Mathematics Test

Result

Mathematics Test - 13

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

A
0

B
1

C
2

D
4

Solution

Hence two values.

Main Concept :
Definition of Complex Numbers A number of the form x + iy where x, y ∈ R and i = √-1 is called a complex number and 'i' is called iota.

A complex number is usually denoted by z and the set of complex number is denoted by C.
Question 2
1 / -0

A

B

C

D

Solution

The following seven step process will work every time. It is rather tedious, and can take more time than necessary. As you gain more practice, you can skip or combine these steps when you recognize other identities.

STEP 1 : Convert all sec, cosec, cot and tan to sin and cos. Most of this can be done using the quotient and reciprocal identities.

STEP 2 : Check all the angles for sums and differences and use the appropriate identities to remove them.

STEP 3 : Check for angle multiples and remove them using the appropriate formulas.

STEP 4 : Expand any equations you can, combine like terms, and simplify the equations.

STEP 5 : Replace cos powers greater than 2 with sin powers using the Pythagorean identities.

STEP 6 : Factor numerators and denominators, then cancel any common factors.

STEP 7 : Now, both sides should be exactly equal, or obviously equal, and you have proven your identify.
Question 3
1 / -0

If the distance between directrices is thrice the distance between focii of an ellipse, then its eccentricity is -

A
1/2

B
2/3

C
1/√3

D
4/5

Solution

By given condition, we have

Main Concept :

Basics of Ellipse(1)   Focus : The fixed point is called the focus of the ellipse.

(2)   Directrix : The fixed straight line is called the directrix of the ellipse.

(3)   Eccentricity : The constant ratio is called the eccentricity of the ellipse and is denoted by e.

(4)   Axis : The straight line passing through the focus and perpendicular to the directrix is called the axis of the ellipse.

(5)   Vertex : The points of intersection of the ellipse and the axis are called vertices of ellipse

(6)   Centre : The point which bisects every chord of the ellipse passing through it, is called the centre of ellipse.

(7)   Latus - rectum : The latus - rectum of a ellipse is the chord passing through the focus and perpendicular to the axis.

(8)   Double ordinate : The double ordinate of a ellipse is a chord perpendicular to the axis.

(9)   Focal chord : A chord passing through the focus of the ellipse is called a focal chord.

(10)   Focal distance : The distance of any point on the ellipse from the focus is called the focal distance of the point.
Question 4
1 / -0

A
continuous at all points except at x = 1

B
Differentiable at all points

C
Differentiable at all points except at x = 1

D
None of these

Solution

If f (x) is not continuous at x = a, we say that f (x) is discontinuous at x = a, f (x) will be discontinuous at x = a in any of the following cases :
Question 5
1 / -0

Suppose an ellipse and a hyperbola have the same pair of foci on the x- axis with centres at the origin and that they intersect at (2,2). If the eccentricity of the ellipse is 1/2, then the eccentricity of the hyperbola is

A

B

C

D

Solution
Question 6
1 / -0

A
4

B
5

C
6

D
7

Solution
Question 7
1 / -0

A
local maximum

B
local minimum

C
neither maximum nor minimum

D
none of these

Solution

Drawing the curve f(x)
Question 8
1 / -0

A line makes some angle $θ$ , with each of the and axis. If the angle $β$ which it makes with axis is such that $\sin^{2} β = 3 \sin^{2} θ$ then $5 \cos^{2} θ$ equals

A
$1$

B
$2$

C
$3$

D
$6$

Solution
Question 9
1 / -0

A

B

C

D

Solution

Main Concept :

Basics of HyperbolaA plane curve generated by a point so moving that the difference of the distances from two fixed points is a constant.

The point on each branch closest to the centre is that branch's "vertex". The vertices are some fixed distance a from the centre. The line going from one vertex, through the center, and ending at the other vertex is called the "transverse" axis. The "foci" of a hyperbola are "inside" each branch, and each focus is located some fixed distance c from the centre. (This means that a < c for hyperbolas.) The values of a and c will vary from one hyperbola to another, but they will be fixed values for any given hyperbola.