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HSC Arts (English Medium) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

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Find the particular solution of the following differential equation:

y(1 + log x) = (log xx) `"dy"/"dx"`, when y(e) = e2

[13] Differential Equations
Chapter: [13] Differential Equations
Concept: undefined >> undefined

Find the particular solution of the following differential equation:

`2e ^(x/y) dx + (y - 2xe^(x/y)) dy = 0," When" y (0) = 1`

[13] Differential Equations
Chapter: [13] Differential Equations
Concept: undefined >> undefined

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Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.

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

Negation of “some men are animal” is ______.

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

State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.

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

Assuming the first statement p and second as q. Write the following statement in symbolic form.

The Sun has set and Moon has risen.

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

Assuming the first statement p and second as q. Write the following statement in symbolic form.

Mona likes Mathematics and Physics.

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

Assuming the first statement p and second as q. Write the following statement in symbolic form.

3 is prime number if 3 is perfect square number.

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

Assuming the first statement p and second as q. Write the following statement in symbolic form.

Kavita is brilliant and brave.

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

If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

Proof is lengthy and it is not interesting.

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

If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

If proof is lengthy then it is interesting.

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

If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is not true that the proof is lengthy but it is interesting.

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

If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

It is interesting iff the proof is lengthy.

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → r

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ p ∨ q

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p→(q ∨ r)

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

p → q

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

(p ∧ q) ∧ ∼ r

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

Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.

∼ (p ∨ q) ∧ r

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

Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.

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