Recent questions tagged maths

Two eggs are drawn successively with replacement from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

asked Nov 19, 2016 by priyanka.c

1 answer

Find the vector and Cartesian equation of the line through the point (5, 2, -4) and which is parallel to the vector $3 \hat{i} +2 \hat{j} -8 \hat{k}$

asked Nov 19, 2016 by priyanka.c

1 answer

$\begin{align}\int_0^1 \frac{\tan^{-1} x}{1+x^2} dx \end{align}$

asked Nov 19, 2016 by priyanka.c

1 answer

Fine the maximum and minimum value of $f(x) = x + \sin 2x $ in the invervat $0, 2\pi $

asked Nov 19, 2016 by priyanka.c

1 answer

Differentiate $\tan^-1 \frac{[\sqrt{1+x^2} + 1}{x}], x \neq 0$

asked Nov 18, 2016 by priyanka.c

1 answer

Find the equation of the line joining (1,3) and B (0, 0) using determinants and find K if D (K,0) is a point such that area of $\triangle ABD$ is 3 sq. units

asked Nov 18, 2016 by priyanka.c

1 answer

Show that function $f : R \to R$ given by $f(x) = x^3 + x $ I a bijection.

asked Nov 18, 2016 by priyanka.c

1 answer

$\begin{align}\int \frac{dx}{\sqrt {x^2 - a^2}} \end{align}$

asked Nov 18, 2016 by priyanka.c

1 answer

Two cards are drawn without replacement from a well shuffled pack of 52 cards. Find the probability that one is spade and other is a queen of red colour.

asked Nov 18, 2016 by priyanka.c

1 answer

A line passes through (2, -1, 3) and is perpendicular to the line $\overrightarrow {r} = ( {\hat{i} + \hat {j} - \hat{k}}) + \lambda (2\hat{i} - 2\hat{j} +\hat{k}) $ and $\overrightarrow {r} = (2\hat{i} - \hat{j} -3\hat {k}) +\mu (\hat{i} + 2 \hat{j} +2\hat{k})$. Obtain its equation.

asked Nov 18, 2016 by priyanka.c

1 answer

If $\overrightarrow {a} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\overrightarrow {b} = 2\hat{i} + 4\hat{j} - 5\hat{k}$ represents two adjacent sides of a parallelogram, find unit vectors parallel to the diagonals of the parallelogram.

asked Nov 18, 2016 by priyanka.c

1 answer

If $A=\begin{bmatrix} 9 & 1 \\ 7 & 8 \end{bmatrix} $, $B =\begin{bmatrix} 1 & 5 \\ 7 & 12 \end{bmatrix}$ find matrix C such that 5A + 3B + 2C is a null matrix.

asked Nov 17, 2016 by priyanka.c

1 answer

If $\cos^{-1} x + cos^{-1} y + cos^{-1} z = \pi $ , Evaluate $x^2 + y^2 + z^2 + 2xyz$

asked Nov 17, 2016 by priyanka.c

1 answer

If the function $ f: [1, \alpha) \ implies [ 1, \alpha)$ defined by $f(x) = 2^{x(x-1)}$ is invertible, find $f^{-1}(x)$

asked Nov 17, 2016 by priyanka.c

1 answer

A die which is marked with 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event 'number is even' and B be the event 'number is red' and Are A and B independent?

asked Nov 17, 2016 by priyanka.c

1 answer

$\begin{equation} \int\limits_0^1 \sin^{-1} x \; \mathrm{d} x \end{equation}$

asked Nov 17, 2016 by priyanka.c

1 answer

If the points $A(-1, 3, 2),\; B(-4, 2, -2)$ and $C (5, 5, \lambda)$ are collinear, find the value of $\lambda$

asked Nov 16, 2016 by priyanka.c

1 answer

Differentiate $a^x$ w.r.t x, where a is a constant

asked Nov 16, 2016 by priyanka.c

1 answer

$\tan ^{-1}x +\tan^{-1} \frac{2x}{1-x^2} = 3 \tan ^{-1}(x) \;, |x| < \frac{1}{\sqrt 3}$ . Is this true ? Justify.

asked Nov 16, 2016 by priyanka.c

1 answer

Let f : N $\to$ Y be a function defined as $f(x) = 4x + 3f(x)=4x+3$ where $Y = \{ y \in N ; y = 4x + 3Y=\{ y \in N; y= 4x+3$ for some $ x \in N \}x \in N \}$. If 'f' is invertible.

asked Nov 14, 2016 by priyanka.c

1 answer

$\begin{align}\int \frac{\sin 4x}{ \sin x} dx \end{align}$

asked Nov 13, 2016 by priyanka.c

1 answer

Form the differential equation representing family of curves $y = A \cos (x + B)$ where A and B are parameters

asked Nov 13, 2016 by priyanka.c

1 answer

Prove that the points A, B and C with position vectors $\overrightarrow{a}, \overrightarrow{b} and \overrightarrow{c}$ respectively are collinear if and only if $\overrightarrow{a} \times \overrightarrow{b} + \overrightarrow{b} \times \overrightarrow{c} + \overrightarrow{c} \times \overrightarrow{a} = 0$

asked Nov 13, 2016 by priyanka.c

2 answers

It is given that a function $f{x} = x^3 - 6x^2 + ax+ b $ on [1,3] , Rolle's theorem holds with $c = 2 + \frac{1}{\sqrt3}$. Find the value of a and b if f(1) = f(3) = 0

asked Nov 10, 2016 by priyanka.c

1 answer

Differentiate w . r . t x $\tan^{-1}\bigg[\large\frac{1-\cos x}{sin x}\bigg]; -\pi < x < \pi$

