Recent questions in Class12

If $A=\begin{bmatrix}0&1&0\\0&0&1\\1&-1&0\end{bmatrix}$ then $A^3+A$ equals

asked Apr 23, 2014 by sreemathi.v

1 answer

If $A$ and $B$ are square matrices of the same order and A is non-singular then for a positive integer n, $(A^{-1}BA)^n$ is equal to

asked Apr 23, 2014 by sreemathi.v

1 answer

If $a,b,c$ are in A.P with common difference d and $\begin{vmatrix}x+1&x+a&x+b\\x+a&x+b&x+c\\x-b+1&x-1&x-a+c\end{vmatrix}$ has absolute value 2 then d is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta_r=\begin{vmatrix}2^{r-1}&\large\frac{(r+1)!}{1+\large\frac{1}{r}}&2r\\a&b&c\\2^n-1&(n+1)!-1&n(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n\Delta_r$ is

asked Apr 23, 2014 by sreemathi.v

1 answer

If $\Delta=\begin{vmatrix} 1+x_1y_1&1+x_1y_2&1+x_1y_3\\1+x_2y_1&1+x_2y_2&1+x_2y_3\\1+x_3y_1&1+x_3y_2&1+x_3y_3\end{vmatrix}$ then $\Delta$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(x)=\begin{vmatrix}1&a&a^2\\\sin(n-1) x&\sin nx&\sin(n+1)x\\\cos(n-1)x&\cos nx&\cos(n+1)x\end{vmatrix}$ then $\int_0^{\large\frac{\pi}{2}}f(x)dx$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

If the system of equations $x+ay+az=0,bx+y+bz=0$ and $cx+cy+z=0$ where $a,b,c$ are non-zero ,non unity has a non-trivial solution then the value of $\large\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

In a triangle ABC $\begin{vmatrix} a^2& b\sin A & C\sin A\\b\sin A&1&\cos(B-C)\\C\sin A&\cos (B-C) & 1\end{vmatrix}$ equals

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A,B,C$ are angles of a triangle and $\begin{vmatrix} 1&1&1\\1+\sin A&1+\sin B&1+\sin C\\\sin A+\sin ^2A&\sin B+\sin^2B& \sin C+\sin^2C\end{vmatrix}=0$

asked Apr 22, 2014 by sreemathi.v

1 answer

If $\alpha,\beta,\gamma$ are such that $\alpha+\beta+\gamma=0$ then $\begin{vmatrix}1&\cos \gamma&\cos \beta\\\cos \alpha& 1&\cos\alpha\\\cos \beta&\cos \alpha&1\end{vmatrix}$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f(n)=\begin{vmatrix} n& 1&5\\n^2&2r+1&2r+1\\n^3&3r^2&3r+1\end{vmatrix}$ then $\sum\limits_{n=1}^ r f(n)$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $S_r=\begin{vmatrix}2r&x&n(n+1)\\6r^2-1&y&n^2(2n+3)\\4r^32nr&z&n^3(n+1)\end{vmatrix}$ then value of $\sum\limits_{r=1}^n S_r$ is independent of

asked Apr 22, 2014 by sreemathi.v

1 answer

If $F(\alpha)=\begin{bmatrix}\cos \alpha&-\sin \alpha&0\\\sin \alpha&\cos \alpha&0\\0&0&1\end{bmatrix}$ $\alpha \in R$ then $[F(\alpha)]^{-1}$ is equal to

asked Apr 22, 2014 by sreemathi.v

1 answer

The repeated factor of $\begin{vmatrix}y+z&x&y\\z+x& z&x\\x+y& y&z\end{vmatrix}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

