NDA MATHEMATICS QUIZ - 25

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Question 1:

If $\tan x, \cos x$ and $\sin x$ are in G.P. then value of $\cot^{6} x - \cot^{2} x$ is equal to

यदि $\tan x, \cos x$ और $\sin x$ G.P. में हैं ,तो $\cot^{6} x - \cot^{2} x$ का मान किसके बराबर होगा ?

0.0

1.0

2.0

3.0

Question 2:

If $α$ and $β$ be the acute angles such that ( $α$ $+ β$ ) and $(α - β)$ satisfy the equation $\tan^{2} x -$ $4 \tan x + 1 = 0$ then

यदि $α$ और $β$ न्यून कोण हो जैसे कि( $α$ $+ β$ ) and $(α - β)$ समीकरण $\tan^{2} x -$ $4 \tan x + 1 = 0$ को संतुष्ट करते है तब

α < β

α < β

β < α

β < α

α = β

α = β

α + β = \frac{7 π}{12}

α + β = \frac{7 π}{12}

Question 3:

\sec (A - B), \sec A

, and

\sec (A + B)

are in A.P. then

यदि

\sec (A - B), \sec A

, और

\sec (A + B)

A.P. में हैं तो

\cos A \cdot Sec \frac{B}{2} = \pm 1

\cos A \cdot Sec \frac{B}{2} = \pm 1

\cos A \cdot \sec \frac{B}{2} = \pm \sqrt{3}

\cos A \cdot \sec \frac{B}{2} = \pm \sqrt{3}

\cos A \cdot \sec B = \pm \sqrt{2}

\cos A \cdot \sec B = \pm \sqrt{2}

\cos A \cdot \sec B = \pm \sqrt{2}

\cos A \cdot \sec B = \pm \sqrt{2}

Question 4:

If $\cos θ + \sin θ = \sqrt{2} \cos θ$ then $\cos θ - \sin θ = k \sin θ$ where

यदि $\cos θ + \sin θ = \sqrt{2} \cos θ$ तो $\cos θ - \sin θ = k \sin θ$ जहां k =

k = \sqrt{3}

k = \sqrt{3}

k = \sqrt{5}

k = \sqrt{5}

k = \sqrt{2}

k = \sqrt{2}

None of these

Question 5:

If $α + β + γ = α β γ$ ,then value of $\frac{α}{1 - α^{2}} + \frac{β}{1 - β^{2}} + \frac{γ}{1 - γ^{2}}$ is

यदि $α + β + γ = α β γ$ ,तब $\frac{α}{1 - α^{2}} + \frac{β}{1 - β^{2}} + \frac{γ}{1 - γ^{2}}$ का मान कितना होगा?

\frac{4 α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{4 α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{8 α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{8 α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{4 α^{2} β^{2} γ^{2}}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{4 α^{2} β^{2} γ^{2}}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

\frac{α β γ}{(1 - α^{2}) (1 - β^{2}) (1 - γ^{2})}

Question 6:

If $A + B + C = \frac{π}{2}$ then $\sin^{2} A + \sin^{2} B + \sin^{2} C$ equals

यदि $A + B + C = \frac{π}{2}$ तो $\sin^{2} A + \sin^{2} B + \sin^{2} C$ का मान क्या होगा ?

1 + 2 \sin A \cdot \sin B \sin C

1 + 2 \sin A \cdot \sin B \sin C

4 \sin A \cdot \sin B \sin C

4 \sin A \cdot \sin B \sin C

1 - 2 \sin A \cdot \sin B \cdot \sin C

1 - 2 \sin A \cdot \sin B \cdot \sin C

2 \sin A \cdot \sin B \cdot \sin C

2 \sin A \cdot \sin B \cdot \sin C

Question 7:

If $α + β + γ = π$ and $\cos α = \cos β \cdot \cos γ$ , then $\cot β \cdot \cot γ$ equal is

यदि $α + β + γ = π$ और $\cos α = \cos β \cdot \cos γ$ , तो $\cot β \cdot \cot γ$ किसके बराबर होगा ?

\frac{1}{2}

\frac{1}{2}

\frac{1}{3}

\frac{1}{3}

Question 8:

Value of $\tan 105^{\circ}$ will be

$\tan 105^{\circ}$ का मान कितना होगा ?

(2 + \sqrt{3})

(2 + \sqrt{3})

- (2 - \sqrt{3})

- (2 - \sqrt{3})

- (2 + 5 \sqrt{3})

- (2 + 5 \sqrt{3})

- (2 + \sqrt{3})

- (2 + \sqrt{3})

Question 9:

Value of $\tan 855^{\circ} \cdot \cot 495^{\circ}$ is equal to

$\tan 855^{\circ} \cdot \cot 495^{\circ}$ का मान निम्न में से क्या होगा ?

1.0

- 1

- 1

2.0

- 2

- 2

Question 10:

If $\cot θ \cdot \cot ϕ = 3$ then $\cos (θ - ϕ)$ equals to.

यदि $\cot θ \cdot \cot ϕ = 3$ तो $\cos (θ - ϕ)$ का मान किसके बराबर होगा ?

2 \cos θ \cos ϕ

2 \cos θ \cos ϕ

\cos (θ + ϕ)

\cos (θ + ϕ)

2 \cos (θ + ϕ)

2 \cos (θ + ϕ)

\cos θ \cos ϕ

]

\cos θ \cos ϕ