shaalaa.com
S

Question Paper - Mathematics 2014 - 2015-CBSE 12th-Class 12 CBSE (Central Board of Secondary Education)

Account
User


Login
Register


      Forgot password?
Share
Notifications

View all notifications
Books Shortlist
Your shortlist is empty
SubjectMathematics
Year2014 - 2015 (March)

Alternate Sets

     
 Topics
 Marks
 Topics
 Marks

Marks: 100
Q: 1[1]

If `vec a=7hati+hatj-4hatk and vecb=2hati+6hatj+3hatk` , then find the projection of `vec a and vecb`

view question and solution
Q: 2[1]

Find λ, if the vectors `veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk`  are coplanar.

view question and solution
Q: 3[1]

If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.

view question and solution
Q: 4[1]

rite the element a23 of a 3 ✕ 3 matrix A = (aij) whose elements aij are given by `a_(ij)=∣(i−j)/2∣`

view question and solution
Q: 5[1]

Find the differential equation representing the family of curves v=A/r+ B, where A and B are arbitrary constants.

 

view question and solution
Q: 6[1]

Find the integrating factor of the differential equation.

`((e^(-2^sqrtx))/sqrtx-y/sqrtx)dy/dx=1`

view question and solution
Q: 7 | Attempt any one[4]
Q: 7.1[4]

If `A=([2,0,1],[2,1,3],[1,-1,0])` find A2-5A+4I and hence find a matrix X such that  A2-5A+4I+X=O

view question and solution
Q: 7.2[4]
 

If A = `[[1,-2,3],[0,-1,4],[-2,2,1]]` ,find (A')-1

 
view question and solution
Q: 8[4]
 

If ` f(x)=|[a,-1,0],[ax,a,-1],[ax^2,ax,a]| ` , using properties of determinants find the value of f(2x) − f(x).

 
view question and solution
Q: 9 | Attempt any one[4]
Q: 9.1[4]

Find: `I=intdx/(sinx+sin2x)`

view question and solution
Q: 9.2[4]

Integrate the following w.r.t. x `(x^3-3x+1)/sqrt(1-x^2)`

view question and solution
Q: 10[4]

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

view question and solution
Q: 11 | Attempt any one:[4]
Q: 11.1[4]

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.

view question and solution
Q: 11.2[4]

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

view question and solution
Q: 12[4]

If `vecr=xhati+yhatj+zhatk` ,find `(vecrxxhati).(vecrxxhatj)+xy`

view question and solution
Q: 13[4]

Find the distance between the point (−1, −5, −10) and the point of intersection of the line `(x-2)/3=(y+1)/4=(z-2)/12` and the plane x-y+z=5

view question and solution
Q: 14 | Attempt any one [4]
Q: 14.1[4]

If sin [cot−1 (x+1)] = cos(tan1x), then find x.

view question and solution
Q: 14.2[4]

If (tan1x)2 + (cot−1x)2 = 5π2/8, then find x.

view question and solution
Q: 15[4]

If `y=tan^(−1) ((sqrt(1+x^2)+sqrt(1−x^2))/(sqrt(1+x^2)−sqrt(1−x^2)))` , x21, then find dy/dx.

view question and solution
Q: 16[4]

If x = a cos θ + b sin θ, y = a sin θ − b cos θ, show that `y^2 (d^2y)/(dx^2)-xdy/dx+y=0`

view question and solution
Q: 17[4]

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 ?

view question and solution
Q: 18[4]

Find : `int(x+3)sqrt(3-4x-x^2dx)`

view question and solution
Q: 19[4]

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:

SchoolArticle   
ABC
Hand-fans402535
Mats504050
Plates203040

Find the funds collected by each school separately by selling the above articles. Also find the total funds collected for the purpose.

Write one value generated by the above situation.

view question and solution
Q: 20[6]

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

view question and solution
Q: 21 | Attempt any one :[6]
Q: 21.1[6]

Using integration find the area of the triangle formed by positive x-axis and tangent and normal of the circle

`x^2+y^2=4 at (1, sqrt3)`

view question and solution
Q: 21.2[6]

Evaluate `int_1^3(e^(2-3x)+x^2+1)dx`  as a limit of sum.

view question and solution
Q: 22 | Attempt any one [6]
Q: 22.1[6]

Solve the differential equation :

(tan1yx)dy=(1+y2)dx.

view question and solution
Q: 22.2[6]

Find the particular solution of the differential equation `dy/dx=(xy)/(x^2+y^2)` given that y = 1, when x = 0.

view question and solution
Q: 23[6]

If lines `(x−1)/2=(y+1)/3=(z−1)/4 and  (x−3)/1=(y−k)/2=z/1` intersect, then find the value of k and hence find the equation of the plane containing these lines.

view question and solution
Q: 24[6]

If A and B are two independent events such that `P(barA∩ B) =2/15 and P(A ∩ barB) = 1/6`, then find P(A) and P(B).

view question and solution
Q: 25[6]

Find the local maxima and local minima, of the function f(x) = sin x − cos x, 0 < x < 2π.

view question and solution
Q: 26[6]

Find graphically, the maximum value of z = 2x + 5y, subject to constraints given below :

2x + 4y  83

x + y  6

x + y  4

x  0, y 0

view question and solution
S