NDA MATHEMATICS QUIZ - 24

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Question 1:

The expression $\cos^{2} (x - y) + \cos^{2} y - 2 \cos (x - y) \cos x \cdot \cos y$ is independent of

व्यंजक $\cos^{2} (x - y) + \cos^{2} y - 2 \cos (x - y) \cos x \cdot \cos y$ किससे स्वतंत्र है ?

x

x

y

y

both

x

and

y

दोनों

x

और

y

Neither

x

nor

y

न तो

x

और न ही

y

Question 2:

If $\sin α (1 + \sin α) + \cos α (1 + \cos α) = a$ and $\sin α (1 - \sin α) + \cos α (1 - \cos α) = b$ then

अगर $\sin α (1 + \sin α) + \cos α (1 + \cos α) = a$ और $\sin α (1 - \sin α) + \cos α (1 - \cos α) = b$ तो निम्न में से क्या होगा ?

a^{2} - 2 a - \sin 2 α = 0

a^{2} - 2 a - \sin 2 α = 0

b^{2} + 2 b - \sin 2 α = 0

b^{2} + 2 b - \sin 2 α = 0

Both (a) & (b) are correct

Neither of (a) & (b) is correct

Question 3:

If $\tan x = \frac{a}{a - 1}$ and $\tan y = \frac{1}{2 a - 1}$ then one of the values of $(x - y)$ is

अगर $\tan x = \frac{a}{a - 1}$ और $\tan y = \frac{1}{2 a - 1}$ तो $(x - y)$ किनमें से एक होगा ?

\frac{π}{3}

\frac{π}{3}

\frac{π}{2}

\frac{π}{2}

\frac{π}{4}

\frac{π}{4}

\frac{π}{6}

\frac{π}{6}

Question 4:

If $\frac{\sin θ}{1 + \cos θ + \sin θ} = x$ then value of $\frac{1 - \cos θ + \sin θ}{1 + \sin θ}$ is equal to:

यदि $\frac{\sin θ}{1 + \cos θ + \sin θ} = x$ तो $\frac{1 - \cos θ + \sin θ}{1 + \sin θ}$ का मान किसके बराबर है ?

2 x

2 x

x^{2}

x^{2}

2 x^{2}

2 x^{2}

\frac{1}{x}

\frac{1}{x}

Question 5:

The equation $\cos 2 θ + p \sin θ = 2 p - 7$ has a solution

समीकरण $\cos 2 θ + p \sin θ = 2 p - 7$ का एक हल है जबकि

2 \leq p \leq 6

2 \leq p \leq 6

p > 7

p > 7

p \leq 1

p \leq 1

0 \leq p \leq 1

0 \leq p \leq 1

Question 6:

If $x \neq n π$ then value of the expression $2 - 4 \sin^{2} x + 3 \sin^{4} x - \sin^{6} x$ is equal to 1

यदि $x \neq n π$ तो व्यंजक का मान $2 - 4 \sin^{2} x + 3 \sin^{4} x - \sin^{6} x$ = 1 हो तब ,

\sin x, \tan x, \cos x

are in G.P.

\sin x, \tan x, \cos x

गुणोत्तर श्रेणी में होंगे

\sin x, \tan x, \cos x

are in A.P.

\sin x, \tan x, \cos x

समान्तर श्रेणी में होंगे

\sin x, \tan x, \cos x

are in H.P.

\sin x, \tan x, \cos x

हरात्मक श्रेणी में होंगे

None of these.

Question 7:

If $0 < α < \frac{π}{2}$ then $\tan α + \tan 2 α + \tan 3 α = 0$ if

यदि $0 < α < \frac{π}{2}$ हो तब $\tan α + \tan 2 α + \tan 3 α = 0$ सम्भव होगा जबकि

\tan 3 α = 0

\tan 3 α = 0

\tan α \cdot \tan 2 α = 2

\tan α \cdot \tan 2 α = 2

Both a and b are correct

Neither of a and b is correct

Question 8:

If $\sin^{2} α = 1 - \sin α$ then the value of $(\cos^{6} α + \cos^{12} α + 3 \cos^{10} α + 3 \cos^{8} α - 1)$ is equal to:

यदि $\sin^{2} α = 1 - \sin α$ तो $(\cos^{6} α + \cos^{12} α + 3 \cos^{10} α + 3 \cos^{8} α - 1)$ का मान किसके बराबर होगा ?

1.0

2.0

- 1

- 1

0.0

Question 9:

Value of the expression $1 - \frac{\sin^{2} x}{1 + \cot x} - \frac{\cos^{2} x}{1 + \tan x}$ is equal to

व्यंजक $1 - \frac{\sin^{2} x}{1 + \cot x} - \frac{\cos^{2} x}{1 + \tan x}$ का मान क्या होगा ?

\sin^{2} x \cdot \cos^{2} x

\sin^{2} x \cdot \cos^{2} x

2 \sin^{2} x

2 \sin^{2} x

2 \cos^{2} x \cdot \sin x

2 \cos^{2} x \cdot \sin x

\sin x \cdot \cos x

\sin x \cdot \cos x

Question 10:

If $A_{n} = \sin^{n} θ + \cos^{n} θ$ then $\frac{A_{3} - A_{5}}{A_{1}}$ equals

अगर $A_{n} = \sin^{n} θ + \cos^{n} θ$ तो $\frac{A_{3} - A_{5}}{A_{1}}$ का मान किसके बराबर होगा ?

\sin^{2} θ \cos^{3} θ

\sin^{2} θ \cos^{3} θ

\sin^{2} θ \cos^{2} θ

\sin^{2} θ \cos^{2} θ

\sin^{3} θ \cos^{3} θ

\sin^{3} θ \cos^{3} θ

\sin θ \cos θ

\sin θ \cos θ