NDA MATHEMATICS QUIZ

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Question 1:

The number of fractional roots of the equation ${(t + \frac{1}{t})}^{2} = 4 + \frac{3}{2} (t - \frac{1}{t})$

समीकरण ${(t + \frac{1}{t})}^{2} = 4 + \frac{3}{2} (t - \frac{1}{t})$ के भिन्नात्मक मूलों की संख्या क्या होगी ?

Question 2:

Three dice are rolled together

the number of possible outcomes in which at least one die shows 4 is

120

100

Question 3:

The number of non negative integral solutions of $p + q + r = 5$ is

$p + q + r = 5$ के गैर ऋणात्मक पूर्णांक समाधानों की संख्या कितनी होगी ?

Question 4:

If in a triangle $ABC$ the altitudes are in H.P. then $\sin A, \sin B$ and $\sin C$ are in

यदि त्रिभुज $ABC$ मेअभिलम्ब हरात्मक श्रेणी में है फिर $\sin A, \sin B$ और $\sin C$ किसमें होगा ?

H.P.

G.P.

A.P.

None of these

Question 5:

In a triangle $ABC$ if $∠ A = 90^{\circ}$ then $\frac{b^{2} + c^{2}}{b^{2} - c^{2}} \sin (B - C)$

किसी त्रिभूज $ABC$ यदि $∠ A = 90^{\circ}$ तब $\frac{b^{2} + c^{2}}{b^{2} - c^{2}} \sin (B - C)$ का मान क्या होगा ?

- 2

- 2

Question 6:

${Lim}_{x \to 0} {(\frac{1 + 7 x^{2}}{1 + 4 x^{2}})}^{\frac{1}{x^{2}}} = \dots \dots$

e^{2}

e^{2}

e^{3}

e^{3}

e^{6}

e^{6}

e^{4}

e^{4}

Question 7:

The circles $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$ and $x^{2} + y^{2} + 2 b x + 2 a y + c = 0$ will touch if $\dots . .$

वृत्त $x^{2} + y^{2} + 2 a x + 2 b y + c = 0$ और $x^{2} + y^{2} + 2 b x + 2 a y + c = 0$ एक दूसरे को स्पर्श करेगी जब

(a + b)^{2} = 2 c

(a + b)^{2} = 2 c

(a - b)^{2} = 2 c

(a - b)^{2} = 2 c

(a + b)^{2} = 2 c^{2}

(a + b)^{2} = 2 c^{2}

a^{2} - b^{2} = c^{2}

a^{2} - b^{2} = c^{2}

Question 8:

Equation of the tangents to the parabola $y^{2} = 4 ax$ which makes an angle $135^{\circ}$ with its axis is

परवलय $y^{2} = 4 ax$ की स्पर्शरेखाओं का समीकरण जो अपनी अक्ष के साथ $135^{\circ}$ का कोण बनाता है, क्या होगा ?

- x + y - a = 0

- x + y - a = 0

x + y = a

x + y = a

x - y = a

x - y = a

x + y = - a

x + y = - a

Question 9:

Focus of the parabola $x^{2} - 6 x - 6 y + 6 = 0$ will be

परवलय $x^{2} - 6 x - 6 y + 6 = 0$ का फोकस क्या होगा ?

(2, 1)

(2, 1)

(3, 1)

(3, 1)

(1, 3)

(1, 3)

(4, 2)

(4, 2)

Question 10:

Locus of point of intersection of the lines $\frac{x}{a} + \frac{y}{b} = 1$ and $\frac{x}{b} + \frac{y}{a} = 1$ passes possibly through

$\frac{x}{a} + \frac{y}{b} = 1$ और $\frac{x}{b} + \frac{y}{a} = 1$ रेखाओं के प्रतिच्छेदन बिंदु का बिंदुपथ संभवतः किससे गुजरता है ?

(2, 1)

(2, 1)

(0, 0)

(0, 0)

(1, 2)

(1, 2)

(2, 3)

(2, 3)