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HSC Arts (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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Mathematics and Statistics
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Solve the following :

State which of the following sentences are statements in logic.
The square of any odd number is even.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Solve the following :

State which of the following sentences are statements in logic.
All integers are natural numbers.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

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Solve the following :

State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Solve the following :

State which of the following sentences are statements in logic.
Do not come inside the room.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Solve the following :

State which of the following sentences are statements in logic.
What a horrible sight it was!

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

The square of every real number is positive.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

a2 − b2 = (a + b) (a − b) for all a, b ∈ R.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

Please carry out my instruction.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

The Himalayas is the highest mountain range.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

What are the causes of rural unemployment?

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

0! = 1

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Which of the following sentence is a statement? In case of a statement, write down the truth value.

The quadratic equation ax2 + bx + c = 0 (a ≠ 0) always has two real roots.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

In the p.m.f. of r.v. X

X 1 2 3 4 5
P (X) `1/20` `3/20` a 2a `1/20`

Find a and obtain c.d.f. of X. 

[14] Probability Distributions
Chapter: [14] Probability Distributions
Concept: undefined >> undefined

Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.

Stock prices are not high or stocks are rising.

[1] Mathematical Logic
Chapter: [1] Mathematical Logic
Concept: undefined >> undefined

Solve the following problem :

A player tosses two coins. He wins ₹ 10 if 2 heads appear, ₹ 5 if 1 head appears, and ₹ 2 if no head appears. Find the expected value and variance of winning amount.

[14] Probability Distributions
Chapter: [14] Probability Distributions
Concept: undefined >> undefined

Find the Cartesian equations of the line passing through A(3, 2, 1) and B(1, 3, 1).

[6] Line and Plane
Chapter: [6] Line and Plane
Concept: undefined >> undefined

`int sqrt(tan x)/(sin x cos x)` dx = _______________

[10] Indefinite Integration
Chapter: [10] Indefinite Integration
Concept: undefined >> undefined

The combined equation of the two lines passing through the origin, each making angle 45° and 135° with the positive X-axis is ______  

[4] Pair of Straight Lines
Chapter: [4] Pair of Straight Lines
Concept: undefined >> undefined

`int 1/(sqrtx + sqrt(x^3))` dx = ______.

[10] Indefinite Integration
Chapter: [10] Indefinite Integration
Concept: undefined >> undefined
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Question Bank Solutions for Maharashtra State Board HSC Arts (English Medium) १२ वीं कक्षा Mathematics and Statistics
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