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
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.
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.
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
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).
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.
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?
Concept: Derivatives as a Rate Measure
Find the values of x, for which the function f(x) = x3 + 12x2 + 36𝑥 + 6 is monotonically decreasing
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`
Concept: Methods of Integration - Integration by Parts
Evaluate: `int_0^(pi/2) (sin^2x)/(1 + cos x)^2 "d"x`
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
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
Concept: Formation of Differential Equations
Given X ~ B (n, p)
If n = 10 and p = 0.4, find E(X) and var (X).
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.
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
Concept: Mean of Binomial Distribution (P.M.F.)
Concept: Basic Concepts of Trigonometric Functions
Find the general solution of the equation sin 2x + sin 4x + sin 6x = 0
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.
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).
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.
Concept: Pair of Straight Lines > Pair of Lines Passing Through Origin - Homogenous Equation
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 2021 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 2021 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 2021 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!