If then find the projection of .
Answer :
Given:
The projection of on is given by
Find Î», if the vectors are coplanar.
Answer :
Since the vectors are coplanar,
Expanding along , we get
Thus, the value of is 7.
If a line makes angles 90Â°, 60Â° and Î¸ with x, y and z-axis respectively, where Î¸ is acute, then find Î¸.
Answer :
We have
Since ,
Write the element a_{23}_{ }of a 3 âœ• 3 matrix A = (a_{ij}) whose elements a_{ij} are given by
Answer :
Find the differential equation representing the family of curves + B, where A and B are arbitrary constants.
Answer :
Find the integrating factor of the differential equation
.
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 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 :
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 :
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 :
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.