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Question Bank Solutions for CBSE (Arts) Class 12 - CBSE - Mathematics

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

[2.01] Determinants
Chapter: [2.01] 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

[4.01] Three - Dimensional Geometry
Chapter: [4.01] 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`

[4.01] Three - Dimensional Geometry
Chapter: [4.01] Three - Dimensional Geometry
Concept: Three - Dimensional Geometry Examples and Solutions

Write the value of `tan(2tan^(-1)(1/5))`

[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

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

[2.01] Determinants
Chapter: [2.01] Determinants
Concept: Applications of Determinants and Matrices

If `|[x+1,x-1],[x-3,x+2]|=|[4,-1],[1,3]|`, then write the value of x.

[2.01] Determinants
Chapter: [2.01] Determinants
Concept: Applications of Determinants and Matrices

Find the value of the following: `tan(1/2)[sin^(-1)((2x)/(1+x^2))+cos^(-1)((1-y^2)/(1+y^2))],|x| <1,y>0 and xy <1`

[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

Using integration, find the area bounded by the curve x2 = 4y and the line x = 4y − 2.

[3.03] Applications of the Integrals
Chapter: [3.03] Applications of the Integrals
Concept: Area of the Region Bounded by a Curve and a Line

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

[3.01] Continuity and Differentiability
Chapter: [3.01] Continuity and Differentiability
Concept: Derivative - Exponential and Log

Solve the equation for x:sin1x+sin1(1x)=cos1x

[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

If `cos^-1( x/a) +cos^-1 (y/b)=alpha` , prove that `x^2/a^2-2(xy)/(ab) cos alpha +y^2/b^2=sin^2alpha`

[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

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.

[3.03] Applications of the Integrals
Chapter: [3.03] Applications of the Integrals
Concept: Area of the Region Bounded by a Curve and a Line

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

[2.02] Matrices
Chapter: [2.02] Matrices
Concept: Introduction of Operations on Matrices
 

Prove that :

`2 tan^-1 (sqrt((a-b)/(a+b))tan(x/2))=cos^-1 ((a cos x+b)/(a+b cosx))`

 
[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

Solve the following for x :

`tan^(-1)((x-2)/(x-3))+tan^(-1)((x+2)/(x+3))=pi/4,|x|<1`

[1.01] Inverse Trigonometric Functions
Chapter: [1.01] Inverse Trigonometric Functions
Concept: Inverse Trigonometric Functions (Simplification and Examples)

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

[3.03] Applications of the Integrals
Chapter: [3.03] Applications of the Integrals
Concept: Area of the Region Bounded by a Curve and a Line

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 π/4 with the plane x + y = 3. Also find the equation of the plane

[4.01] Three - Dimensional Geometry
Chapter: [4.01] Three - Dimensional Geometry
Concept: Three - Dimensional Geometry Examples and Solutions

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

[3.04] Differential Equations
Chapter: [3.04] Differential Equations
Concept: Methods of Solving First Order, First Degree Differential Equations > Linear Differential Equations

Find the coordinates of the foot of perpendicular drawn from the point A (-1,8,4) to the line joining the points B(0,-1,3) and C(2,-3,-1). Hence find the image of the point A in the line BC.

[4.01] Three - Dimensional Geometry
Chapter: [4.01] Three - Dimensional Geometry
Concept: Three - Dimensional Geometry Examples and Solutions

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

[2.02] Matrices
Chapter: [2.02] Matrices
Concept: Introduction of Operations on Matrices
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Question Bank Solutions for CBSE (Arts) Class 12 CBSE Mathematics. You can further filter Question Bank Solutions by subjects and topics. Solutions for most of the questions for CBSE can be found here on Shaalaa.com. You can use these solutions to prepare for your studies and ace in exams. Solving questions is a great way to practice and with Shaalaa.com, you can answer a question and then also check your answer with the solutions provided.
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