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 number of vectors of unit length perpendicular to both the vectors a=2i^+j^+2k^ and b=j^+k^. 

    VIEW SOLUTION

  • Q2

    Write the number of all possible matrices of order 2 × 2 with each entry 1, 2 or 3. 

    VIEW SOLUTION

  • Q3

    If x ∈ N and x+3-2-3x 2x = 8, then find the value of x. 

    VIEW SOLUTION

  • Q4

    Write the position vector of the point which divides the join of points with position vectors 3a-2b and 2a+3b in the ratio 2 : 1. 

    VIEW SOLUTION

  • Q5

    Find the vector equation of the plane with intercepts 3, –4 and 2 on x, y and z-axis respectively. 

    VIEW SOLUTION

  • Q6

    Use elementary column operation C2 → C2 + 2C1 in the following matrix equation :

    2120=3120  10-11 

    VIEW SOLUTION

  • Q7

    The equation of tangent at (2, 3) on the curve y2 = ax3 + b is y = 4x – 5. Find the values of a and b. 

    VIEW SOLUTION

  • Q8

    Find the coordinates of the point where the line through the points A(3, 4, 1) and B(5, 1, 6) crosses the XZ plane. Also find the angle which this line makes with the XZ plane. 

    VIEW SOLUTION

  • Q9

    Find : 3x+14-3x-2x2dx 

    VIEW SOLUTION

  • Q10

    The two adjacent sides of a parallelogram are 2i^-4j^-5k^ and 2i^+2j^+3k^. Find the two unit vectors parallel to its diagonals. Using the diagonal vectors, find the area of the parallelogram. 

    VIEW SOLUTION

  • Q11

    Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes. 

    VIEW SOLUTION

  • Q12

    In a game, a man wins Rs 5 for getting a number greater than 4 and loses Rs 1 otherwise, when a fair die is thrown. The man decided to thrown a die thrice but to quit as and when he gets a number greater than 4. Find the expected value of the amount he wins/loses.


    OR

    A bag contains 4 balls. Two balls are drawn at random (without replacement) and are found to be white. What is the probability that all balls in the bag are white? 

    VIEW SOLUTION

  • Q13

    A trust invested some money in two type of bonds. The first bond pays 10% interest and second bond pays 12% interest. The trust received Rs 2,800 as interest. However, if trust had interchanged money in bonds, they would have got Rs 100 less as interest. Using matrix method, find the amount invested by the trust. Interest received on this amount will be given to Helpage India as donation. Which value is reflected in this question? 

    VIEW SOLUTION

  • Q14

    Differentiate xsinx+sinxcosx with respect to x.
     

    OR
     
    If y=2 coslogx+3 sinlogx, prove that x2d2ydx2+xdydx+y=0. 

    VIEW SOLUTION

  • Q15

    Solve the equation for x:sin-1x+sin-11-x=cos-1x


    OR
     
    If cos-1xa+cos-1yb=α, prove that x2a2-2xyabcos α+y2b2=sin2α 

    VIEW SOLUTION

  • Q16

    If x=a sin 2t1+cos 2t and y=b cos 2t1-cos 2t, find dydxat t=π4. 

    VIEW SOLUTION

  • Q17

    Solve the differential equation :

    y+xdydx=x-ydydx 

    VIEW SOLUTION

  • Q18

    Evaluate : 0π2sin2xsinx+cosxdx
     

    OR

    Evaluate : 032x cosπxdx 

    VIEW SOLUTION

  • Q19

    Find : x2x4+x2-2dx 

    VIEW SOLUTION

  • Q20

    Using properties of determinants, show that ΔABC is isosceles if:

    1111+cosA1+cosB1+cosCcos2A+cosAcos2B+cosBcos2C+cosC=0

                                                                          OR

    A shopkeeper has 3 varieties of pens 'A', 'B' and 'C'. Meenu purchased 1 pen of each variety for a total of Rs 21. Jeevan purchased 4 pens of 'A' variety 3 pens of 'B' variety and 2 pens of 'C' variety for Rs 60. While Shikha purchased 6 pens of 'A' variety, 2 pens of 'B' variety and 3 pens of 'C' variety for Rs 70. Using matrix method, find cost of each variety of pen. 

    VIEW SOLUTION

  • Q21

    There are two types of fertilisers 'A' and 'B'. 'A' consists of 12% nitrogen and 5% phosphoric acid whereas 'B' consists of 4% nitrogen and 5% phosphoric acid. After testing the soil conditions, farmer finds that he needs at least 12 kg of nitrogen and 12 kg of phosphoric acid for his crops. If 'A' costs Rs 10 per kg and 'B' cost Rs 8 per kg, then graphically determine how much of each type of fertiliser should be used so that nutrient requirements are met at a minimum cost. 

    VIEW SOLUTION

  • Q22

    Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is 63r.
     

    OR

    If the sum of lengths of hypotenuse and a side of a right angled triangle is given, show that area of triangle is maximum, when the angle between them is π3. 

    VIEW SOLUTION

  • Q23

    Five bad oranges are accidently mixed with 20 good ones. If four oranges are drawn one by one successively with replacement, then find the probability distribution of number of bad oranges drawn. Hence find the mean and variance of the distribution. 

    VIEW SOLUTION

  • Q24

    Prove that the curves y2 = 4x and x2 = 4y divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts. 

    VIEW SOLUTION

  • Q25

    Show that the binary operation * on A = R – { – 1} defined as a*b = a + b + ab for all a, b ∈ A is commutative and associative on A. Also find the identity element of * in A and prove that every element of A is invertible. 

    VIEW SOLUTION

  • Q26

    Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector 2i^+3j^+4k^ to the plane r.2i^+j^+3k^-26=0. Also find image of P in the plane. 

    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