MATHS – IMPORTANT QUESTION BANK FOR MAHARASHTRA BOARD HSC 2016 EXAMINATION

(Section I)

UNIT NO 1

MATHEMATICAL LOGIC’S

Points to remember 

1: Statement and truth values.

2: Open sentence.

3: Quantifiers

4: Compound Statement and it’s truth table.

5: Tautology , contradiction , contingency.

6: Logical equivalence.

7: Duality

8: Negation of a compound statement and quantifiers

9: Switching Circuit.

UNIT NO 2

MATRICES

Que. If A is square matrix then A+A Is

(A) Symmetric matrix     (B) Singular matrix

(C) Diagonal matrix         (D) Skew symmetric

Ans: A

UNIT NO 3

TRIGONOMETRIC FUNCTIONS

Points to remember

1.Trigonometric Equations a d it s solutions. principal (the solution lies between 0 and 2 π ) and general solution

2.Solution of triangle. Sine, cosine, projection Rule, Half angle formula.

3. Inverse trigonometric functions. Properties of inverse trigonometric functions

UNIT NO 4

PAIR Of STRAIGHT LINES

Points to remember

1. Joint or combined equation of two lines.

2 .Homogneous Equation of second degree

3. Sum and Product of Slopes.

4. Angle between two lines represented by homogeneous equation.

5. General second degree equation in x and y.

6. Theory questions.

UNIT NO 5

VECTORS

Points to remember

1. Collinearity and coplanarity.
2. Section formula.
3. Scalar Triple Product.
4. Application of vector to geometry.
5. Theory Questions

UNIT NO 6

THREE DIMENSIONAL GEOMETRY

Points to remember

1. Direction angles.
2. Direction cosines.
3. : Direction ratios.
4. Relation between the direction ratios and cosines of a line.
5. Angle between two lines.

UNIT NO 7

LINE

Points to remember

1. Vector equation of line.

(i) Passing through given point and parallel to given vector

.(ii) Passing through two given points.

1. Cartesian or symmetric form of equation of line.
2. Distance of a point from a line.
3. Skew lines.

(i) Distance between two skew lines.

(ii) Distance between two parallel lines.

UNIT NO 8

PLANE

Points to remember

1. Vector and Cartesian equation of plane.

(i) Normal form.

(ii) Passing through given point and perpendicular to given vector.

(iii)Passing through given point and parallel to two given vector.

(iv)Passing through three non collinear points.

(v) Passing through intersection of two lines.

1. Angle between two planes.
2. Angle between line and plane.
3. Distance of a point from a plane.

UNIT NO 9

LINEAR PROGRAMMING PROBLEM

Points to remember

1. Formation of LPP.
2. Graphical solution of LPP.
3. special Cases of LPP.

Que. If the value of the objective at two consecutive vertices of the feasible region is optimal solution then the LPP has.

(A) No solution                                        (B) Two solutions

(C) Infinite solutions                                (D) None of these

Ans: C

(Section II)

UNIT NO 1

CONTUNITY

Points to remember

1. Continuity of a function at a point
2.  Types of discontinuity.
3. Continuity in an interval

UNIT NO 2

DIFFERENTIATION

Points to remember

1. Relation between continuity and differentiation.
2. Derivatives of

(i) Composite Function.
(ii) Inverse Function.
(iii) Implicit Function
(iv) Parametric Functions.

3. Logarithmic differentiation.

4. Higher ordered Derivative

5. Theorems.

UNIT NO 3

APPLICATIONS OF DERIVATIVE

Points to remember

1. Geometrical Applications.
2. Rate Measure.
3. Roll’s and Lagranges Theorem.
4. Approximation
5. Increasing and decreasing function.
6. Maxima and Minima.

UNIT NO 4

INDEFINITE INTEGRAL

Points to remember

1:Standard Formulae.

2: Integration by substitution.

3: Special Integrals.

4: Integration by parts.

5: Integration by partial fractions.

UNIT NO 5

DEFINITE INTEGRAL AND ITS APPLICATIONS

Points to remember

1. Definite integral as limit of sum
2. Fundamental Theorem of integral Calculus.
3. Definite integral by substitutions.
4. Definite integral by parts.
5. Properties of definite Integral.
6. Application of definite integral (Area)

UNIT NO 6

DIFFERENTIAL EQUATIONS

Points to remember

1. Order and degree of differential equation.
2. Solution of differential equation.
3. Formation of differential equation
4. Solution of first ordered first degree differential equation

(I) Variable separable form.

(ii) Method Of substitution.

(iii) Homogeneous differential equation.

(iv) Linear differential equation

5. Application of differential equation (Growth and Decay)

UNIT NO 7

PROBABILITY DISTRIBUTION

Points to remember

1. Random variable and its types.
2. Probability mass function (p.m.f.).

(i) Probability distributions.

(ii) Cumulative distribution functions.

(iii) Expected value, variance and standard deviation.

      3. Probability distribution function (p.d.f.)

UNIT NO 8

BINOMIAL DISTRIBUTION

Points to remember

1. Bernoullis Trial.
2. Binomial distribution.
3. Conditions for binomial distribution.
4. Mean and variance of binomial distribution.