Question Paper - Mathematics 2013 - 2014-CBSE 12th-Class 12 CBSE (Central Board of Secondary Education) (CBSE)

Account
Register

Share

Books Shortlist
Courses [3]
SubjectMathematics
Year2013 - 2014 (March)

Alternate Sets

Marks: 100
Q: 1[1]

If R=[(x, y) : x+2y=8] is a relation on N, write the range of R.

view solution
Q: 2[1]

If tan-1x+tan-1y=π/4,xy<1, then write the value of x+y+xy.

view solution
Q: 3[1]

If A is a square matrix, such that A2=A, then write the value of 7A(I+A)3, where I is an identity matrix.

view solution
Q: 4[1]

If [[x-y,z],[2x-y,w]]=[[-1,4],[0,5]] find the value of x+y.

view solution
Q: 5[1]

If [[3x,7],[-2,4]]=[[8,7],[6,4]] , find the value of x

view solution
Q: 6[1]

If f(x) =∫_0^xt sin t dt , then write the value of f ' (x).

view solution
Q: 7[1]

find ∫_2^4 x/(x^2 + 1)dx

view solution
Q: 8[1]

Find the value of 'p' for which the vectors 3hati+2hatj+9hatk and hati-2phatj+3hatk are parallel

view solution
Q: 9[1]

Find veca.(vecbxxvecc), " if " veca=2hati+hatj+3hatk, vecb=-hati+2hatj+hatk  " and " vecc=3hati+hatj+2hatk

view solution
Q: 10[1]

If the Cartesian equations of a line are  (3-x)/5=(y+4)/7=(2z-6)/4 , write the vector equation for the line.

view solution
Q: 11[4]

If the function f : R → R be given by f[x] = x2 + 2 and g : R ​→ R be given by  g(x)=x/(x−1) , x1, find fog and gof and hence find fog (2) and gof (−3).

view solution
Q: 12 | Attempt any one[4]
Q: 12.1[4]

Prove that

tan^(-1) [(sqrt(1+x)-sqrt(1-x))/(sqrt(1+x)+sqrt(1-x))]=pi/4-1/2 cos^(-1)x,-1/sqrt2<=x<=1

view solution
Q: 12.2[4]

If tan^(-1)((x-2)/(x-4)) +tan^(-1)((x+2)/(x+4))=pi/4 ,find the value of x

view solution
Q: 13[4]

Using properties of determinants, prove that

|[x+y,x,x],[5x+4y,4x,2x],[10x+8y,8x,3x]|=x^3

view solution
Q: 14[4]

Find the value of dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)

view solution
Q: 15[4]

If y = P eax + Q ebx, show that

(d^y)/(dx^2)=(a+b)dy/dx+aby=0

view solution
Q: 16[4]
Q: 16.1[4]

Find the value(s) of x for which y = [x(x − 2)]2 is an increasing function.

view solution
Q: 16.2[4]

Find the equations of the tangent and normal to the curve x^2/a^2−y^2/b^2=1 at the point (sqrt2a,b) .

view solution
Q: 17[4]
Q: 17.1[4]

Evaluate :

∫_0^π(4x sin x)/(1+cos^2 x) dx

view solution
Q: 17.2[4]

Evaluate :

∫(x+2)/sqrt(x^2+5x+6)dx

view solution
Q: 18[4]

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

view solution
Q: 19[4]

Solve the differential equation  (1 + x2) dy/dx+y=e^(tan^(−1))x.

view solution
Q: 20[4]
Q: 20.1[4]

Show that four points A, B, C and D whose position vectors are

4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk) respectively are coplanar.

view solution
Q: 20.2[4]

The scalar product of the vector veca=hati+hatj+hatk with a unit vector along the sum of vectors vecb=2hati+4hatj−5hatk and vecc=λhati+2hatj+3hatk is equal to one. Find the value of λ and hence, find the unit vector along vecb +vecc

view solution
Q: 21[4]

A line passes through (2, −1, 3) and is perpendicular to the lines vecr=(hati+hatj-hatk)+lambda(2hati-2hatj+hatk) and vecr=(2hati-hatj-3hatk)+mu(hati+2hatj+2hatk) . Obtain its equation in vector and Cartesian from.

view solution
Q: 22[4]

An experiment succeeds thrice as often as it fails. Find the probability that in the next five trials, there will be at least 3 successes.

view solution
Q: 23[6]

Two schools A and B want to award their selected students on the values of sincerity, truthfulness and helpfulness. School A wants to award Rs x each, Rs y each and Rs z each for the three respective values to 3, 2 and 1 students, respectively with a total award money of Rs 1,600. School B wants to spend Rs 2,300 to award 4, 1 and 3 students on the respective values (by giving the same award money to the three values as before). If the total amount of award for one prize on each value is Rs 900, using matrices, find the award money for each value. Apart from these three values, suggest one more value which should be considered for an award.

view solution
Q: 24[6]

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

Show that the altitude of a right circular cone of maximum volume that can be inscribed in a sphere of radius r is (4r)/3 . Also, show that the maximum volume of the cone is 8/27  of the volume of the sphere.

view solution
Q: 25[6]

Evaluate:

∫1/(cos^4x+sin^4x)dx﻿

view solution
Q: 26[6]

Using integration, find the area of the region bounded by the triangle whose vertices are (−1, 2), (1, 5) and (3, 4).

view solution
Q: 27 | Attempt any one[6]
Q: 27.1[6]

Find the equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x − y + z = 0. Also find the distance of the plane, obtained above, from the origin.

view solution
Q: 27.2[6]

Find the distance of the point (2, 12, 5) from the point of intersection of the line

vecr=2hati-4hat+2hatk+lambda(3hati+4hatj+2hatk)

view solution
Q: 28[6]

A manufacturing company makes two types of teaching aids A and B of Mathematics for class XII. Each type of A requires 9 labour hours for fabricating and 1 labour hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30, respectively. The company makes a profit of Rs 80 on each piece of type A and Rs 120 on each piece of type B. How many pieces of type A and type B should be manufactured per week to get maximum profit? Make it as an LPP and solve graphically. What is the maximum profit per week?

view solution
Q: 29 | Attempt any one [6]
Q: 29.1[6]

There are three coins. One is a two-headed coin (having head on both faces), another is a biased coin that comes up heads 75% of the times and the third is also a biased coin that comes up tails 40% of the time. One of the three coins is chosen at random and tossed and it shows heads. What is the probability that it was the two-headed coin?

view solution
Q: 29.2[6]

Two the numbers are selected at random (without replacement) from first six positive integers. Let X denote the larger of the two numbers obtained. Find the probability distribution of X. Find the mean and variance of this distribution.

view solution

Other Solutions

Ncert Biology Textbook for Class 12
Ncert Chemistry Textbook for Class 12 Part 1
Ncert Chemistry Textbook for Class 12 Part 2
Ncert Physics Textbook for Class 12 Part 1
Ncert Physics Textbook for Class 12 Part 2
S