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Question Bank Solutions for HSC Science (General) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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Mathematics and Statistics
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The cost of 4 dozen pencils, 3 dozen pens and 2 dozen erasers is Rs. 60. The cost of 2 dozen pencils, 4 dozen pens and 6 dozen erasers is Rs. 90 whereas the cost of 6 dozen pencils, 2 dozen pens and 3 dozen erasers is Rs. 70. Find the cost of each item per dozen by using matrices.

[2] Matrices
Chapter: [2] Matrices
Concept: Elementary Operation (Transformation) of a Matrix
Appears in 2 question papers

The equation of tangent to the curve y=`y=x^2+4x+1` at

(-1,-2) is...............

(a)  2x -y = 0                        (b)  2x+y-5 = 0

(c)  2x-y-1=0                        (d)  x+y-1=0

[6] Conics
Chapter: [6] Conics
Concept: Conics - Tangents and normals - equations of tangent and normal at a point
Appears in 1 question paper

Given that X ~ B(n= 10, p). If E(X) = 8 then the value of

p is ...........

(a) 0.6

(b) 0.7

(c) 0.8

(d) 0.4

[20] Bernoulli Trials and Binomial Distribution
Chapter: [20] Bernoulli Trials and Binomial Distribution
Concept: Bernoulli Trials and Binomial Distribution
Appears in 1 question paper

Find the area bounded by the curve y2 = 4axx-axis and the lines x = 0 and x = a.

[16] Applications of Definite Integral
Chapter: [16] Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line
Appears in 2 question papers

Evaluate : `int (sinx)/sqrt(36-cos^2x)dx`

[15] Integration
Chapter: [15] Integration
Concept: Methods of Integration - Integration by Substitution
Appears in 1 question paper

Evaluate : `int_0^pi(x)/(a^2cos^2x+b^2sin^2x)dx`

[15] Integration
Chapter: [15] Integration
Concept: Methods of Integration - Integration by Substitution
Appears in 1 question paper

The sum of three numbers is 6. When second number is subtracted from thrice the sum of first and third number, we get number 10. Four times the sum of third number is subtracted from five times the sum of first and second number, the result is 3. Using above information, find these three numbers by matrix method.

[2] Matrices
Chapter: [2] Matrices
Concept: Elementary Operation (Transformation) of a Matrix
Appears in 1 question paper

A fair coin is tossed five times. Find the probability that it shows exactly three times head.

[19] Probability Distribution
Chapter: [19] Probability Distribution
Concept: Conditional Probability
Appears in 1 question paper

Find the inverse of the matrix,  `A=[[1,3,3],[1,4,3],[1,3,4]]`by using column transformations.

[2] Matrices
Chapter: [2] Matrices
Concept: Elementary Operation (Transformation) of a Matrix
Appears in 1 question paper

Find the area of the region bounded by the parabola y2 = 4ax and its latus rectum.

[16] Applications of Definite Integral
Chapter: [16] Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line

Show that:  `int1/(x^2sqrt(a^2+x^2))dx=-1/a^2(sqrt(a^2+x^2)/x)+c`

[15] Integration
Chapter: [15] Integration
Concept: Methods of Integration - Integration by Substitution
Appears in 1 question paper

Find the joint equation of the pair of lines through the origin each of which is making an angle of 30° with the line 3x + 2y - 11 = 0

[4] Pair of Straight Lines
Chapter: [4] Pair of Straight Lines
Concept: Pair of Straight Lines - Pair of Lines Passing Through Origin - Combined Equation
Appears in 1 question paper

Solve the following equations by the method of reduction :

2x-y + z=1,  x + 2y +3z = 8, 3x + y-4z=1.

[2] Matrices
Chapter: [2] Matrices
Concept: Elementary Operation (Transformation) of a Matrix
Appears in 1 question paper

Evaluate :`intxlogxdx`

[15] Integration
Chapter: [15] Integration
Concept: Methods of Integration - Integration by Substitution
Appears in 1 question paper

The probability that a certain kind of component will survive a check test is 0.5. Find the probability that exactly two of the next four components tested will survive.

[19] Probability Distribution
Chapter: [19] Probability Distribution
Concept: Conditional Probability
Appears in 1 question paper

Find the area of the region bounded by the curve y = sinx, the lines x=-π/2 , x=π/2 and X-axis

[16] Applications of Definite Integral
Chapter: [16] Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line
Appears in 1 question paper

Show that the function defined by f(x) =|cosx| is continuous function.

[12] Continuity
Chapter: [12] Continuity
Concept: Introduction of Continuity
Appears in 1 question paper

A bakerman sells 5 types of cakes. Profits due to the sale of each type of cake is respectively Rs. 3, Rs. 2.5, Rs. 2, Rs. 1.5, Rs. 1. The demands for these cakes are 10%, 5%, 25%, 45% and 15% respectively. What is the expected profit per cake?

[18] Statistics
Chapter: [18] Statistics
Concept: Statistics - Bivariate Frequency Distribution
Appears in 1 question paper

Verify Lagrange’s mean value theorem for the function f(x)=x+1/x, x ∈ [1, 3]

[14] Applications of Derivative
Chapter: [14] Applications of Derivative
Concept: Mean Value Theorem
Appears in 1 question paper

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`

[15] Integration
Chapter: [15] Integration
Concept: Methods of Integration - Integration by Substitution
Appears in 1 question paper
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Question Bank Solutions for HSC Science (General) 12th Board Exam Maharashtra State Board Mathematics and Statistics. You can further filter Question Bank Solutions by subjects and chapters. Solutions for most of the questions for Maharashtra State Board 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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