@yahoo.com

Phone No. 9929160320

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