011-40705070  or  
Call me
Download our Mobile App
Select Board & Class
  • Select Board
  • Select Class
General Instructions :
(i) All questions are compulsory.
(ii) Please check that this Question Paper contains 26 Questions.
(iii) Marks for each question are indicated against it.
(iv) Questions 1 to 6 in Section-A are Very Short Answer Type Questions carrying one mark each.
(v) Questions 7 to 19 in Section-B are Long Answer I Type Questions carrying 4 marks each.
(vi) Questions 20 to 26 in Section-C are Long Answer II Type Questions carrying 6 marks each.
(vii) Please write down the serial number of the Question before attempting it.
* Kindly update your browser if you are unable to view the equations.
Question 1
  • Q1

    Write the value of  a . b  × a. 

    VIEW SOLUTION

  • Q2

    If a= i^ + 2 j^ - k^, b = 2 i^ + j^ + k^ and c = 5 i^ - 4 j^ + 3 k^, then find the value of a + b. c. 

    VIEW SOLUTION

  • Q3

    Write the direction ratios of the following line :

    x = -3, y-43 = 2 -z1 

    VIEW SOLUTION

  • Q4

    If A = 235-2, then write A−1. 

    VIEW SOLUTION

  • Q5

    Find the differential equation representing the curve y = cx + c2. 

    VIEW SOLUTION

  • Q6

    Write the integrating factor of the following differential equation:

    (1+y2) dx-(tan-1 y-x) dy=0 

    VIEW SOLUTION

  • Q7

    Using the properties of determinants, prove the following:

    1xx+12xx(x-1)x(x+1)3x(1-x)   x(x-1) (x-2) x(x+1) (x-1)=6x2 1-x2 

    VIEW SOLUTION

  • Q8

    If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1-cos 2t), show that dydx=βαtan t. 

    VIEW SOLUTION

  • Q9

    Find : ddxcos-1 x-x-1x+x-1 

    VIEW SOLUTION

  • Q10

    Find the derivative of the following function f(x) w.r.t. x, at x = 1 :
    cos-1 sin 1+x2+xx 

    VIEW SOLUTION

  • Q11

    Evaluate :
    0π22sin x2sin x+2cos xdx
     

    OR

    Evaluate :03/2 x·cos πxdx 

    VIEW SOLUTION

  • Q12

    To raise money for an orphanage, students of three schools A, B and C organised an exhibition in their locality, where they sold paper bags, scrap-books and pastel sheets made by them using recycled paper, at the rate of Rs 20, Rs 15 and Rs 5 per unit respectively. School A sold 25 paper bags, 12 scrap-books and 34 pastel sheets. School B sold 22 paper bags, 15 scrap-books and 28 pastel sheets while School C sold 26 paper bags, 18 scrap-books and 36 pastel sheets. Using matrices, find the total amount raised by each school.

    By such exhibition, which values are generated in the students? 

    VIEW SOLUTION

  • Q13

    Prove that :

    2 tan-1a-ba+btanx2=cos-1a cos x+ba+b cos x


    OR

    Solve the following for x :

    tan-1x-2x-3+tan-1x+2x+3=π4, x<1. 

    VIEW SOLUTION

  • Q14

    If A = 2   0  12   1  31-1  0, find A2 − 5 A + 16 I. 

    VIEW SOLUTION

  • Q15

    Show that four points A, B, C and D whose position vectors are 4i^+5j^+k^, -j^ -k^,  3i^+9j^+4k^ and 4-i^+j^+k^ respectively are coplanar. 

    VIEW SOLUTION

  • Q16

    Show that the following two lines are coplanar:

    x-a+dα-δ= y-aα=z-a-dα+δ and x-b+cβ-γ=y-bβ=z-b-cβ+γ

     
    OR

    Find the acute angle between the plane 5x − 4y + 7z − 13 = 0 and the y-axis. 

    VIEW SOLUTION

  • Q17

    A and B throw a die alternatively till one of them gets a number greater than four and wins the game. If A starts the game, what is the probability of B winning?


    OR
     
    A die is thrown three times. Events A and B are defined as below:
    A : 5 on the first and 6 on the second throw.
    B: 3 or 4 on the third throw.

    Find the probability of B, given that A has already occurred.
     

    VIEW SOLUTION

  • Q18

    Evaluate :
    cot x+tan x dx 

    VIEW SOLUTION

  • Q19

    Find :

    x3-1x3+xdx 

    VIEW SOLUTION

  • Q20

    Using integration, find the area of the region bounded by the lines y = 2 + x, y = 2 – x and x = 2. 

    VIEW SOLUTION

  • Q21

    Find the the differential equation for all the straight lines, which are at a unit distance from the origin.


    OR

    Show that the differential  equation 2xydydx=x2+3y2 is homogeneous and solve it. 

    VIEW SOLUTION

  • Q22

    Find the direction ratios of the normal to the plane, which passes through the points (1, 0, 0) and (0, 1, 0) and makes angle π4 with the plane x + y = 3. Also find the equation of the plane. 

    VIEW SOLUTION

  • Q23

    If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x3 + 5, then find the value of (fog)−1 (x).
     

    OR

    Let A = Q ✕ Q, where Q is the set of all rational numbers, and * be a binary operation defined on A by
    (a, b) * (c, d) = (ac, b + ad), for all (a, b) (c, d) ∈ A.
    Find
    (i) the identity element in A
    (ii) the invertible element of A. 

    VIEW SOLUTION

  • Q24

    If the function f(x)=2x3-9mx2+12m2x+1, where m>0 attains its maximum and minimum at p and q respectively such that p2=q, then find the value of m. 

    VIEW SOLUTION

  • Q25

    The postmaster of a local post office wishes to hire extra helpers during the Deepawali season, because of a large increase in the volume of mail handling and delivery. Because of the limited office space and the budgetary conditions, the number of temporary helpers must not exceed 10. According to past experience, a man can handle 300 letters and 80 packages per day, on the average, and a woman can handle 400 letters and 50 packets per day. The postmaster believes that the daily volume of extra mail and packages will be no less than 3400 and 680 respectively. A man receives Rs 225 a day and a woman receives Rs 200 a day. How many men and women helpers should be hired to keep the pay-roll at a minimum ? Formulate an LPP and solve it graphically. 

    VIEW SOLUTION

  • Q26

    40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ? 

    VIEW SOLUTION

Board Papers 2014, Board Paper Solutions 2014, Sample Papers for CBSE Board, CBSE Boards Previous Years Question Paper, Board Exam Solutions 2014, Board Exams Solutions Maths, Board Exams Solutions English, Board Exams Solutions Hindi, Board Exams Solutions Physics, Board Exams Solutions Chemistry, Board Exams Solutions Biology, Board Exams Solutions Economics, Board Exams Solutions Business Studies, Maths Board Papers Solutions, Science Board Paper Solutions, Economics Board Paper Solutions, English Board Papers Solutions, Physics Board Paper Solutions, Chemistry Board Paper Solutions, Hindi Board Paper Solutions, Political Science Board Paper Solutions, Answers of Previous Year Board Papers, Delhi Board Paper Solutions, All India Board Papers Solutions, Abroad/Foreign Board Paper Solutions, cbse class 12 board papers, Cbse board papers with solutions, CBSE solved Board Papers, ssc board papers.

close