Mathematics

Sample Papers

Question:

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius r is 4r/3. Also find maximum volume in terms of volume of the sphere.

Answer:

cbse-previous-year-solved-papers-class-12-maths-delhi-2016-61
cbse-previous-year-solved-papers-class-12-maths-delhi-2016-62
cbse-previous-year-solved-papers-class-12-maths-delhi-2016-63
cbse-previous-year-solved-papers-class-12-maths-delhi-2016-64

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Sample Papers

Q 2.

Using integration find the area of the region {(x, y): x2 +y2 ≤2ax, y2 ≥ ax, x,y≥ 0}

Q 7.

A bag ‘A’ contains 4 black and 6 red balls and bag ‘B’ contains 7 black and 3 red balls. A die is thrown. If 1 or 2 appears on it, then bag A is chosen, otherwise bag B. If two balls are drawn at random (without replacement) from the selected bag, find the probability of one of them being red and another black.

Q 8.

The side of an equilateral triangle is increasing at the rate of 2 cm/s. At what rate is its area increasing when the side of the triangle is 20 cm ?

Q 10.


cbse-previous-year-solved-papers-class-12-maths-delhi-2016-33

Q 11.

cbse-previous-year-solved-papers-class-12-maths-delhi-2016-38

Q 12.

Let N denote the set of all natural numbers and R be the relation on N x N defined by (a, b) R(c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.

Q 13.

Using integration find the area of the triangle formed by positive x-axis and tangent and normal to the circle x2 + y2= 4 at (1, √3).

Q 14.

cbse-previous-year-solved-papers-class-12-maths-delhi-2016-36

Q 15.

Q 16.

cbse-previous-year-solved-papers-class-12-maths-delhi-2016-11

Q 17.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-29

Q 18.

Q 19.

If A is a square matrix such that A2 = I, then find the simplified value of (A -1)3 + (A +1)3 – 7A.

Q 20.

Three persons A, B and C apply for a job of Manager in a Private Company. Chances of their selection (A, B and C) are in the ratio 1:2:4. The probabilities that A, B and C can introduce changes to improve profits of the , company are 0.8,0.5 and 0.3 respectively. If the change does not take place, find the probability that it is due to the appointment of C.

Q 21.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-7

Q 22.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-34

Q 23.


cbse-previous-year-solved-papers-class-12-maths-delhi-2015-41

Q 24.

Find the local maxima and local minima, of the function f(x) = sin x – cos x, 0 < x < 2Ï€. Also find the local maximum and local minimum values.

Q 25.

Q 26.

Q 27.

Q 28.

Q 29.

Q 30.


cbse-previous-year-solved-papers-class-12-maths-delhi-2016-23

Q 31.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-16

Q 32.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-37

Q 33.


cbse-previous-year-solved-papers-class-12-maths-delhi-2015-51

Q 34.


cbse-previous-year-solved-papers-class-12-maths-delhi-2015-77

Q 35.

Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below:
2x + 4y ≤ 8
3x + y ≤ 6
x + y ≤ 4
x≥ 0, y ≤ 0.6

Q 36.

Q 37.

Q 38.

A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a . spade. [6]

Q 39.

Prove that:
cbse-previous-year-solved-papers-class-12-maths-delhi-2016-15

Q 40.

Show that the equation of normal at any point on the curve x = 3 cost t – cos3 t and y = 3 sin t – sin3 t is 4(ycos3 t- sin3t) = 3 sin 4t.

Q 41.

Find the intervals in which f(x) = sin 3x – cos 3x, 0 < x < Ï€, is strictly increasing or strictly decreasing.

Q 42.

cbse-previous-year-solved-papers-class-12-maths-delhi-2015-3

Q 43.

Find the integrating factor of the differential equation
cbse-previous-year-solved-papers-class-12-maths-delhi-2015-10

Q 44.

An unbiased coin is tossed 4 times. Find the mean and variance of the number of heads obtained.

Q 45.

Solve the differential equation: (tan-1 y-x)dy = (1 + y2) dx.
Solution. Same as solution Q. 23 (OR) Set 1 (Outside Delhi) up to eq.
x = tan-1 y -1 + ce -tan-1 y
OR
cbse-previous-year-solved-papers-class-12-maths-delhi-2015-69

Q 46.

Q 47.

Q 48.

Q 49.

Q 50.