Recent questions tagged isi2016-dcg

1 votes
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31
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32
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35
Let $A,B$ and $C$ be three non empty sets. Consider the two relations given below:$A-(B-C)=(A-B)\cup C$$A-(B\cup C)=(A-B)-C$Both (1) and (2) are correct.(1) is correct bu...
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36
Suppose $X$ and $Y$ are finite sets, each with cardinality $n$.. The number of bijective functions from $X$ to $Y$ is$n^{n}$$n\log_{2}n$$n^{2}$$n!$
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38
The length of the chord on the straight line $3x-4y+5=0$ intercepted by the circle passing through the points $(1,2),(3,-4)$ and $(5,6)$ is$12$$14$$16$$18$
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39
The medians $AD$ and $BE$ of the triangle with vertices $A(0,b),B(0,0)$ and $C(a,0)$ are mutually perpendicular if$b=\sqrt{2}a$$a=\pm\sqrt{2}b$$b=-\sqrt{2}a$$b=a$
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40
The equations $x=a\cos\theta+b\sin\theta$ and $y=a\sin\theta+b\cos\theta,(0\leq\theta\leq2\pi$ and $a,b$ are arbitrary constants$)$ representa circlea parabolaan ellipsea...
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41
A straight line touches the circle $x^{2}+y^{2}=2a^{2}$ and also the parabola $y^{2}=8ax.$ Then the equation of the straight line is$y=\pm x$$y=\pm(x+a)$$y=\pm(x+2a)$$y=...
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42
In an ellipse, the distance between its foci is $6$ and its minor axis is $8.$ Then its eccentricity is$\frac{4}{5}$$\frac{1}{\sqrt{52}}$$\frac{3}{5}$$\frac{1}{2}$
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43
Four tangents are drawn to the ellipse $\dfrac{x^{2}}{9}+\dfrac{y^{2}}{5}=1$ at the ends of its latera recta. The area of the quadrilateral so formed is$27$$\frac{13}{2}$...
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44
If the distance between the foci of a hyperbola is $16$ and its eccentricity is $\sqrt{2},$ then the equation of the hyperbola is$y^{2}-x^{2}=32$$x^{2}-y^{2}=16$$y^{2}-x^...
2 votes
2 answers
45
The value of $\underset{x \to 0}{\lim} \dfrac{\tan^{2}\:x-x\:\tan\:x}{\sin\:x}$ is$\frac{\sqrt{3}}{2}$$\frac{1}{2}$$0$None of these
1 votes
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46
Let $I=\int(\sin\:x-\cos\:x)(\sin\:x+\cos\:x)^{3}dx$ and $K$ be a constant of integration. Then the value of $I$ is$(\sin\:x+\cos\:x)^{4}+K$$(\sin\:x+\cos\:x)^{2}+K$$-\fr...
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47
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49
$\underset{x\rightarrow 1}{\lim}\dfrac{x^{\frac{1}{3}}-1}{x^{\frac{1}{4}}-1}$ equals$\frac{4}{3}$$\frac{3}{4}$$1$None of these
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50
The domain of the function $\ln(3x^{2}-4x+5)$ isset of positive real numbersset of real numbersset of negative real numbersset of real numbers larger than $5$
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52
The area bounded by $y=x^{2}-4,y=0$ and $x=4$ is$\frac{64}{3}$$6$$\frac{16}{3}$$\frac{32}{3}$
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53
$\underset{x\rightarrow-1}{\lim}\dfrac{1+\sqrt[3]{x}}{1+\sqrt[5]{x}}$ equals$\frac{3}{5}$$\frac{5}{3}$$1$$\infty$
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54
$\underset{x\rightarrow 0}{\lim}x\sin\left(\dfrac{1}{x}\right)$ equals$-1$$0$$1$Does not exist
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55
$\underset{x\rightarrow 0}{\lim}\sin\left(\dfrac{1}{x}\right)$ equals$-1$$0$$1$Does not exist
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56
$\underset{x\rightarrow \infty}{\lim} \left(1+\dfrac{1}{x^{2}}\right)^{x}$ equals$-1$$0$$1$Does not exist
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57
$\underset{x\rightarrow 1}{\lim} \dfrac{x^{16}-1}{\mid x-1\mid}$ equals$-1$$0$$1$Does not exist
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58
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59
If in a $\triangle ABC,\angle B=\dfrac{2\pi}{3},$ then $\cos A+\cos C$ lies in$\left[\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:-\sqrt{3},\sqrt{3}\:\right]$$\left(\:\frac{3}{...
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60
Which of the following relations is true for the following figure?$b^{2}=c(c+a)$$c^{2}=a(a+b)$$a^{2}=b(b+c)$All of these