# Question Bank Solutions for HSC Commerce (Marketing and Salesmanship) 12th Board Exam - Maharashtra State Board - Mathematics and Statistics

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Evaluate : intsec^nxtanxdx

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Test whether the function is increasing or decreasing.

f(x) = "x" -1/"x", x ∈ R, x ≠ 0,

[0.05] Applications of Derivative
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions

If int_0^alpha(3x^2+2x+1)dx=14 then alpha=

(A) 1

(B) 2

(C) –1

(D) –2

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Find the probability distribution of number of heads in two tosses of a coin.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

Find the probability distribution of number of tails in the simultaneous tosses of three coins.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

Find the probability distribution of number of heads in four tosses of a coin

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

From a lot of 30 bulbs which include 6 defectives, a sample of 4 bulbs is drawn at random with replacement. Find the probability distribution of the number of defective bulbs.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

Two numbers are selected at random (without replacement) from the first six positive integers. Let X denotes the larger of the two numbers obtained. Find E(X).

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

In a bivariate data, n = 10, bar x = 25, bary = 30 and sum xy = 7900. Find cov(X,Y)

[0.12] Bivariate Data and Correlation
Chapter: [0.12] Bivariate Data and Correlation
Concept: Statistics (Entrance Exam) > Bivariate Frequency Distribution

Define differentiability of a function at a point.

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

Find the inverse of the matrix A=[[1,2],[1,3]] using elementry transformations.

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Introduction of Matrices

Examine the continuity of f(x)=x^2-x+9  "for"  x<=3

=4x+3  "for"  x>3,  "at"  x=3

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

find dy/dx, if y= cos ^-1 (sin 5x)

[0.11] Demography
Chapter: [0.11] Demography
Concept: Concept of Demography

The price P for demand D is given as P = 183 + 120 D – 3D2.
Find D for which the price is increasing.

[0.05] Applications of Derivative
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions

Evaluateint (1)/(x(3+log x))dx

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Find cofactors of the elements of the matrix A = [[-1,2],[-3,4]]

[0.02] Matrices
Chapter: [0.02] Matrices
Concept: Introduction of Matrices

Find k, if f(x) =log (1+3x)/(5x) for x ≠ 0

= k                    for x = 0

is continuous at x = 0.

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

If x = cos2 θ and y = cot θ then find dy/dx  at  θ=pi/4

[0.05] Applications of Derivative
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions
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