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# Question Bank Solutions for HSC Science (General) 12th Board Exam - Maharashtra State Board - 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.

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Elementary Operation (Transformation) of a Matrix

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

[0.06] Conics
Chapter: [0.06] Conics
Concept: Conics > Tangents and normals - equations of tangent and normal at a point

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

[0.2] Bernoulli Trials and Binomial Distribution
Chapter: [0.2] Bernoulli Trials and Binomial Distribution
Concept: Bernoulli Trials and Binomial Distribution

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

[0.16] Applications of Definite Integral
Chapter: [0.16] Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line

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

[0.15] Integration
Chapter: [0.15] Integration
Concept: Methods of Integration - Integration by Substitution

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

[0.15] Integration
Chapter: [0.15] Integration
Concept: Methods of Integration - Integration by Substitution

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.

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Elementary Operation (Transformation) of a Matrix

A random variable X has the following probability distribution:

then E(X)=....................

[0.027000000000000003] Probability Distributions
Chapter: [0.027000000000000003] Probability Distributions
Concept: Random Variables and Its Probability Distributions

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

[0.19] Probability Distribution
Chapter: [0.19] Probability Distribution
Concept: Conditional Probability

From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -

(a) exactly 1 defective bulb.

(b) at least 1 defective bulb.

[0.027000000000000003] Probability Distributions
Chapter: [0.027000000000000003] Probability Distributions
Concept: Random Variables and Its Probability Distributions

If p ˄ q = F, p → q = F, then the truth value of p and q is :

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Mathematical Logic > Truth Value of Statement in Logic

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

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Elementary Operation (Transformation) of a Matrix

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

[0.16] Applications of Definite Integral
Chapter: [0.16] 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

[0.15] Integration
Chapter: [0.15] Integration
Concept: Methods of Integration - Integration by Substitution

Write truth values of the following statements :sqrt5 is an irrational number but 3 +sqrt 5 is a complex number.

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Mathematical Logic > Truth Value of Statement in Logic

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

[0.04] Pair of Straight Lines
Chapter: [0.04] Pair of Straight Lines
Concept: Pair of Straight Lines > Pair of Lines Passing Through Origin - Combined Equation

Solve the following equations by the method of reduction :

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

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Elementary Operation (Transformation) of a Matrix

Evaluate :intxlogxdx

[0.15] Integration
Chapter: [0.15] Integration
Concept: Methods of Integration - Integration by Substitution

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.

[0.19] Probability Distribution
Chapter: [0.19] Probability Distribution
Concept: Conditional Probability

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

[0.16] Applications of Definite Integral
Chapter: [0.16] Applications of Definite Integral
Concept: Area of the Region Bounded by a Curve and a Line
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