Explore topic-wise InterviewSolutions in Current Affairs.

It is given that

f(x) = -2x + 7

By differentiating w.r.t. x

f’(x) = – 2 < 0 for all value of x

Therefore, f(x) is strictly decreasing function on R.

It is given that

f(x) = e^2x

By differentiating w.r.t. x

f’(x) = 2(e^2x) > 0

Therefore, f(x) is strictly increasing function on R.

Consider f(x) = (x - 2)/(x+1),

f'(x) = 3/(x+1)²

f’(x) at x = -1 is not defined

and for all x ∈ R - {-1}

f’(x)>0

hence f(x) is increasing.

It is given that

f(x) = ax + b

By differentiating w.r.t. x

f’(x) = a > 0 for all x

Therefore, f(x) is strictly increasing function on R.

Domain of the function is R

Finding derivative f’(x) = -2

Which is less than 0

Means strictly decreasing in its domain i.e R

Domain of the function is R

Finding derivative i.e f’(x) = a

As given in question it is given that a > 0

Derivative > 0

Means strictly increasing in its domain i.e R

Correct option is: B) x + 7 = 18

Correct option is: B) Deductive

Correct answer is

(b) 2

Answer is : C. does not exist

f(x) = x^3/2

⇒ f’(x) = 3/2√x

As x → 0, f’(x) → ∞

∴ f’(x) does not exist.

You need to turn over B and 8 only. If B has an even number then the rule has broken. Similarly if 8 has a consonant on the other side then also the rule has been broken.

i) From the above statements we can deduce that Jeevan is mortal as it is given that all humans are mortal and Jeevan is a human.

ii) No. X may belong to any other language like Tamil, Kannada, Malayali…. etc.

iii) Gulag had red, tongue.

iv) All smarts need not be a President. There could be some other persons who are smart too.

If x = – 8 and y = – 10 

Here x > y 

x² = (- 8)² = 64 and y² = (- 10)² = 100 

But x² > y² is false here. [ ∵ 64 < 100] 

(This can be proved for any set of negative numbers or a negative number and a positive number)

A linear equation in two variables is of the form ax + by = c, where a≠0,b≠0.

Example:

2x + 3y = 5, x - 2y = 6, -6x + y =8

A pair of values of x and y that satisfy a given linear equation in two variables is said to be its solution.

Two angles are said to be equal, if they have the same measure.

From figure, y = 25° [Vertically opposite angles are equal] 

Now ∠x + ∠y = 180° [Linear pair of angles] 

x = 180 – 25

x = 155° 

Also, z = x = 155° [Vertically opposite angles] 

Answer: y = 25° and z = 155°.

Correct option is (C) 130°

y and \(50^\circ\) are interior angles on the same side of a transversal n of two parallel lines.

\(\therefore\) \(y+50^\circ=180^\circ\)

\(\Rightarrow\) \(y=180^\circ-50^\circ=130^\circ\)

Correct option is  C) 130°

Correct option is  B) 45°

Correct option is  C) 70°

Correct option is (D) 20°

\(\because\) Both angles 6x and 3x form a linear pair.

\(\therefore\) 6x+3x = \(180^\circ\)

\(\Rightarrow\) 9x = \(180^\circ\)

\(\Rightarrow\) x = \(\frac{180^\circ}9\) = \(20^\circ\)

Correct option is  D) 20°

(b) a is true and b is false

∠AOE = ∠BOF = 5x [Vertically opposite angles] 

∠COA +∠AOE +∠EOD = 180° [Linear pair] 

3x + 5x + 2x = 180°

10x = 180° 

x = 180/10 

x = 18°

The value of x = 180°

When two lines intersect each other, then the opposite angles, formed due to intersection are called vertical angles or vertically opposite angles.

Example of Vertical opposite angles in our surrounding

• 4 road junction
• Rail road crossing signs
• Open scissors
• Corners of the room

(i) Angle – When two rays originate from the same end point, then an angle is formed.

(ii) Interior of an angle – The interior of ∠BAC is the set of all points in its plane which lie on the same side of AB as C and also on the same side of AC as B.

(iii) Obtuse angle – An angle whose measure is more than 90° but less than 180° is called an obtuse angle.

(iv) Reflex angle – An angle whose measure is more than 180° but less than 360° is called a reflex angle.

(v) Complementary angles – Two angles are said to be complementary, if the sum of their measure is 90°.

(vi) Supplementary angles – Two angles are said to be supplementary if the sum of their measures is 180°.

Electric pole, Tree/Pen stand, etc.

From figure Vertically opposite angles are respectively 

∠AOB = ∠COD and ∠AOD = ∠BOC

(i) Given that,

x = 60°

y =?

∠AOC + ∠DOC = 180°(Linear pair)

2x + y = 180°

120° + y = 180°

y = 60°

(ii) Given that,

y = 40°

x =?

