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TN 12th Computer Applications மின்னணு தரவு பரிமாற்றம் Sample Question Papers Study Material - QB365 Set A

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12th Standard

TN 12th Computer Applications மின் - வணிக பாதுகாப்பு அமைப்புகள் Sample Question Papers Study Material - QB365 Set A

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12th Standard

TN 12th Computer Applications மின்னணு செலுத்தல் முறைகள் Sample Question Papers Study Material - QB365 Set A

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12th Standard

TN 12th Computer Applications மின் - வணிகம் Sample Question Papers Study Material - QB365 Set A

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12th Standard

TN 12th Computer Applications திறந்த மூல கருத்துருக்கள் Sample Question Papers Study Material - QB365 Set A

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12th Standard

TN 12th Computer Applications வலையமைப்பு வடமிடல் Sample Question Papers Study Material - QB365 Set A

12th Standard Maths Application of Differential Calculus English Medium Free Online Test One Mark Questions 2020 - 2021

Published on: 05/11/2020

Download Tamil Nadu 12th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.

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Std: 12th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

10 x 1 = 10

\(\underset { x\rightarrow 0 }{ lim } \frac { x }{ tanx } \) is _________

(a)

(b)

-1

(c)

(d)

∞

The function -3x+12 is ________ function on R.

(a)

decreasing

(b)

strictly decreasing

(c)

increasing

(d)

strictly increasing

If the slope of the curve 2y²= ax²+b at (1,-1) is - 1, then the values of a, b is __________

(a)

2, 0

(b)

0, 2

(c)

0, 0

(d)

2, 2

The angle made by any tangent to the curve y = x⁵ + 8x + 1 with the X-axis is a __________

(a)

obtuse

(b)

right angle

(c)

acute angle

(d)

no angle

The least value of a when f f(x) = x²+ ax + 1 is increasing on (1, 2) is __________

(a)

-2

(b)

(c)

(d)

-1

If a particle moves in a straight line according to s = t³-6t²-15t, the time interval during which the velocity is negative and acceleration is positive is __________

(a)

2 < t < 5

(b)

2 ≤ t ≤ 5

(c)

t ≥ 2

(d)

t ≤ 2

One of the closest points on the curve x² - y² = 4 to the point (6, 0) is

(a)

(2,0)

(b)

\(\left( \sqrt { 5 } ,1 \right) \)

(c)

\(\left( 3,\sqrt { 5 } \right) \)

(d)

\(\left( \sqrt { 13 } ,-\sqrt { 3 } \right) \)

The number given by the Rolle's theorem for the functlon x³- 3x², x ∈ [0, 3] is

(a)

(b)

\(\sqrt { 2 } \)

(c)

\(\frac { 3 }{ 2 } \)

(d)

The slope of the line normal to the curve f(x) = 2cos 4x at \(x=\cfrac { \pi }{ 12 } \) is

(a)

\(-4\sqrt { 3 } \)

(b)

-4

(c)

\(\cfrac { \sqrt { 3 } }{ 12 } \)

(d)

\(4\sqrt { 3 } \)

10.

The volume of a sphere is increasing in volume at the rate of 3 πcm³ / sec. The rate of change of its radius when radius is \(\frac { 1 }{ 2 } \) cm

(a)

3 cm/s

(b)

2 cm/s

(c)

1 cm/s

(d)

\(\cfrac { 1 }{ 2 } cm/s\)

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Answers Key:

Multiple Choice Question

10 x 1 = 10

(a)
1

(b)
strictly decreasing

(a)
2, 0

(a)
-2

(a)
2 < t < 5

(d)
2

Given equation of the curve is y = 1 + x³ and the line is x + 12y = 12
Slope of the tangent to the curve
m₁ = \(\frac { dy }{ dx } \) = 3x² and the
Slope of the line = m₂
= \(\frac{-1}{2}\) \(\left[ \because m=\frac { co-efficient\quad of\quad x }{ co-efficient\quad of\quad y } \right] \)
Since the slope of the tangent to the curve and the line are orthogonal, m₁ m₂ = - 1.
∴ 3x²\(\left( \frac { -1 }{ 2 } \right) \) = -1
⇒ \(\frac{x^2}{4}\) = 1
⇒ x² = 4
⇒ x = ±2
When x = 2, y = 1 + 2³ = 9
When x = -2, y = 1+ (-2)³
= 1-8 = -7
∴ Equation of the tangent at (2, 9) is
y-9 = 12(x-2) [∵ m₁= 3x²= 3(2)² = 12]
∴ y - 9 = 12x - 24
∴ 12x - y = 15
Equation of the tangent at (-2, -7) is
y + 7= 12(x + 2)
⇒ y + 7 = 12x + 24
⇒ 12x - y = -17