text: Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
  
  # Important Questions for PUC Karnataka Science Class 12 - Department of Pre-University Education, Karnataka - Mathematics
  
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  Find the distance of the point (−1, −5, −10) from the point of intersection of the line vecr=2hati-hatj+2hatk+lambda(3hati+4hatj+2hatk)  and the plane vec r (hati-hatj+hatk)=5
  
  Appears in 7 question papers
  Chapter: [4.01] Three - Dimensional Geometry
  Concept: Three - Dimensional Geometry Examples and Solutions
  
  Find the area of the region in the first quadrant enclosed by the x-axis, the line y = x and the circle x2 + y2 = 32.
  
  Appears in 5 question papers
  Chapter: [3.03] Applications of the Integrals
  Concept: Area Under Simple Curves
  
  If y = xx, prove that (d^2y)/(dx^2)−1/y(dy/dx)^2−y/x=0.
  
  Appears in 4 question papers
  Chapter: [3.02] Applications of Derivatives
  Concept: Simple Problems on Applications of Derivatives
  
  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
  
  Appears in 4 question papers
  Chapter: [3.02] Applications of Derivatives
  Concept: Maxima and Minima
  
  Find : int(x+3)sqrt(3-4x-x^2dx)
  
  Appears in 4 question papers
  Chapter: [3.05] Integrals
  Concept: Methods of Integration - Integration by Substitution
  
  Find: I=intdx/(sinx+sin2x)
  
  Appears in 4 question papers
  Chapter: [3.05] Integrals
  Concept: Methods of Integration - Integration Using Partial Fractions
  
  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.
  
  Appears in 4 question papers
  Chapter: [4.01] Three - Dimensional Geometry
  Concept: Coplanarity of Two Lines
  
  If a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.
  
  Appears in 3 question papers
  Chapter: [1.01] Inverse Trigonometric Functions
  Concept: Properties of Inverse Trigonometric Functions
  
  Let A = {1, 2, 3,......, 9} and R be the relation in A × A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation. Also, obtain the equivalence class [(2, 5)].
  
  Appears in 3 question papers
  Chapter: [1.02] Relations and Functions
  Concept: Types of Relations
  
  Let f : N→N be a function defined as f(x)=9x^2+6x−5. Show that f : N→S, where S is the range of f, is invertible. Find the inverse of f and hence find f^-1(43) and f^−1(163).
  
  Appears in 3 question papers
  Chapter: [1.02] Relations and Functions
  Concept: Inverse of a Function
  
  The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?
  
  Appears in 3 question papers
  Chapter: [2.01] Determinants
  Concept: Inverse of a Matrix > Inverse of a Square Matrix by the Adjoint Method
  
  Prove that  |(yz-x^2,zx-y^2,xy-z^2),(zx-y^2,xy-z^2,yz-x^2),(xy-z^2,yz-x^2,zx-y^2)|is divisible by (x + y + z) and hence find the quotient.
  
  Appears in 3 question papers
  Chapter: [2.01] Determinants
  Concept: Elementary Transformations
  
  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).
  
  Appears in 3 question papers
  Chapter: [2.01] Determinants
  Concept: Properties of Determinants
  
  if 2[[3,4],[5,x]]+[[1,y],[0,1]]=[[7,0],[10,5]] , find (xy).
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Equality of Matrices
  
  Solve the following matrix equation for x: [x 1] [[1,0],[−2,0]]=0
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Operations on Matrices > Addition of Matrices
  
  Write the element a23 of a 3 ✕ 3 matrix A = (aij) whose elements aij are given by a_(ij)=∣(i−j)/2∣
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Introduction of Operations on Matrices
  
  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 = 0
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Operations on Matrices > Addition of Matrices
  
  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 A B C Hand-fans 40 25 35 Mats 50 40 50 Plates 20 30 40
  
  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.
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Multiplication of Two Matrices
  
  If [[3x,7],[-2,4]]=[[8,7],[6,4]], find the value of x
  
  Appears in 3 question papers
  Chapter: [2.02] Matrices
  Concept: Introduction of Operations on Matrices
  
  If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of  dy/dx at t = pi/4
  
  Appears in 3 question papers
  Chapter: [3.01] Continuity and Differentiability
  Concept: Derivatives of Functions in Parametric Forms
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  Important Questions for PUC Karnataka Science Class 12 Department of Pre-University Education, Karnataka Mathematics. You can further filter Important Questions by subjects and topics. Chapter wise important Questions for Class 12 Department of Pre-University Education, Karnataka. it gets easy to find all Class 12 important questions with answers in a single place for students. Saving time and can then focus on their studies and practice. Important questions for Class 12 chapter wise with solutions
  
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