If cos x = | sin x | then, the general solution is

x = ( 2 n + 1 ) π ± π 4 , n ∈ Z

x = n π + ( - 1 ) n π 4 , n ∈ Z

The solution of sin x = - 3 2 is

x = n π + - 1 n - π 3 , where n ∈ Z

x = n π + - 1 n 2 π 3 , where n ∈ Z

x = n π + - 1 n 3 π 3 , where n ∈ Z

MEDIUM

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Choose the correct one

(a) Growth cannot be taken as a defining property of a living organism.
(b) A dead organism does not grow.
(c) Reproduction cannot be a defining characteristic of living organisms.
(d) No non-living object is capable of replicating itself.
(e) Metabolism in a test tube is non-living.
(f) Metabolism is a defining feature of all living organisms.

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Important Questions on The Living World

HARD

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\cos x = | \sin x |

then, the general solution is

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

Which is the National Aquatic Animal of India?

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\sec^{4} θ - \sec^{2} θ = 3

the value of

\tan^{4} θ + \tan^{2} θ

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The value of

\sin^{4} \frac{π}{8} + \sin^{4} \frac{3 π}{8}

is equal to

HARD

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The number of principal solutions of

\tan 2 θ = 1

is:

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

tanx + tany = \frac{5}{6}

and

cotx + coty = 5

, then

\tan (x + y)

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\sin A + \sin^{2} A = 1,

then find the values of

\cos^{2} A + \cos^{4} A .

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\frac{\sin 91 ° + \sin 1 °}{\sin 91 ° - \sin 1 °} =

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The number of values of $α$ in $[0, 2 π]$ for which $2 \sin^{3} α - 7 \sin^{2} α + 7 sinα = 2$ , is :

HARD

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

If sum of all the solutions of the equation

8 \cos x \cdot (\cos (\frac{π}{6} + x) \cdot \cos (\frac{π}{6} - x) - \frac{1}{2}) = 1

[0, π]

k π

, then

k

is equal to:

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The value of

θ

with

0 \leq θ \leq 90 °

and

\sin^{2} θ + 2 \cos^{2} θ = \frac{7}{4}

is equal to

HARD

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

One of the solutions of the equation

8 \sin^{3} θ - 7 + \sin θ + \sqrt{3} \cos θ = 0

lies in the interval

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The values of

x

0 \leq x \leq π

such that

\cos 2 x = cosx

are

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\sec 4 θ = cosec (θ + 20^{o})

, then

θ

is equal to:

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The value of

\sin^{2} 1 ° + \sin^{2} 2 ° + \sin^{2} 3 ° + \dots + \sin^{2} 88 ° + \sin^{2} 89 °

is equal to

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The solution of

\sin x = - \frac{\sqrt{3}}{2}

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The value of

\sin (45 ° + θ) - \cos (45 ° - θ)

is equal to

MEDIUM

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

\sin φ - \cos φ = 0,

then the value of

\sin^{4} ϕ + \cos^{4} ϕ + \tan^{2} ϕ

is:

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

The general solution of

\sqrt{3} \cos x + \sin x = \sqrt{2},

for an integer

n

EASY

Biology>Diversity in the Living World>The Living World>Characteristics of Living Organisms

Which of the following is not a defining feature of all living organisms?

Important Questions on The Living World

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