# HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

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Find the co-ordinates of the foot of the perpendicular drawn from the point (0, 2, 3) to the line (x + 3)/(5) = (y - 1)/(2) = (z + 4)/(3).

Appears in 3 question papers
Chapter: [0.016] Line and Plane
Concept: Equation of a Plane

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and  B at a profit of Rs 4. Find the production level per day for maximum profit graphically.

Appears in 3 question papers
Chapter: [0.017] Linear Programming
Concept: Graphical Method of Solving Linear Programming Problems

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

Appears in 3 question papers
Chapter: [0.021] Differentiation
Concept: Derivatives of Inverse Functions

If y = cos(m cos–1x), then show that (1 - x^2) ("d"^2y)/("d"x^2) - x("d"y)/("d"x) + "m"^2y = 0

Appears in 3 question papers
Chapter: [0.021] Differentiation
Concept: Higher Order Derivatives

The displacement of a particle at time t is given by s = 2t3 – 5t2 + 4t – 3. Find the velocity when ЁЭСб = 2 sec

Appears in 3 question papers
Chapter: [0.022000000000000002] Applications of Derivatives
Concept: Derivatives as a Rate Measure

Find intsqrtx/sqrt(a^3-x^3)dx

Appears in 3 question papers
Chapter: [0.023] Indefinite Integration
Concept: Methods of Integration: Integration by Substitution

Choose the correct alternative:

int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x, then p = ?

Appears in 3 question papers
Chapter: [0.023] Indefinite Integration
Concept: Methods of Integration: Integration Using Partial Fractions

If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? ("Given" sqrt(3/2) = 1.2247)

Appears in 3 question papers
Chapter: [0.026000000000000002] Differential Equations
Concept: Application of Differential Equations

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.

Appears in 3 question papers
Chapter: [0.027000000000000003] Probability Distributions
Concept: Random Variables and Its Probability Distributions

If θ is the measure of acute angle between the pair of lines given by ax^2+2hxy+by^2=0, then prove that tantheta=|(2sqrt(h^2-ab))/(a+b)|,a+bne0

Appears in 3 question papers
Chapter: [0.04] Pair of Straight Lines
Concept: Acute Angle Between the Lines

Find λ, if the vectors veca=hati+3hatj+hatk,vecb=2hati−hatj−hatk and vecc=λhatj+3hatk  are coplanar.

Appears in 3 question papers
Chapter: [0.07] Vectors
Concept: Scalar Triple Product of Vectors

If the lines (x-1)/2=(y+1)/3=(z-1)/4  and (x-3)/1=(y-k)/2=z/1 intersect each other then find value of k

Appears in 3 question papers
Chapter: [0.09] Line
Concept: Distance of a Point from a Line

A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and  B at a profit of Rs 4. Find the production level per day for maximum profit graphically.

Appears in 3 question papers
Chapter: [0.11] Linear Programming Problems
Concept: Graphical Method of Solving Linear Programming Problems

If x = a sin 2t (1 + cos2t) and y = b cos 2t (1 – cos 2t), find the values of  dy/dx at t = pi/4

Appears in 3 question papers
Chapter: [0.13] Differentiation
Concept: Derivatives of Functions in Parametric Forms

If y = f(x) is a differentiable function of x such that inverse function x = f–1 (y) exists, then prove that x is a differentiable function of y and dx/dy=1/((dy/dx)) " where " dy/dx≠0

Appears in 3 question papers
Chapter: [0.13] Differentiation
Concept: The Concept of Derivative > Derivative of Inverse Function

Find intsqrtx/sqrt(a^3-x^3)dx

Appears in 3 question papers
Chapter: [0.15] Integration
Concept: Methods of Integration: Integration by Substitution

Evaluate :

∫_(-pi)^pi (cos ax−sin bx)^2 dx

Appears in 3 question papers
Chapter: [0.15] Integration
Concept: Evaluation of Definite Integrals by Substitution

Choose the correct alternative:

int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x, then p = ?

Appears in 3 question papers
Chapter: [0.15] Integration
Concept: Methods of Integration: Integration Using Partial Fractions

If y = P eax + Q ebx, show that

(d^y)/(dx^2)=(a+b)dy/dx+aby=0

Appears in 3 question papers
Chapter: [0.17] Differential Equation
Concept: General and Particular Solutions of a Differential Equation

From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.

Appears in 3 question papers
Chapter: [0.19] Probability Distribution
Concept: Random Variables and Its Probability Distributions
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