Mathematics All India Set 1 E 2015-2016 Commerce (English Medium) Class 12 Question Paper Solution

Mathematics [All India Set 1 E]
Marks: 100 CBSE
Commerce (English Medium)
Science (English Medium)
Arts (English Medium)

Academic Year: 2015-2016
Date & Time: 14th March 2016, 10:30 am
Duration: 3h

(i) All questions are compulsory.

(ii) Please check that this question paper contains 26 questions.

(iii) Questions 1 - 6 in Section A are very short-answer type questions carrying 1 mark each.

(iv) Questions 7 - 19 in Section B are long-answer I type questions carrying 4 marks each.

(v) Questions 20 - 26 in Section C are long-answer II type questions carrying 6 marks each.


Write the value of `|(a-b, b- c, c-a),(b-c, c-a, a-b),(c-a, a-b, b-c)|`

Concept: Applications of Determinants and Matrices
Chapter: [0.04] Determinants

If A = `((1, -2, 3),(-4,2,5)) and B = ((2,3),(4,5),(2,1))` and BA = (bij), find b21 + b32.

Concept: Algebraic Operations on Matrices - Properties of Scalar Multiplication of a Matrix
Chapter: [0.03] Matrices

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

Concept: Order of a Matrix
Chapter: [0.03] Matrices

Write the coordinates of the point which is the reflection of the point (α, β,  γ) in the XZ-plane.

Concept: Distance of a Point from a Plane
Chapter: [0.11] Three - Dimensional Geometry

Find the position vector of the point which divides the join of points with position vectors `vec"a" + 3vec"b" and vec"a"- vec"b"` internally in the ratio 1 : 3. 

Concept: Position Vector of a Point Dividing a Line Segment in a Given Ratio
Chapter: [0.1] Vectors

If `|vec"a"| = 4, |vec"b"| = 3` and `vec"a".vec"b" = 6 sqrt(3)`, then find the value of `|vec"a" xx vec"b"|`.

Concept: Multiplication of a Vector by a Scalar
Chapter: [0.1] Vectors

Solve for x : `tan^-1 ((2-"x")/(2+"x")) = (1)/(2)tan^-1  ("x")/(2), "x">0.`

Concept: Properties of Inverse Trigonometric Functions
Chapter: [0.02] Inverse Trigonometric Functions

Prove that : `2sin^-1 (3/5) -tan^-1 (17/31) = pi/4.`

Concept: Proof Derivative X^n Sin Cos Tan
Chapter: [0.05] Continuity and Differentiability

On her birthday Seema decided to donate some money to children of an orphanage home. If there were 8 children less, everyone would have got ₹ 10 more. However, if there were 16 children more, everyone would have got ₹ 10 less. Using the matrix method, find the number of children and the amount distributed by Seema. What values are reflected by Seema’s decision?

Concept: Applications of Determinants and Matrices
Chapter: [0.04] Determinants

If `"x" = "e"^(cos2"t")  "and"  "y" = "e"^(sin2"t")`, prove that `(d"y")/(d"x") = - ("y"log"x")/("x"log"y")`.

Concept: Exponential and Logarithmic Functions
Chapter: [0.05] Continuity and Differentiability

Verify Mean value theorem for the function f(x) = 2sin x + sin 2x on [0, π].

Concept: Mean Value Theorem
Chapter: [0.05] Continuity and Differentiability

Show that the function f given by:


is discontinuous at x = 0.

Concept: Concept of Continuity
Chapter: [0.05] Continuity and Differentiability

Find the equation of the tangent line to the curve `"y" = sqrt(5"x" -3) -5`, which is parallel to the line  `4"x" - 2"y" + 5 = 0`.

Concept: Tangents and Normals
Chapter: [0.06] Applications of Derivatives

Evaluate: `int_1^5{|"x"-1|+|"x"-2|+|"x"-3|}d"x"`.

Concept: Evaluation of Definite Integrals by Substitution
Chapter: [0.07] Integrals

Evaluate: `int_0^pi ("x"sin "x")/(1+ 3cos^2 "x") d"x"`.

Concept: Properties of Definite Integrals
Chapter: [0.07] Integrals

Find : `int_  (2"x"+1)/(("x"^2+1)("x"^2+4))d"x"`.

Concept: Properties of Definite Integrals
Chapter: [0.07] Integrals

Find: `int_  (3"x"+ 5)sqrt(5 + 4"x"-2"x"^2)d"x"`.

Concept: Evaluation of Definite Integrals by Substitution
Chapter: [0.07] Integrals

Solve the differential equation : `"x"(d"y")/(d"x") + "y" - "x" + "xy"cot"x" = 0; "x" != 0.`

Concept: Solutions of Linear Differential Equation
Chapter: [0.09] Differential Equations

Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0  "given that"  "y" = 0  "when"  "x" = 1`.

Concept: General and Particular Solutions of a Differential Equation
Chapter: [0.09] Differential Equations

Find the angle between the vectors `vec"a" + vec"b" and  vec"a" -vec"b" if  vec"a" = 2hat"i"-hat"j"+3hat"k" and vec"b" = 3hat"i" + hat"j"-2hat"k", and"hence find a vector perpendicular to both"  vec"a" + vec"b" and vec"a" - vec"b"`.