The value of $\begin{vmatrix}1&a&a^2-bc\\1&b& b^2-ca\\1&c&c^2-ab\end{vmatrix}$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $A=\begin{bmatrix}\large\frac{1}{a}&a^2&bc\\\large\frac{1}{b}&b^2&ca\\\large\frac{1}{c}&c^2&ab\end{bmatrix}$ then $|A|$ is

asked Apr 22, 2014 by sreemathi.v

1 answer

If $a,b,c$ are non zero real numbers,then $\begin{vmatrix}bc&ca&ab\\ca&ab&bc\\ab&bc&ca\end{vmatrix}$ vanishes when

asked Apr 22, 2014 by sreemathi.v

1 answer

If $f_k(x) = \large\frac{1}{k}$ $(\sin^k x + \cos^k x)$ , where $x\in R$ and $k \geq 1$ . The $f_4(x) - f_6(x)$ equals

asked Apr 6, 2014 by balaji.thirumalai

1 answer

If $\alpha, \beta \neq 0$ , and $f(n) = \alpha^n+\beta^n$ and $\begin{vmatrix} 3 & 1+f(1) & 1+f(2)\\ 1+f(1)& 1+f(2) &1+f(3) \\ 1+f(2)&1+f(3) & 1+f(4) \end{vmatrix}$ $=K(1-\alpha)^2\;(1-\beta)^2\;(\alpha-\beta)^2$ , then $K$ is equal to

asked Apr 6, 2014 by balaji.thirumalai

0 answers

The integral $\large\int ($ $1+x- \large\frac{1}{x})$ $e^{x+\large\frac{1}{x}}$ $dx$ is equal to

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If $A$ is an $3\times 3$ non-singular matrix such that $A A' = A' A$ and $B = A^{-1} A'$ , then $B B'$ equals

asked Apr 6, 2014 by balaji.thirumalai

0 answers

The integral $\Large \int \limits_{\normalsize 0}^{\normalsize \pi}$ $\sqrt{1 + 4 \sin^2\large\frac{x}{2} \normalsize- \normalsize 4 \normalsize\sin \large\frac{x}{2}}$ $\;dx$

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If $\large[$ $\vec{a} \times \vec{b}\; \vec{b} \times \vec{c}\; \vec{c} \times \vec{a}$ $\large]$ $=\lambda \large[$ $\vec{a}\vec{b}\vec{c}\large]$ $^2$ , then $\lambda$ is equal to:

asked Apr 6, 2014 by balaji.thirumalai

0 answers

If $a\in R$ and the equation $-3 (x-[x])^2 + 2(x-[x])+a^2 = 0$ , (where $[x]$ denotes the greatest integer $\leq x$ ) has no integral solution, then all possible values lie in the interval:

asked Apr 6, 2014 by balaji.thirumalai

0 answers

Integrate : $\int \large\frac{ax^3+bx+c}{\sqrt x}$ $dx$

asked Mar 26, 2014 by balaji.thirumalai

1 answer

If the marginal cost of manufacturing a product is $C' = 3 + 0.25x$ , find the total cost of function $C$ given that $C(0) = 60$ .

asked Mar 20, 2014 by balaji.thirumalai

1 answer

The rate at which the population of a bacteria culture grows is proportional to the number of bacteria present. If the number of bacteria grew from $1000$ to $5000$ in $10$ hours find the number of bacteria after $15$ hours

asked Mar 20, 2014 by balaji.thirumalai

1 answer

The population of a country doubles in 40 years. Assuming that the rate of increase is proportional to number of inhabitants, find the number of years in which the population would treble itself?

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Find the general solution of $xy' - 2y = x^2$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Evaluate $\large \int \limits_{\normalsize 0}^{\frac{\pi}{2}}$ $\bigg (\sqrt {\tan x} + \large\frac{1}{\sqrt {\tan x} }$ $\bigg)\;$ $dx$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

Evaluate $\displaystyle \lim_{n \rightarrow \infty} \bigg[ \large\frac{1^p + 2^p + 3^p....+ n^p}{n^{p+1}} \bigg ]$ , where $p \gt -1$

asked Mar 20, 2014 by balaji.thirumalai

1 answer

6 boys and 6 girls sit randomly in a row, what is thae probability that boys and girls sit alternately?

