Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12

# Question Bank Solutions for PUC Karnataka Science Class 12 - Department of Pre-University Education, Karnataka - Mathematics

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If |[2x,5],[8,x]|=|[6,-2],[7,3]|, write the value of x.

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

Show that the lines (x+1)/3=(y+3)/5=(z+5)/7 and (x−2)/1=(y−4)/3=(z−6)/5 intersect. Also find their point of intersection

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

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

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

Find the value of a if [[a-b,2a+c],[2a-b,3c+d]]=[[-1,5],[0,13]]

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

Differentiate xsinx+(sinx)cosx with respect to x.

[0.05] Continuity and Differentiability
Chapter: [0.05] Continuity and Differentiability
Concept: Derivative - Exponential and Log

If A=[[2,0,1],[2,1,3],[1,-1,0]] , find A2 − 5 A + 16 I.

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

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

[0.09] Differential Equations
Chapter: [0.09] Differential Equations
Concept: Methods of Solving First Order, First Degree Differential Equations > Linear Differential Equations

Write the element a12 of the matrix A = [aij]2 × 2, whose elements aij are given by aij = e2ix sin jx.

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

[0.08] Applications of the Integrals
Chapter: [0.08] Applications of the Integrals
Concept: Area of the Region Bounded by a Curve and a Line

Write the element a23 of a 3 ✕ 3 matrix A = (aij) whose elements aij are given by a_(ij)=∣(i−j)/2∣

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

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

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Find the equation of the curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of the coordinates of the point.

[0.09] Differential Equations
Chapter: [0.09] Differential Equations
Concept: Methods of Solving First Order, First Degree Differential Equations > Linear Differential Equations

If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

If A = [aij] =[[2,3,-5],[1,4,9],[0,7,-2]]and B = [bij] [[2,-1],[-3,4],[1,2]]

then find (i) a22 + b21 (ii) a11 b11 + a22 b22

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Let A be a matrix of order 3 × 4. If R1 denotes the first row of A and C2 denotes its second column, then determine the orders of matrices R1 and C2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Construct a 2 × 2  matrix whose elements a_(ij)

are given by: (i+j)^2/2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Construct a 2 × 2 matrix whose elements aij are given by:

aij=(i-j)^2/2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Construct a 2 × 2 matrix whose elements aij are given by:

a_(ij)=(i-2_j)^2/2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Construct a 2 × 2 matrix whose elements aij are given by:

a_(ij)= (2i +j)^2/2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices

Construct a 2 × 2 matrix whose elements aij are given by:

a_(ij)=|2_i - 3_i|/2

[0.03] Matrices
Chapter: [0.03] Matrices
Concept: Introduction of Operations on Matrices
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