Recent questions in Mathematics

. If f = →\ \ is defined by f x 2x 2 x for x ( ) = [ ] − ∈ [ ] \. where [x] is the greatest integer not exceeding x, then the range of f is

asked May 13, 2015 by _1

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If $\large\frac{dy}{dx}=\frac{y+ x \tan \Large\frac{y}{x}}{x}$ then $\sin \large\frac{y}{x}$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

Observe the following statements:I. If $dy+2xy\;dx=2e^{-x^{2}} dx$ then $ye^{x^{2}}=2x+c$ II. If $ye^{-x^{2}}-2x=c$ then $dx=(2e^{-x^{2}}-2xy)dy$ Which of the following is a correct statement ?

asked Nov 13, 2013 by meena.p

1 answer

If $x^2 y-x^3 \large\frac{dy}{dx}$ $=y^4 \cos x$ then $x^3\;y$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

If $dx+dy=(x+y)(dx-dy)$ then $\log (x+y)$ is equal to:

asked Nov 13, 2013 by meena.p

1 answer

The area (in square units) bonded by the curves $y^2=4x$ and $x^2=4y$ in the plane is :

asked Nov 13, 2013 by meena.p

1 answer

If $\int \sin ^{-1} \bigg( \large\frac{2x}{1+x^2}\bigg)$ $dx-=f(x)-\log (1+x^2)+c$ then $f(x)$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

$\int \limits_0^{\pi} \large\frac{\theta \sin \theta}{1+\cos ^2 \theta}$ $d \theta$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

$\int \limits_0^{\pi/2} \large\frac{200 \sin x+100 \cos x}{\sin x+\cos x}$ $dx$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

$\int \large\frac{x^{49} \tan^{-1} (x^{50})}{(1+x^{100})}$ $dx=k(\tan^{-1}(x^{50})^2+c$ then k is equal to :

asked Nov 13, 2013 by meena.p

1 answer

If $\int \large\frac{\sin x}{\cos x(1+\cos x)dx}$ $=f(x)+c$ then $f(x)$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

If $u= \sin^{-1} \bigg(\large\frac{x}{y}\bigg)$ $+\tan^{-1} \bigg(\large\frac{y}{x}\bigg)$ , then the value of $x \large\frac{\partial u}{\partial x}$ $+y \large\frac{\partial u}{\partial y}$ is :

asked Nov 13, 2013 by meena.p

1 answer

Observe the following statements :A : $f(x)=2x^3-9x^2+12x-3$ is increasing outside the interval $(1,2)$ R : f'(x) < 0 for $x \in (1,2)$ Then which of the following is true ?

asked Nov 13, 2013 by meena.p

1 answer

The radius of a circular plate is increasing at the rate of $0.01\;cm/sec$ when the radius is $12\; cm$ . Then the rate at which the area increases, is :

asked Nov 13, 2013 by meena.p

1 answer

A stone thrown upwards, has its equation of motion $s=490t-4.9t^2$ . Then the maximum height reached by it , is:

asked Nov 13, 2013 by meena.p

1 answer

If $x \sqrt {1+y}+y \sqrt {1+x}=0$ then $\large\frac{dy}{dx}$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

If $f(x) =10 \cos x +(13+2x) \sin x$ then $f''(x)+f(x)$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

Observe the following statements: $I. f(x) =ax^{41}+bx^{-40}=> \large\frac{f''(x)}{f(x)}$ $=1640\;x^{-2} \quad II. \large\frac{d}{dx}$ $\tan ^{-1} \bigg(\large\frac{2x}{1-x^2}\bigg)=\frac{1}{1+x^2}$ Which of the following is correct ?

asked Nov 13, 2013 by meena.p

1 answer

If $R \to R$ is an even function which is twice differentiable on R and $f''(\pi)=1,$ then $f''(-\pi)$ is equal to :

asked Nov 13, 2013 by meena.p

1 answer

If $f: R \to R$ is defined by $f(x)= \left\{ \begin{array}{1 1} \large\frac{x+2}{x^2-3x+2} & \quad if & \quad x\in R -[-1,-2] \\ -1 & \quad if & \quad x=-2 \\ 0 & \quad if & \quad x=-1 \end{array} \right.$ then $f$ is continuous on the set :

asked Nov 13, 2013 by meena.p

1 answer

If $f: R \to R$ is defined by $f(x)= \left\{ \begin{array}{1 1} \large\frac{x-2}{x^2-3x+2} & \quad if & \quad x\in R -[1,2] \\ 2 & \quad if & \quad x=2 \\ 1 & \quad if & \quad x=2 \end{array} \right.$ then $\lim \limits_{x \to 2} \large\frac{f(x)-f(2)}{x-2}=$

asked Nov 13, 2013 by meena.p

1 answer

$\lim \limits_{x \to 0} x^2 \sin \large\frac{\pi}{x}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

Which of the following equations gives a circle?