asked Feb 14, 2014 by bharathdon.999

1 answer

Lets say you enter a Chess tournament. The probability of winning a game against half the players is 0.3, the probability of winning against one quarter of them is 0.4 and the probability of winning against the remaining one quarter is 0.5. Let's say you play against a randomly chosen opponent. What is your probability of winning?

asked Feb 12, 2014 by balaji.thirumalai

1 answer

A tow truck drags a stationary car along the road. The chain makes an angle of 30 degrees with the road and the tension in the chain is 1500 N. How much work is done (in Joules) by the truck in pulling the car 1 km (approximate answer, rounded off)?

asked Feb 11, 2014 by balaji.thirumalai

1 answer

The tangent to a curve intersects x axis at $B$ and $y$ at $A$ . The normal to same curve intersects $x$ axis at $C$ and $Y$ axis at $D$ . Given $\large\frac{AO}{OB}= \frac{OC}{CD}$ curve passes through $(2,3)$ . Find the curve

asked Feb 10, 2014 by meena.p

1 answer

Equation of conic defined by : $9yy'+4x=0$ and given $y(0)=2$ , find length of latus rectum

asked Feb 10, 2014 by meena.p

1 answer

Equation of conic defined by : $9yy'+4x=0 \qquad y(0)=2$ find length of latus rectum

asked Feb 10, 2014 by meena.p

0 answers

$\large\frac{dy}{dx}$ $=1$ passes through $\large[$ $0,\large\frac{3}{2}]$ and $\large\frac{dy}{dx}$ $=2$ passes through $[0,1]$ represents two curve which passes through a point whose coordinates are zeroes of a quadratic polynomial . The quadratic equation is gradient polynomial. Find sum of coefficients of $x^3,x^2,x$

asked Feb 7, 2014 by meena.p

1 answer

A tank contains $200\; gal$ of water of $40\; lb$ salt dissolves. $5\; gal$ of brine , each containing $2\; lb$ of dissolved salt, run into tank per minute and mixture kept uniform by stirring runs out at same rate. Find amount of salt $y(t)$ in tank at any time $(t)$

asked Feb 7, 2014 by meena.p

1 answer

Solve : $2e^{\Large\frac{x}{y}}(dx-dy)+dx-2e^{\Large\frac{x}{y}} \large\frac{x}{y}$ $dy=0$

asked Feb 7, 2014 by meena.p

1 answer

Solve : $y'= 1+y^2$

asked Feb 7, 2014 by meena.p

1 answer

The two curves represents by $9yy'+4x=0,\; y(0)=2,\; yy'+x=0,\; y(0)=3$ then number of common normals for two curves will be

asked Feb 7, 2014 by meena.p

1 answer

Find solution of differential equation $(y-x+1) dy -(y+x+2)dx=0$

asked Feb 7, 2014 by meena.p

1 answer

Find solution : $(x-2y+1) dy -(3x-6y+2)dx=0$

asked Feb 7, 2014 by meena.p

1 answer

Eliminate arbitrary constant and obtain differential equation $x^2-y^2= a(x^2+y^2)^2$

asked Feb 7, 2014 by meena.p

1 answer

Solve: $(3xy+y^2)dx+(x^2+xy)dy=0 \qquad y(1)=1$

asked Feb 7, 2014 by meena.p

1 answer

Solve: $\large\frac{dy}{dx}=\frac{-\sqrt {1-y^2}}{x-e^{\Large\sin ^{-1}y}}$

asked Feb 7, 2014 by meena.p

1 answer

Solve : $y''+e^{2y}(y')^3=0$

asked Feb 7, 2014 by meena.p

1 answer

Find general solution of equation $y'-2y+a=0$ a=fixed

asked Feb 7, 2014 by meena.p

1 answer

Find all values of m for which $y-e^{mx}$ is solution of equation $y'''-2y''-y'+2y=0$

asked Feb 7, 2014 by meena.p

1 answer

Ask Questions, Get Answers