Show that every homogeneous equation of degree two in x and y, i.e., ax^{2} + 2hxy + by^{2} = 0 represents a pair of lines passing through origin if h^{2}−ab≥0.

Concept: Pair of Straight Lines > Pair of Lines Passing Through Origin - Homogenous Equation

Show that four points A, B, C and D whose position vectors are

`4hati+5hatj+hatk,-hatj-hatk-hatk, 3hati+9hatj+4hatk and 4(-hati+hatj+hatk)` respectively are coplanar.

Concept: Coplanarity of Two Lines

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius *r* is `(4r)/3`. Also find maximum volume in terms of volume of the sphere

Concept: Maxima and Minima

If u and v are two functions of x then prove that

`intuvdx=uintvdx-int[du/dxintvdx]dx`

Hence evaluate, `int xe^xdx`

Concept: Methods of Integration - Integration by Parts

Find : `int(x+3)sqrt(3-4x-x^2dx)`

Concept: Methods of Integration - Integration by Substitution

Find: `I=intdx/(sinx+sin2x)`

Concept: Methods of Integration - Integration Using Partial Fractions

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`

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.

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

Concept: Line > 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.

Concept: Graphical Method of Solving Linear Programming Problems

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

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`

Concept: Derivative > Derivative of Inverse Function

Prove that : `int_-a^af(x)dx=2int_0^af(x)dx` , if f (x) is an even function.

= 0, if f (x) is an odd function.

Concept: Methods of Integration - Integration by Parts

Find `intsqrtx/sqrt(a^3-x^3)dx`

Concept: Methods of Integration - Integration by Substitution

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

Concept: Evaluation of Definite Integrals by Substitution

If y = P e^{ax} + Q e^{bx}, show that

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

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.

Concept: Random Variables and Its Probability Distributions

find the symbolic fom of the following switching circuit, construct its switching table and interpret it.

Concept: Mathematical Logic > Application - Introduction to Switching Circuits

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.

Concept: Elementary Operation (Transformation) of a Matrix

Show that:

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

Concept: Basic Concepts of Trigonometric Functions

12th Board Exam Mathematics and Statistics can be very challenging and complicated. But with the right ideas and support, you will be able to make it work. That’s why we have the 12th board exam Mathematics and Statistics important questions with answers pdf ready for you. All you need is to acquire the PDF with all the content and then start preparing for the exam. It really helps and it can bring in front an amazing experience every time if you're tackling it at the highest possible level.

## Mathematics and Statistics exams made easy

We make sure that you have access to the important questions for 12th Board Exam Mathematics and Statistics H.S.C Maharashtra State Board. This way you can be fully prepared for any specific question without a problem. There are a plethora of different questions that you need to prepare. And that's why we are covering the most important ones. They are the questions that will end up being more and more interesting and the results themselves can be staggering every time thanks to that. The quality itself will be quite amazing every time, and you can check the important questions for 12th Board Exam Mathematics and Statistics Maharashtra State Board whenever you see fit.

The important questions for 12th Board Exam Mathematics and Statistics 2020 we provide on this page are very accurate and to the point. You will have all the information already prepared and that will make it a lot simpler to ace the exam. Plus, you get to browse through these important questions for 12th Board Exam Mathematics and Statistics 2020 H.S.C and really see what works, what you need to adapt or adjust and what still needs some adjustment in the long run. It's all a matter of figuring out these things and once you do that it will be a very good experience.

All you have to do is to browse the important questions for upcoming Maharashtra State Board 12th Board Exam 2020 on our website. Once you do, you will know what needs to be handled, what approach works for you and what you need to do better. That will certainly be an incredible approach and the results themselves can be nothing short of staggering every time. We encourage you to browse all these amazing questions and solutions multiple times and master them. Once you do that the best way you can, you will have a much higher chance of passing the exam, and that's what really matters the most!