∠AOC + ∠BOC = 180°(Linear pair)

2x + y = 180°

2x = 140°

x = 70°

Given that,

AB and CD are two lines intersecting at O

To prove:

∠BOC = 90°

∠AOC = 90°

∠AOD = 90°

∠BOD = 90°

Proof: Given that,

∠BOC = 90°

∠BOC = ∠AOD = 90°(Vertically opposite angle)

∠AOC + ∠BOC = 180°(Linear pair)

∠AOC + 90° = 180°

∠AOC = 90°

∠AOC = ∠BOD = 90°(Vertically opposite angles)

Therefore,

∠AOC = ∠BOC = ∠BOD = ∠AOD = 90°

Hence, proved

\(\overrightarrow {PQ}\) is a straight line. But \(\overrightarrow {SR}\) is not a straight line.

If \(\overrightarrow {PQ}\) and \(\overrightarrow {SR}\) are intersecting lines the x and y become vertically opposite angles.

So, x and y are not vertically opposite angles.

Vertically opposite angles are 

∠AOC, ∠BOD and ∠BOC, ∠AOD

Correct option is (D) 20°

2y+5y+2y = \(180^\circ\)

\(\Rightarrow\) 9y = \(180^\circ\)

\(\Rightarrow\) y = \(\frac{180^\circ}9=20^\circ\)

Correct option is  D) 20°

Correct option is (B) complementary

\(\because35^\circ+55^\circ=90^\circ\)

\(\therefore35^\circ\,and\;55^\circ\) are complementary angles of each other.

Hence, the pair of angles \(35^\circ\,and\;55^\circ\) are called complementary.

B) complementary

(a) Total 13 angles are formed, namely ∠AOB, ∠BOC, ∠COD, ∠DOA, ∠AOC, ∠BOD, ∠DOB, ∠AOD, ∠BOA, ∠COB, ∠DOC, ∠AOA.

(b) Following types of angles are formed:

(i) Linear pair
(ii) Supplementary
(iii) Vertically opposite
(iv) Adjacent

(c) Following are the pair of vertically opposite angles:

∠1, ∠3; ∠2, ∠4.

By definition of adjacent angles and complementary angles, we can say that following pairs are adjacent angles and complementary angles.

(i) Adjacent angles: ∠x, ∠y; ∠x + ∠y, ∠z; ∠y, ∠z; ∠x, ∠y + ∠z.

(ii) Complementary angles: ∠x, ∠y

(a) Complementary angles are those whose sum is 90°.

∴ ∠TQS and ∠SQR are pair of complementary angles, as their sum is 90°.

(b) Supplementary angles are those whose sum is 180°.

∴ ∠SQR, ∠SQP; ∠TQR, ∠TQP are pair so supplementary angles.

(c) Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points.

∴ ∠SQR, ∠SQT, ∠TQR, ∠TQP, ∠SQT, ∠TQP; ∠PQS, ∠SQR are pairs of adjacent angles.

When a line segment is extended indefinitely in both directions it forms a line.

A line segment which can be extended in only one direction is called a ray.

Given that,

l₁ ‖ l₂

Let m and n be two transversal cutting them

∠w + ∠x = 180°(Consecutive interior angle)

x = 180° – w (i)

z = y (Alternate angles) (ii)

From (i) and (ii), we get

x + y = 180° – w + z

When large sized habitats are broken into smaller parts due to human activities they are called fragmented habitat and it leads to population decline. Example, a small forest near an urban settlement.

Given that,

l₁ ‖ l₂ and l₃ is transversal

∠1 = 3x (Vertically opposite angle)

y = ∠1 (Corresponding angle)

y = 3x (i)

y + x = 180°(Linear pair)

3x + x = 180°[From (i)]

4x = 180°

x = 45°

Therefore,

y = 3x = 3 x 45°

= 135°

It is a genetic disorder caused due to the extra X-chromosome resulting into a karyotype with 47 chromosomes, XXY.

Given that,

l₁ ‖ l₂ and l₃ ‖ l₄

Let,

∠1 = x

∠2 = y

∠3 = y

∠1 = ∠4 (Alternate angle)

∠4 = x

∠5 = ∠2 (Vertically opposite angle)

∠6 = ∠3 (Vertically opposite angle)

∠5 = ∠6 = y

Now,

∠4 + ∠5 + ∠6 = 180°(Consecutive interior angle)

y = 90° - \(\frac{x}{2}\)

The ecological importance of biodiversity: 

i. Biodiversity is required for maintaining and sustainable use of goods and services from ecosystem. 

ii. Various insects help in pollination. 

iii. Various micro-organisms help in the decomposition of organic matter thereby increasing the soil fertility and cleaning the environment. 

iv. Various drugs and medicines are extracted from plants.

Given that,

l ‖ m

Let,

∠1 = 3y

∠2 = 2y + 25°

∠3 = x + 15°

∠1 = ∠2 (Alternate angle)

3y = 2y + 25°

y = 25°

∠2 = ∠3 (Vertically opposite angle)

x + 15° = 2 (25°) + 25°

x = 60°