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# Important Questions for HSC Science (General) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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If bar("a"), bar("b") and bar("c") are position vectors of the points A, B, C respectively and 5bar("a") - 3bar("b") - 2bar("c") = bar(0), then find the ratio in which the point C divides the line segement BA

Appears in 2 question papers
Chapter: [0.015] Vectors
Concept: Section formula

Solve the following LPP by using graphical method.

Maximize : Z = 6x + 4y

Subject to x ≤ 2, x + y ≤  3, -2x + y ≤  1, x ≥  0, y ≥ 0.

Also find maximum value of Z.

Appears in 2 question papers
Chapter: [0.017] Linear Programming
Concept: Graphical Method of Solving Linear Programming Problems

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.

Appears in 2 question papers
Chapter: [0.02] Matrices
Concept: Elementary Operation (Transformation) of a Matrix

Find the derivative of the inverse of function y = 2x3 – 6x and calculate its value at x = −2

Appears in 2 question papers
Chapter: [0.021] Differentiation
Concept: Derivatives of Inverse Functions

Examine the maxima and minima of the function f(x) = 2x3 - 21x2 + 36x - 20 . Also, find the maximum and minimum values of f(x).

Appears in 2 question papers
Chapter: [0.022000000000000002] Applications of Derivatives
Concept: Maxima and Minima

Show that the height of the cylinder of maximum volume, which can be inscribed in a sphere of radius R is (2R)/sqrt3.  Also find the maximum volume.

Appears in 2 question papers
Chapter: [0.022000000000000002] Applications of Derivatives
Concept: Maxima and Minima

A car is moving in such a way that the distance it covers, is given by the equation s = 4t2 + 3t, where s is in meters and t is in seconds. What would be the velocity and the acceleration of the car at time t = 20 seconds?

Appears in 2 question papers
Chapter: [0.022000000000000002] Applications of Derivatives
Concept: Derivatives as a Rate Measure

Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing

Appears in 2 question papers
Chapter: [0.022000000000000002] Applications of Derivatives
Concept: Increasing and Decreasing Functions

Prove that int sqrt(x^2-a^2)dx=x/2sqrt(x^2-a^2)-a^2/2log|x+sqrt(x^2-a^2)|+c

Appears in 2 question papers
Chapter: [0.023] Indefinite Integration
Concept: Methods of Integration - Integration by Parts

Evaluate: int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x

Appears in 2 question papers
Chapter: [0.024] Definite Integration
Concept: Methods of Evaluation and Properties of Definite Integral

Order and degree of the differential equation [1+(dy/dx)^3]^(7/3)=7(d^2y)/(dx^2) are respectively

(A) 2, 3

(B) 3, 2

(C) 7, 2

(D) 3, 7

Appears in 2 question papers
Chapter: [0.026000000000000002] Differential Equations
Concept: Order and Degree of a Differential Equation

Verify y = log x + c is the solution of differential equation x ("d"^2y)/("d"x^2) + ("d"y)/("d"x) = 0

Appears in 2 question papers
Chapter: [0.026000000000000002] Differential Equations
Concept: Formation of Differential Equations

Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).

Appears in 2 question papers
Chapter: [0.027999999999999997] Binomial Distribution
Concept: Bernoulli Trials and Binomial Distribution

The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is

 X = x 0 1 2 3 4 P(X = x) 0.08 0.15 0.45 0.27 0.05

Find the expected value and variance of X.

Appears in 2 question papers
Chapter: [0.027999999999999997] Binomial Distribution
Concept: Variance of Binomial Distribution (P.M.F.)

The probability that certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components survive

Appears in 2 question papers
Chapter: [0.027999999999999997] Binomial Distribution
Concept: Mean of Binomial Distribution (P.M.F.)

Show that:

cos^(-1)(4/5)+cos^(-1)(12/13)=cos^(-1)(33/65)

Appears in 2 question papers
Chapter: [0.03] Trigonometric Functions
Concept: Basic Concepts of Trigonometric Functions

Find the general solution of the equation sin 2x + sin 4x + sin 6x = 0

Appears in 2 question papers
Chapter: [0.03] Trigonometric Functions
Concept: Trigonometric Functions > General Solution of Trigonometric Equation of the Type

If a line makes angles α, β, γ with co-ordinate axes, prove that cos 2α + cos2β + cos2γ+ 1 = 0.

Appears in 2 question papers
Chapter: [0.03] Trigonometric Functions
Concept: Trigonometric Functions > Trigonometric equations

Find the cartesian equation of the line passing throught the points A(3, 4, -7) and B(6,-1, 1).

Appears in 2 question papers
Chapter: [0.04] Pair of Straight Lines
Concept: Pair of Straight Lines > Pair of Lines Passing Through Origin - Combined Equation

Find the joint equation of the pair of lines passing through the origin which are perpendicular respectively to the lines represented by 5x2 +2xy- 3y2 = 0.

Appears in 2 question papers
Chapter: [0.04] Pair of Straight Lines
Concept: Pair of Straight Lines > Pair of Lines Passing Through Origin - Homogenous Equation
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