asked Nov 10, 2016 by priyanka.c

1 answer

Solve for $x . \begin{vmatrix} x+a & x & x \\ x & x+a & x \\ x & x & x+a \end{vmatrix} = 0 $

asked Nov 10, 2016 by priyanka.c

1 answer

Let $F(x) =\begin{pmatrix} \cos x & -\sin x & 0 \\ \sin x & cos x & 0 \\ 0 & 0 & 1 \end{pmatrix} $ Show that F(x) F(y) = F (x+y)

asked Nov 10, 2016 by priyanka.c

1 answer

Prove that $ \cos^{-1}x = 2 \sin^{-1} \sqrt{\frac{1-x}{2}}$

asked Nov 10, 2016 by priyanka.c

1 answer

If $12$ identical balls are to be placed in 3 identical boxes ,then the probability that one of the boxes contains exactly 3 balls is :

asked Nov 17, 2015 by meena.p

1 answer

The area (in sq.units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\large\frac{x^2}{9} + \frac{y^2}{5} $$=1$ is :

asked Nov 17, 2015 by meena.p

1 answer

Let $f(x) $ be a polynomial of degree four having extreme values at $x=1$ and $ x=2$ If $\lim\limits_{x \to 0} \bigg[1+\large\frac{f(x)}{x^2}\bigg]$$=3$ then $(2)$ is equal to :

asked Nov 17, 2015 by meena.p

1 answer

Let $\alpha$ and $\beta$ be the roots of equation $x^2-6x-2 =0$. If $a_n = \alpha ^n -\beta^n$ , for $n \geq 1$, then the value of $\large\frac{a_{10}-2_{a8}}{2_{a9}}$ is equal to :

asked Nov 17, 2015 by meena.p

1 answer

The integral $\int \limits_2^4 \large\frac{\log x^2}{\log x^2+\log(36-12x+x^2)}$$dx$is equal to :

asked Nov 17, 2015 by meena.p

1 answer

The mean of the data set comprising of 16 observations is $16$ . If one of the observation valued 16 is deleted and three new observations, valued 16 is deleted and three new observation valued $3,4$ and $5$ are added to the mean of the resultant data, is :

asked Nov 17, 2015 by meena.p

1 answer

If the function $g(x) = \left\{ \begin{array} {1 1} k \sqrt{x+1} , & \quad 0 \leq x \leq 3 \\ mx+2,& \quad 3 < x \leq 5 \end{array} \right. $ is differentiable , then the value of $k+m$ is :

asked Nov 17, 2015 by meena.p

1 answer

Let $ \tan^{-1}y = \tan ^{-1}x + \tan^{-1} \bigg(\large\frac{2x}{1-x^2}\bigg)$, where $|x| < \frac{1}{\sqrt 3 }$. Then a value of y is :

asked Nov 17, 2015 by meena.p

1 answer

The normal to the curve , $x^2+2xy-3y^2=0$ at (1,1):

asked Nov 17, 2015 by meena.p

1 answer

The integral $\int \frac{dx}{x^2(x^4+1)^{3/4}}$ equals :

asked Nov 17, 2015 by meena.p

1 answer

The negation of $\sim S \vee ( \sim r \wedge s)$ is equivalent to :

asked Nov 13, 2015 by meena.p

1 answer

If m is the A.M of two distinct real number l and n (l,n >1) and $G_1,G_2$ and $G_3$ are three geometric means between l and n, then $G_1^4 +2 G_2^4+G_3^4$ equals

asked Nov 13, 2015 by meena.p

1 answer

If $A=\begin{bmatrix}1 & 2 & 2 \\ 2 & 1 & -2\\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T=9I$ , where I is $ 3 \times 3$ identity matrix , then the ordered pair $(a,b)$ is equal to :

asked Nov 13, 2015 by meena.p

1 answer

Let $y(x)$ be the solution of the differential equation $(x log x) \frac{dy}{dz} $$+y=2x \log x , x (\geq 1)$ Then $y(e) $ i equal to :

asked Nov 13, 2015 by meena.p

1 answer

The number of integers greater than $6,000$ that can be formed , using the digits $3,5,6,7$ and $8$, with out repetion, is :

asked Nov 13, 2015 by meena.p

1 answer

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$, is :

asked Nov 13, 2015 by meena.p

1 answer

A complex number z is said to be uni modular if $|z|=1$. suppose $z_1$ and $z_2$ are complex numbers such that $ \large\frac{z_1-2z_2}{2-z_1z_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

asked Nov 13, 2015 by meena.p

1 answer

The set of all values of $\lambda$ for which the system of linear of linear equations : $2x_1-2x_2+x_3 =\lambda x_1 \\ 2x_1-3x_2+2x_3 =\lambda x_2 \\ -x_1 + 2x_2 = \lambda x_3$ has a non- trivital solution,

asked Nov 13, 2015 by meena.p

1 answer

The area (in sq.units ) of the region described by : $\{(x,y):y^2 \leq 2x\;and\;y \geq 4x-1\}$ is :

asked Nov 13, 2015 by meena.p

1 answer

The sum of first 9 terms of the series $\large\frac{1^3}{1} +\frac{1^3+2^3}{1+3}+\frac{1^3+2^3+3^3}{1+3+5}$+.....is :

asked Nov 13, 2015 by meena.p

1 answer

The sum of coefficient on integral powers of x in the binomial expansion of $(1-2 \sqrt {x})^{50}$ is :

asked Nov 13, 2015 by meena.p

1 answer

The distance of the point $(1,0,2)$ from the point of intersection of the line $\large\frac{x-2}{3} =\frac{y+1}{4} =\frac{z-2}{12}$ and the plane $x-y+z=16,$ is :

asked Nov 13, 2015 by meena.p

1 answer

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