# Recent questions tagged q2-1

### Find the differential $dy$ and evaluate $dy$ for the given values of $x$ and $dx$ $y$$=1-x^{2},x$$=5,dx$$=\large\frac{1}{2} ### If Z is a standard normal variate. Find the value of c for the following P(0< Z < c)=0.25 ### If the probability of a defective fuse from a manufactuning unit is 2\% in a box of 200 fuses find the probability that exactly 4 fuses are defective ### Form the differential equuations by eliminating arbitary constants given in brackets against each. y^{2}=4ax [a] ### Find the equation of the tangent and normal at (3 , 4 ) to the rectangular hyperbola xy=12 ### Find the equation of the hyperbola if the asymptotes are 2x+3y-8=0 and 3x-2y+1=0 and (5 , 3 ) is a point on the hyperbola. ### Find the equation of the tangent and normal to the parabola y^{2}=8x at t=\large\frac{1}{2} ### Find the equation and the length of the transverse and conjugate axis of the following hyperbola :144x^{2}-25y^{2}=3600 ### Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. y^{2}=-8x ### Can a vector have direction angles 30^{\circ},45^{\circ},60^{\circ}? ### Find the real and imaginary parts of the following complex numbers: \large\frac{1}{1+i} ### For each operation \ast defined below, determine whether \ast is binary, commutative or associative: On Z, define a \ast b = a-b ### Check the injectivity and surjectivity of the following functions: (i) $f : N\to N\; given\; by\; f(x)\; = x^2$ ### Compute the following (i)\;\begin{bmatrix}a & b\\-b & a\end{bmatrix}+\begin{bmatrix}a & b\\b & a\end{bmatrix} ### If a matrix has 24 elements,what are the possible orders it can have? (Note: This question has been split into 2 questions) ### If a matrix has 12 elements, what are the possible order it can have? ### What is the order of the matrix A=\begin{bmatrix} a & 1 & x \\ 2 & \sqrt 3 & x^2 y \\ 0 & 5 & \frac{2}{5} \end{bmatrix} ### Classify the following measures as scalars and vectors. (i)\;10\: kg ### verify that the given function (implicit or explicit) is a solution of the corresponding differential equation ### Write Minors and Cofactors of the elements of following determinants: (i) \quad \begin{vmatrix} 1&0&0 \\ 0&1&0 \\ 0&0&1 \end{vmatrix} ### Evaluate the determinant: \begin{vmatrix} cos\theta &-sin\theta \\ sin\theta & cos\theta \end{vmatrix} ### Find the maximum and minimum values, if any, of the following functions given by f (x) = |x + 2| - 1 ### if A = \begin{bmatrix} -1 & 2 & 3 \\ 5 & 7 & 9 \\ -2 & 1 & 1 \end{bmatrix} \text{ and } B = \begin{bmatrix} -4 & 1 & -5 \\ 1 & 2 & 0 \\ 1 & 3 & 1 \end{bmatrix} \text{, then verify that }$$ \text{ (i) } (A+B)' = A' + B'$$### Let $f,\, g\, and\, h$ be functions from $R\, to\, R.$ Show that $(f+g) oh = foh + goh$ ### Check the injectivity and surjectivity of the function:$f : N\to N\; given\; by\; f(x)\; = x^2 \$

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