asked Nov 12, 2013 by meena.p

1 answer

The cartesian from of the polar equation $\theta=\tan^{-1} 2$ is :

asked Nov 12, 2013 by meena.p

1 answer

The line among the following which touches the parabola $y^2=4ax,$ is :

asked Nov 12, 2013 by meena.p

1 answer

The parabola with directrix $x+2y-1=0$ and focus (1,0) is :

asked Nov 12, 2013 by meena.p

1 answer

If $y=3x$ is a tangent to a circle with center $(1,1),$ then the other tangent drawn through $(0,0)$ to the circle is:

asked Nov 12, 2013 by meena.p

1 answer

If $x-y+1=0$ meets the circle $x^2+y^2+y-1=0$ at A and B , then the equation of the circle with AB as diameter is :

asked Nov 12, 2013 by meena.p

1 answer

The equation of the circle whose diameter is the common chord of the circles $x^2+y^2+2x+3y+2=0$ and $x^2+y^2+2x-3y-4=0$ is :

asked Nov 12, 2013 by meena.p

1 answer

The point collinear with $(1,-2,-3)$ and $(2,0,0)$ among the following is :

asked Nov 12, 2013 by meena.p

0 answers

The direction cosines of the line passing through $P(2,3,-1)$ and the orgin are :

asked Nov 12, 2013 by meena.p

1 answer

The product of the perpendicular distances from the origin on the pair of straight lines $12x^2+25xy+12y^2+10x+11y+z=0$ is :

asked Nov 12, 2013 by meena.p

1 answer

The area of the triangle formed by the pair of straight lines $(ax+by)^2-3(bx-ay)^2=0$ and $ax+by+c=0$ , is :

asked Nov 12, 2013 by meena.p

1 answer

The equation of the straight line perpendicular to $5x-2y=7$ and passing through the point of intersection of the lines $2x+3y=1$ and $3x+4y=6$ is :

asked Nov 12, 2013 by meena.p

1 answer

If PM is the perpendicular from $P(2,3)$ onto the line $x+y=3, then the co-ordinates of M are :

asked Nov 12, 2013 by meena.p

1 answer

The area (in square units) of the triangle formed by the lines $x=0,y=0$ and $3x+4y=12,$ is :

asked Nov 12, 2013 by meena.p

1 answer

If a point P moves such that its distances from the point $A(1,1)$ and the line $x+y+z=0$ are equal, then locus of P is :

asked Nov 12, 2013 by meena.p

1 answer

For a binomial variate X with $n=6,$ if $P(X=2)=9\;P(X=4),$ then its variance is :

asked Nov 12, 2013 by meena.p

1 answer

If the range of a random variable X is $\{0,1,2,3,4.......\}$ with $P(X =k)= \large\frac{(k+1)a}{3^k}$ for $k \leq 0,$ then a is equal to :

asked Nov 12, 2013 by meena.p

1 answer

Box A contains 2 black and 3 red balls, white Box contains 3 black and 4 red balls. Out of these two boxes one is selected at random ; and the probability of choosing Box A is double that of Box B. If a red ball is drawn from the selected box, then the probability that it has come from Box B, is :

asked Nov 12, 2013 by meena.p

2 answers

A number n is chosen at random from $S=\{1,2,3,.....,50\}$ .Let $A= \bigg \{ n \in S:n +\large\frac{50}{n}$ $> 27 \bigg\}$ $,B= (n \in S:n$ is a Prime) and $C=\{n \in S:n \;is\; a\; square \}$ . Then correct order of their probabilities is :

asked Nov 12, 2013 by meena.p

1 answer

A coin and six faced die, both unbiassed, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is :

asked Nov 12, 2013 by meena.p

1 answer

Observe the following statements:A: Three vectors are coplanar if one of them is expressible as a linear combination of the other two. R: Any three coplanar vectors are linearly dependent . Then which of the following is true?

asked Nov 12, 2013 by meena.p

1 answer

Observe the following lists :

asked Nov 12, 2013 by meena.p

1 answer

I : Two non-zero , non-collinear vectors are linearly independent. II. Any three coplanar vectors are linearly dependent .Which of the above statements is /are true?

asked Nov 12, 2013 by meena.p

1 answer

If $\overrightarrow {a}$ and $\overrightarrow{b}$ are unit vectors, then the vector $(\overrightarrow a+\overrightarrow b) \times (\overrightarrow{a} \times \overrightarrow{b})$ is parallel to the vector:

asked Nov 12, 2013 by meena.p

1 answer

If the vector $\overrightarrow{a} =2 \hat i+3 \hat j+6 \hat k$ and $\overrightarrow {b}$ are collinear and $|\overrightarrow {b}|=21,$ then $\overrightarrow {b}$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

A tower, of x meters high, has a flagstaff at its top. The tower and the flagstaff subtend equal angles at a point distant y meters from the foot of the tower. Then the length of the flagstaff(in meters), is :

asked Nov 12, 2013 by meena.p

1 answer

Two sides of a triangle are given by the roots of the equation $x^2-5x+6=0$ and the angle between the sides is $\large\frac{\pi}{3}$ . Then the perimeter of the triangle is :

asked Nov 12, 2013 by meena.p

2 answers

In $\Delta ABC, \sum (b+c) \tan \large\frac{A}{2}$ $\tan \bigg(\large\frac{B-C}{2}\bigg)$ is equal to :

asked Nov 12, 2013 by meena.p

1 answer

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