NDA MATHEMATICS QUIZ

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Question 1:

Equation of the normal to the ellipse $9 x^{2} + 16 y^{2} = 180$ at the point $(2, 3)$ is

दीर्घवृत्त $9 x^{2} + 16 y^{2} = 180$ के लिए बिंदु $(2, 3)$ पर अभिलम्ब का समीकरण क्या होगा

4 y = 8 x - 4

4 y = 8 x - 4

3 y - 8 x - 7 = 0

3 y - 8 x - 7 = 0

3 y - 8 x + 7 = 0

3 y - 8 x + 7 = 0

3 x + 2 y + 11 = 0

3 x + 2 y + 11 = 0

Question 2:

Equation of the hyperbola having its accetricity 2 and the distance between the focii is will be

\frac{x^{2}}{4} - \frac{y^{2}}{12} = 1

\frac{x^{2}}{4} - \frac{y^{2}}{12} = 1

\frac{x^{2}}{12} - \frac{y^{2}}{3} = 1

\frac{x^{2}}{12} - \frac{y^{2}}{3} = 1

\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1

\frac{x^{2}}{16} - \frac{y^{2}}{25} = 1

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1

Question 3:

Square root of

(23 - 10 \sqrt{- 2})

(23 - 10 \sqrt{- 2})

का वर्गमूल क्या होगा ?

(5 + \sqrt{2} i)

(5 + \sqrt{2} i)

(5 - \sqrt{2} i)

(5 - \sqrt{2} i)

(3 + \sqrt{2} i)

(3 + \sqrt{2} i)

(3 - \sqrt{2} i)

(3 - \sqrt{2} i)

Question 4:

The function $f : R_{0}^{t} \to R$ defined by $f (x)$ $= \log_{a} x (a > 0)$ is

फलन $f : R_{0}^{t} \to R$ $f (x)$ $= \log_{a} x (a > 0)$ द्वारा परिभाषित है

one-one only

one - one and into

abjection

Neither one - one nor onto

Question 5:

If $X = [\begin{array}{ll} 3 & 2 \\ 2 & 5 \end{array}]$ and $Y = [\begin{array}{cc} 2 & 1 \\ - 4 & 0 \end{array}]$ then $(X Y)^{- 1} = \dots . .$

यदि $X = [\begin{array}{ll} 3 & 2 \\ 2 & 5 \end{array}]$ और $Y = [\begin{array}{cc} 2 & 1 \\ - 4 & 0 \end{array}]$ तब $(X Y)^{- 1} = \dots . .$

\frac{1}{44} [\begin{array}{ll} 2 & 3 \\ 16 & 2 \end{array}]

\frac{1}{44} [\begin{array}{ll} 2 & 3 \\ 16 & 2 \end{array}]

\frac{1}{44} [\begin{array}{ll} 2 & - 3 \\ - 16 & 2 \end{array}]

\frac{1}{44} [\begin{array}{ll} 2 & - 3 \\ - 16 & 2 \end{array}]

[\begin{array}{ll} 2 & - 3 \\ 16 & - 2 \end{array}]

[\begin{array}{ll} 2 & - 3 \\ 16 & - 2 \end{array}]

\frac{1}{- 44} [\begin{array}{ll} - 2 & 3 \\ - 16 & 2 \end{array}]

\frac{1}{- 44} [\begin{array}{ll} - 2 & 3 \\ - 16 & 2 \end{array}]

Question 6:

Value of the determinant $| \begin{array}{ccc} a & b & c \\ a + 2 x & b + 2 y & c + 2 z \\ x & y & z \end{array} |$ is

सारणिक $| \begin{array}{ccc} a & b & c \\ a + 2 x & b + 2 y & c + 2 z \\ x & y & z \end{array} |$ का मान क्या होगा ?

x y z

x y z

a x + b y + c z

a x + b y + c z

Question 7:

Differential of

\log_{5} (\log x)

w.r.t.

x

will be

\log_{5} (\log x)

के अवकल

x

के सापेक्ष क्या होगा ?

\frac{1}{x \log x \log 5}

\frac{1}{x \log x \log 5}

\frac{1}{5 x \log x}

\frac{1}{5 x \log x}

\frac{5}{x \log x}

\frac{5}{x \log x}

\frac{\log 5}{x \log x}

\frac{\log 5}{x \log x}

Question 8:

If the tangent at $(2, 3)$ on the curve $y^{2} = a x^{3}$ $+ b$ is $y = 4 x - 5$ then value of $a - b$ equals

यदि वक्र $y^{2} = a x^{3}$ $+ b$ के बिंदु $(2, 3)$ पर स्पर्शरेखा का समीकरण $y = 4 x - 5$ है तो $a - b$ का मान क्या होगा ?

8.0

10.0

9.0

12.0

Question 9:

It the line $y = k x$ is out side the circle $x^{2} + y^{2}$ $- 20 y + 90 = 0$ , then

यह रेखा $y = k x$ वृत्त $x^{2} + y^{2}$ $- 20 y + 90 = 0$ , के बाहर स्थित है फिर

| k | > 2

| k | > 2

| k | = 3

| k | = 3

| k | < 3

| k | < 3

| k | > 3

| k | > 3

Question 10:

Equation of common tangent to the parabola $y^{2} = 4 a x$ and the circle $x^{2} + y^{2} = 4 a x$ will be

परवलय $y^{2} = 4 a x$ और वृत्त $x^{2} + y^{2} = 4 a x$ के लिए उभयनिष्ठ स्पर्शरेखा का समीकरण क्या होगा ?

y = x

y = x

y = x + 1

y = x + 1

y = 2 x + 3

y = 2 x + 3

None of these