Find the differential equation representing the family of curves + B, where A and B are arbitrary constants.
Answer :
The equation of the family of curves is , where A and B are arbitrary constants.
We have
Differentiating both sides with respect to r, we get
Again, differentiating both sides with respect to r, we get
This is the differential equation representing the family of the given curves.
Find the integrating factor of the differential equation
.
Answer :
We have
It is in the form , where P and Q are the constants or functions of x.
Thus, the integrating factor of the given differential equation is
If then find the projection of .
Answer :
Given:
The projection of on is given by
Find Î», if the vectors are coplanar.
Answer :
If a line makes angles 90Â°, 60Â° and Î¸ with x, y and z-axis respectively, where Î¸ is acute, then find Î¸.
Answer :
Write the element a_{23}_{ }of a 3 âœ• 3 matrix A = (a_{ij}) whose elements a_{ij} are given by
Answer :
If x = a cos Î¸ + b sin Î¸, y = a sin Î¸ âˆ’ b cos Î¸, show that
Answer :
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 ?
Answer :
Three schools A, B and C organized a mela for collecting funds
for helping the rehabilitation of flood victims. They sold hand
made fans, mats and plates from recycled material at a cost of Rs
25, Rs 100 and Rs 50 each. The number of articles sold are given
below:
School | |||
Article | A | B | C |
Hand-fans | 40 | 25 | 35 |
Mats | 50 | 40 | 50 |
Plates | 20 | 30 | 40 |
Answer :
If find and hence find a matrix X such that
OR
If
Answer :
If , using properties of determinants find the value of f(2x) âˆ’ f(x).
Answer :
Find :
Answer :
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.
Answer :
Answer :
Find the distance between the point (âˆ’1, âˆ’5, âˆ’10) and the point of intersection of the line and the plane x âˆ’ y + z = 5.
Answer :
If sin [cot^{âˆ’1} (x+1)] = cos(tan^{âˆ’}^{1}x), then find x.
Answer :
If A and B are two independent events such that then find P(A) and P(B).
Answer :
Find the local maxima and local minima, of the function f(x) = sin x − cos x, 0 < x < 2Ï€.
Answer :
Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below :
Answer :
Let N denote the set of all natural numbers and R be the relation on N Ã— N defined by (a, b) R (c, d) if ad (b + c) = bc (a + d). Show that R is an equivalence relation.
Answer :
Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle
OR
Evaluate as a limit of a sum.
Answer :
Solve the differential equation :
OR
Find the particular solution of the differential equation given that y = 1, when x = 0.
Answer :
If lines intersect, then find the value of k and hence find the equation of the plane containing these lines.
Answer :
12th Maths Paper Solutions Set 1 : CBSE All India Previous Year 2013 will be available online in PDF book soon. The solutions are absolutely Free. Soon you will be able to download the solutions.