Concept: Vectors Examples and Solutions
Chapter: [0.1] Vectors

Show that the lines `("x"-1)/(3) = ("y"-1)/(-1) = ("z"+1)/(0) = λ and  ("x"-4)/(2) = ("y")/(0) = ("z"+1)/(3)` intersect. Find their point of intersection. 

Concept: Equation of a Plane - Plane Passing Through the Intersection of Two Given Planes
Chapter: [0.11] Three - Dimensional Geometry

A committee of 4 students is selected at random from a group consisting of 7 boys and 4 girls. Find the probability that there are exactly 2 boys in the committee, given that at least one girl must be there in the committee.

Concept: Introduction of Probability
Chapter: [0.13] Probability

A random variable X has the following probability distribution :

X 0 1 2 3 4 5 6
P(X) C 2C 2C 3C C2 2C2 7C2+C

Find the value of C and also calculate the mean of this distribution.

Concept: Random Variables and Its Probability Distributions
Chapter: [0.13] Probability

Show that the relation R defined by (a, b)R(c,d) ⇒ a + d = b + c   on the A x A  , where A =  {1, 2,3,...,10}  is an equivalence relation. Hence write the equivalence class [(3, 4)]; a, b, c,d ∈ A.

Concept: Types of Relations
Chapter: [0.01] Relations and Functions

Solve for x : `|("a"+"x","a"-"x","a"-"x"),("a"-"x","a"+"x","a"-"x"),("a"-"x","a"-"x","a"+"x")| = 0`, using properties of determinants. 

Concept: Properties of Determinants
Chapter: [0.04] Determinants

Using elementary row operations, find the inverse of the matrix A = `((3, 3,4),(2,-3,4),(0,-1,1))` and hence solve the following system of equations :  3x - 3y + 4z = 21, 2x -3y + 4z = 20, -y + z = 5.

Concept: Elementary Transformations
Chapter: [0.03] Matrices [0.04] Determinants

Show that height of the cylinder of greatest volume which can be inscribed in a right circular cone of height h and semi-vertical angle α is one-third that of the cone and the greatest volume of the cylinder is `(4)/(27) pi"h"^3 tan^2 α`.

Concept: Maximum and Minimum Values of a Function in a Closed Interval
Chapter: [0.06] Applications of Derivatives

Find the intervals in which the function `f("x") = (4sin"x")/(2+cos"x") -"x";0≤"x"≤2pi` is strictly increasing or strictly decreasing. 

Concept: Increasing and Decreasing Functions
Chapter: [0.06] Applications of Derivatives

Using integration find the area of the triangle formed by negative x-axis and tangent and normal to the circle `"x"^2 + "y"^2 = 9  "at" (-1,2sqrt2)`.

Concept: Area Under Simple Curves
Chapter: [0.08] Applications of the Integrals

Find the coordinates of the foot of perpendicular and perpendicular distance from the point P(4,3,2) to the plane x + 2y + 3z = 2. Also find the image of P in the plane.

Concept: Three - Dimensional Geometry Examples and Solutions
Chapter: [0.11] Three - Dimensional Geometry

A, B and C throw a pair of dice in that order alternatively till one of them gets a total of 9 and wins the game. Find their respective probabilities of winning, if A starts first.

Concept: Probability Examples and Solutions
Chapter: [0.13] Probability

A company manufactures two types of cardigans: type A and type B. It costs ₹ 360 to make a type A cardigan and ₹ 120 to make a type B cardigan. The company can make at most 300 cardigans and spend at most ₹ 72000 a day. The number of cardigans of type B cannot exceed the number of cardigans of type A by more than 200. The company makes a profit of ₹ 100 for each cardigan of type A and ₹ 50 for every cardigan of type B. 

Formulate this problem as a linear programming problem to maximize the profit to the company. Solve it graphically and find the maximum profit.

Concept: Graphical Method of Solving Linear Programming Problems
Chapter: [0.12] Linear Programming

Other Solutions

Submit Question Paper

Help us maintain new question papers on, so we can continue to help students

only jpg, png and pdf files

CBSE previous year question papers Class 12 Mathematics with solutions 2015 - 2016

     CBSE Class 12 Maths question paper solution is key to score more marks in final exams. Students who have used our past year paper solution have significantly improved in speed and boosted their confidence to solve any question in the examination. Our CBSE Class 12 Maths question paper 2016 serve as a catalyst to prepare for your Mathematics board examination.
     Previous year Question paper for CBSE Class 12 Maths-2016 is solved by experts. Solved question papers gives you the chance to check yourself after your mock test.
     By referring the question paper Solutions for Mathematics, you can scale your preparation level and work on your weak areas. It will also help the candidates in developing the time-management skills. Practice makes perfect, and there is no better way to practice than to attempt previous year question paper solutions of CBSE Class 12.

How CBSE Class 12 Question Paper solutions Help Students ?
• Question paper solutions for Mathematics will helps students to prepare for exam.
• Question paper with answer will boost students confidence in exam time and also give you an idea About the important questions and topics to be prepared for the board exam.
• For finding solution of question papers no need to refer so multiple sources like textbook or guides.

      Forgot password?
Use app×