P A 1 = 3 / 8 ; P A 2 = 2 / 3 ; P A 1 ∩ A 2 = 1 / 4 then A 1 and A 2 will be:

Mutually exclusive & independent

EASY

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$P (A_{1}) = 3 / 8; P (A_{2}) = 2 / 3; P (A_{1} \cap A_{2}) = 1 / 4$ then $A_{1}$ and $A_{2}$ will be:

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Important Questions on Differentiation

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The line

y = x + 1

is a tangent to the curve

y^{2} = 4 x

at the point

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The tangent to the curve,

y = x e^{x^{2}}

passing through the point

(1, e)

also passes through the point:

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The length of the perpendicular from the origin, on normal to the curve,

x^{2} + 2 x y - 3 y^{2} = 0

, at the point

(2, 2)

, is.

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

Consider the curve

y = b e^{- x / a}

, where

a

and

b

are non-zero real numbers. Then

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The tangent at the point

(2, - 2)

to the curve,

x^{2} y^{2} - 2 x = 4 (1 - y)

does not pass through the point:

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

A tangent to the curve

x = a t^{2}, y = 2 a t

is perpendicular to

x

-axis, then the point of contact is

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the tangent to the curve

y = \frac{x}{x^{2} - 3}, x \in R, (x \neq \pm \sqrt{3}),

at a point

(α, β) \neq (0, 0)

on it is parallel to the line

2 x + 6 y - 11 = 0,

then:

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the tangent to the curve

x y + a x + b y = 0

(1, 1)

makes an angle

\tan {}^{- 1}2

with

x

-axis, then

\frac{a + b}{a b} =

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

Let C be a curve given by

y (x) = 1 + \sqrt{4 x - 3}

x > \frac{3}{4}

. If

P

is a point on C, such that the tangent at

P

has slope

\frac{2}{3}

, then a point through which the normal at

P

passes, is :

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the tangent at a point

P

, with parameter

t

, on the curve

x = 4 t^{2} + 3, y = 8 t^{3} - 1, t \in R,

meets the curve again at a point

Q

, then the coordinates of

Q

are :

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The equation of the normal to the curve

y = e^{x}

(0, 1)

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The normal to the curve

y (x - 2) (x - 3) = x + 6

at the point where the curve intersects the

y

-axis passes through the point:

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The point at which the tangent line to the curve of

y = \frac{16}{x} - x^{2}

is horizontal, is

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the curves

2 x = y^{2}

and

2 x y = K

intersect perpendicularly, then the value of

K^{2}

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The equation of the tangent to the curve

y = π e^{\frac{- x}{π}}

at the point where it crosses

y

-axis is

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the two curves

x = y^{2}

and

x y = k

cut each other at right angles, then a possible value of

k

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The equation of the tangent to the curve

x y^{5} + 2 x^{2} y - x^{3} + y + 1 = 0

x = 0

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

If the tangents on the ellipse

4 x^{2} + y^{2} = 8

at the points

(1, 2)

and

(a, b)

are perpendicular to each other, then

a^{2}

is equal to

MEDIUM

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The point on the curve

y = \sqrt{x - 1}

where the tangent is perpendicular to the line

2 x + y - 5 = 0

EASY

Mathematics>Differential Calculus>Differentiation>Geometrical Meaning of Derivative

The equation of the tangent and normal to the ellipse

x^{2} + 2 y^{2} + 2 x - 4 y - 14 = 0

(2, - 1)

PA1=3/8;PA2=2/3;PA1∩A2=1/4 then A1 and A2 will be:

Important Questions on Differentiation

Learn and Prepare for any exam you want !

$P (A_{1}) = 3 / 8; P (A_{2}) = 2 / 3; P (A_{1} \cap A_{2}) = 1 / 4$ then $A_{1}$ and $A_{2}$ will be: