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Recent questions tagged p17

The least value of 'a' such that the function $ f(x)=x^2+ax+1 $ is strictly increasing on (1,2) is \[(a)\;-2\qquad(b)\;2\qquad(c)\;\frac{1}{2}\qquad(d)\;-\frac{1}{2}\]

asked Jan 29, 2013 by meena.p

0 answers

The function $ f(x)=-\Large\frac{x}{2}\normalsize+ \sin x $ is always increasing in \[(a)\;\bigg(-\frac{\pi}{2},\frac{\pi}{2}\bigg)\qquad(b)\;\bigg(0,\frac{\pi}{4}\bigg)\qquad(c)\;\bigg(\frac{\pi}{4},\frac{\pi}{2}\bigg)\qquad(d)\;\bigg(-\frac{\pi}{3},\frac{\pi}{3}\bigg)\qquad\]

asked Jan 29, 2013 by meena.p

0 answers

If the slope of the tangent is zero at $ (x_1,y_1)$then the equation of the tangent at $(x_1,y_1)$ is \[y_1=mx_1+c \qquad(b)\;y_1=mx_1\qquad(c)\;y-y_1\qquad(d)\;y=0\]

asked Jan 29, 2013 by meena.p

0 answers

If $ \Large\frac{dy}{dx} \normalsize =0$ then the tangent is \[(a)\;Parallel to x-axis\qquad(b)\;parallel to y-axis\qquad(c)\;Perpendicular to x-axis\qquad\]\[(d)\;perpendicular to y-axis\]

asked Jan 29, 2013 by meena.p

0 answers

The tangents to the curve $ y=x^3+6 $ at the points (-1,5) and (1,7) are \[(a)\;Perpendicular\qquad(b)\;parallel\qquad(c)\;coincident\qquad(d)\;none\; of\; these\]

asked Jan 29, 2013 by meena.p

0 answers

The values of a and b for which the function$f(x)= \left\{ \begin{array}{1 1} ax+1 & \quad x\leq3 \\ bx+3 & \quad x>3 \end{array} \right. $ is continuous at x=3 are \[(a)\;3a+2b=5 \qquad(b)\;3a=2+3b\qquad(c)\;3,2\qquad(d)\;none\;of\;these.\]

asked Jan 29, 2013 by meena.p

0 answers

'C' on LMV for $f(x)=x^2-3x$ in [0,1] is \[(a)\;0 \qquad(b)\;\frac{1}{2}\qquad(c)\;-\frac{1}{2}\qquad(d)\;does\;not\;exist\]

asked Jan 29, 2013 by meena.p

0 answers

If $ y=log \tan \bigg(\Large\frac{\pi}{4}+\frac{\pi}{2}\bigg)$then$\Large\frac{dy}{dx}$is\[(a)\;0 \qquad(b)\;\cos x\qquad(c)\;-\sec x\qquad(d)\;\sec x\]

asked Jan 29, 2013 by meena.p

0 answers

If $ x=a(\theta-\sin \theta).y=a(1-\cos \theta) \;then\; \Large\frac{d^2y}{dx^2}\;\normalsize at\;\theta=\Large\frac{\pi}{2}\;is.$\[(a)\;\frac{1}{a}\qquad(b)\;\frac{1}{2}\qquad(c)\;-\frac{1}{a}\qquad(d)\;-\frac{1}{2a}\qquad\]

asked Jan 29, 2013 by meena.p

0 answers

The tangent to the curve\[x=a\sqrt{\cos 2\theta} \cos\theta y=a\sqrt{cos2\theta}\sin \theta\]at the point corresponding to $ \theta =\frac{\pi}{6}$ is \begin{array}{1 1}(a)\;Parallel\; to\; the\; x-axis & \qquad (b)\;Parallel\; to\; the\; y-axis \\ (c)\;Parallel\; to\; the\; line\; y = x & \qquad(d)\;none\;of\;these\end{array}

asked Jan 28, 2013 by meena.p

0 answers

If the line ax+by+c = 0 is normal to the curve xy = 1 then \[(a)\;a>0,b>0 \qquad (b)\;a<0,b<0 \qquad(c)\;a<0,b>0\qquad(d)\;a<0,b<0.\]

asked Jan 28, 2013 by meena.p

1 answer

$f(x)=\Large\frac{x^2-1}{x^2+1} $ for every real number then minimum value of \begin{array}{1 1}(a)\;does\; not\; exist & \qquad(b)\;is\;not\;attained\;even\;though\;f\;is\;bounded\\(c)\;is\;equal\;to\;1 & \qquad(d)\;is\;equal\;to\;-1\end{array}

asked Jan 28, 2013 by meena.p

0 answers

True or False: A binary operation on a set has always the identity element.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every function is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is associative

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The composition of functions is commutative.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: The relation R on the set A={1,2,3} defined as R={(1,1),(1,2),(2,1),(3,3)} is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let A={0,1} and N be the set of natural numbers.Then the mapping $f:N \rightarrow A$ defined by f(2n-1)=0,f(2n)=1,$\quad n\in N$,is onto.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: An integer m is said to be related to another integer n if m is a integral multiple of n.This relation in Z is reflexive,symmetric and transitive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Every relation which is symmetric and transitive is also reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let $f:R \rightarrow R$ be the function defined by f(x)=sin (3x+2)$\quad x\in R$.Then f is invertible.

asked Dec 20, 2012 by sreemathi.v

1 answer

True or False: Let R={(3,1),(1,3),(3,3)} be a relation defined on the set A={1,2,3}.Then R is symmetric,transitive but not reflexive.

asked Dec 20, 2012 by sreemathi.v

1 answer

If $f(x)=(4-(x-7)^3\},then\;f^{-1}(x)$=____________.

asked Dec 20, 2012 by sreemathi.v

1 answer

Let $f:R \rightarrow R$ be defined by $f(x)=\Large {\frac{x}{\sqrt{1+x^2}}}$.Then ( f o f o f )(x)=____________.

asked Dec 20, 2012 by sreemathi.v

1 answer

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