NDA MATHEMATICS QUIZ-7

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Question 1:

It $\vec{a}, \bar{b}, \vec{c}$ be three vectors satisfing $\vec{a} + \bar{b} + \vec{c}$ $= 0$ where $| \bar{a} | = | \bar{b} | = | \vec{c} | = 1$ then the angle between $\bar{b}$ and $\vec{c}$ is

यह $\vec{a}, \bar{b}, \vec{c}$ तीन वैक्टर हो संतुष्ट $- g \bar{a} + \bar{b} + \vec{c}$ $= 0$ कहाँ पे $| \bar{a} | = | \bar{b} | = | \vec{c} | = 1$

फिर के बीच का कोण $\bar{b}$ तथा $\vec{c}$ है

\frac{π}{4}

\frac{π}{4}

\frac{π}{2}

\frac{π}{2}

\frac{π}{3}

\frac{π}{3}

\frac{2 π}{3}

\frac{2 π}{3}

Question 2:

Solution of the differential equation $x^{2} \frac{d y}{d x} + (1 - 2 x) y = x^{2}$ will be

अवकल समीकरण $x^{2} - \frac{d y}{d x} + (1 - 2 x) y = x^{2}$ का हल होगा

y = x^{2} (1 + c e^{- 1 / x})

y = x^{2} (1 + c e^{- 1 / x})

y = x^{2} (1 - c e^{- x^{2}})

y = x^{2} (1 - c e^{- x^{2}})

y = x^{2} (1 + c e^{- \frac{1}{x^{2}}})

y = x^{2} (1 + c e^{- \frac{1}{x^{2}}})

y = x c (1 + e^{- \frac{1}{x}})

y = x c (1 + 0^{- \frac{1}{x}})

Question 3:

$\int \frac{x d x}{(x + 2) \sqrt{x + 1}}$ is equal to:

$\int \frac{x d x}{(x + 2) \sqrt{x + 1}}$ के बराबर है:

2 \sqrt{x + 1} - 4 \tan^{- 1} \sqrt{x + 1} + c

2 \sqrt{x + 1} - 4 \tan^{- 1} \sqrt{x + 1} + c

\sqrt{x + 1} - 2 \tan^{- 1} \sqrt{x + 1} + c

\sqrt{x + 1} - 2 \tan^{- 1} \sqrt{x + 1} + c

3 \tan^{- 1} \sqrt{x + 1} - 4 \sqrt{x + 1} + c

3 \tan^{- 1} \sqrt{x + 1} - 4 \sqrt{x + 1} + c

\tan^{- 1} \sqrt{x + 1} - 2 \sqrt{x + 1} + c

\tan^{- 1} \sqrt{x + 1} - 2 \sqrt{x + 1} + c

Question 4:

The number of integral points at which the function $f (x) = \frac{1}{\log | (x^{2} - 1) |}$ is discontinuous is:

उन पूर्णांक बिन्दुओं को संख्या क्या होगी जहाँ $f (x) =$ $\frac{1}{\log | (x^{2} - 1) |}$ असंतत है ?

2.0

3.0

4.0

5.0

Question 5:

If $α \neq β$ but $x^{2} = 8 x - 15$ , then the equation with roots $\frac{α}{β}, \frac{β}{α}$ is:

यदि $α \neq β$ लेकिन $x^{2} = 8 x - 15$ , तब $\frac{α}{β}, \frac{β}{α}$ मूल होने पर समीकरण है

3 x^{2} - 25 x + 3 = 0

3 x^{2} - 25 x + 3 = 0

9 x^{2} + 27 x - 15 = 0

9 x^{2} + 27 x - 15 = 0

14 x^{2} - 25 x + 3 = 0

14 x^{2} - 25 x + 3 = 0

15 x^{2} - 34 x + 15 = 0

15 x^{2} - 34 x + 15 = 0

Question 6:

The Number of ways it which 6 beads of different colors to form a necklace is

60.0

120.0

90.0

100.0

Question 7:

From which point the tangents to ellipse $9 x^{2} + 16 y^{2} = 144$ are perpendicular?

(\frac{5}{\sqrt{2}}, \frac{5}{\sqrt{2}})

(\frac{5}{\sqrt{2}}, \frac{5}{\sqrt{2}})

(5 \sqrt{3}, 5 \sqrt{2})

(5 \sqrt{3}, 5 \sqrt{2})

(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{3}})

(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{3}})

(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{2}})

(\frac{5}{\sqrt{3}}, \frac{5}{\sqrt{2}})

Question 8:

In a class of 20 students a foot ball team of 11 players is to be selected. number of selections when a particular student is always left will be.

19_{C_{11}}

19_{C_{11}}

20_{C_{10}}

20_{C_{10}}

18_{C_{11}}

18_{C_{11}}

20_{C_{9}}

20_{C_{9}}

Question 9:

If the line of shortest distance between two lines passing through respectively $(α_{1}, β_{1}, γ_{1})$ and $(α_{2}, β_{2}, γ_{2})$ is having $l, m, n$ as the direction cosines then the length of shortest distance between the lines will be

यदि दो रेखाओं के बीच सबसे छोटी दूरी की रेखा क्रमशः $(α_{1}, β_{1} + λ_{1})$ से गुजरती है और $(α_{2}, β_{2} + λ_{2})$ में दिशा कोसाइन के रूप में l, m, n है तो रेखाओं के बीच सबसे छोटी दूरी की लंबाई होगी

l (α_{2} - α_{1}) + m (β_{2} - β_{1}) + n (γ_{2} - γ_{1})

l (α_{2} - α_{1}) + m (β_{2} - β_{1}) + b (λ_{2} - λ_{1})

l^{2} {(α_{2} - α_{1})}^{2} + m^{2} {(β_{2} - β_{1})}^{2} + n^{2} {(γ_{2} - γ_{1})}^{2}

l^{2} {(α_{2} - α_{1})}^{2} + m^{2} {(β_{2} - β_{1})}^{2} + λ^{2} {(λ_{2} - λ_{1})}^{2}

mn (α_{2} - α_{1}) + l n (β_{2} - β_{1}) + mn (γ_{2} - γ_{1})

mn (α_{2} - α_{1}) + \ln (β_{2} - β_{1}) + mn (λ_{2} - λ_{1})

l {(α_{2} - α_{1})}^{2} + m {(β_{2} - β_{1})}^{2} + n {(γ_{2} - γ_{1})}^{2}

l {(α_{2} - α_{1})}^{2} + m {(β_{2} - β_{1})}^{2} + n {(λ_{2} - λ_{1})}^{2}

Question 10:

If $\cos^{- 1} \frac{α}{2} + \cos^{- 1} \frac{β}{3} = x$ then value of $9 α^{2} - 12 α β \cos x + 4 β^{2}$ is.

यदि $\cos^{- 1} \frac{α}{2} + \cos^{- 1} \frac{β}{3} = x$ तो $9 α^{2} - 12 α β \cos x + 4 β^{2}$ का मान है.

36 \sin^{2} x

36 \sin^{2} x

24 \sin^{2} x

24 \sin^{2} x

48 \cos^{2} x

48 \cos^{2} x

72 \cos^{2} x

72 \cos^{2} x