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If $|z+2-i|=5,$ then the maximum value of $|3z+9-7i|$ is

Question 69. Consider the following matrix-

Select a suitable figure from the four alternatives that would complete the figure matrix.

Solve for x if (x-1) (x-2) (x-5) > 0

Let $f\left(x\right)=\log \left({\log }_{1/3}\right({\log }_7(\sin x+a)\left)\right)$ be defined for every real values of $x$, then the range of $a$

How to write statements in solutions of permutation based questions?

If a set $A$ has ${}^{\prime }{n}^{\prime }$ distinct elements, then the number of all relations on $A$ is

If $f\left(x\right)=2\sqrt{x-1}+5\sqrt{1-x}+(x^2+x+1{)}^{3/2}$ exists, then domain of $f\left(x\right)$ is

what is an easy way to find the domain and range of a function?

Let A and B be independent events with P (A ) = 0.3 and P (B) = 0.4 . Find
$P(A\cap B)$

$P(A\cup B)$

$P\left(\frac{A}{B}\right)$.

$P\left(\frac{B}{A}\right)$

For the given differential equation find the general solution.

$x\frac{dy}{dx}+2y=x^{2}logx$

Integrate the rational functions.
$\int \frac{5x}{(x+1)(x^2-4)}dx.$

For the given differential equation find the particular solution satisfying the given conditions.

$[xsi{n}^2\left(\frac{y}{x}\right)-y]dx+xdy=0,y=\frac{\pi }{4}whenx=1.$

Find the centroid of a triangle, mid-points of whose sides are (1, 2, -3), (3, 0, 1) and (- 1, 1, - 4).

Or

The mid-points of the sides of a triangle are (1, 5, - 1), (0, 4, - 2) and (2, 3, 4). Find its vertices.

Find the equation for the ellipse that satisfies the given conditions,
$b=3,c=4,$ centre at origin; foci on the x - axis.

Sum of three prime numbers is $40,$ then their product can be

A straight line passes through a fixed point $(h,k)$. The locus of the foot of perpendicular on it drawn from the origin is

The solution of the differential equation $\frac{dy}{dx}-\frac{y+3x}{{\log }_e(y+3x)}+3=0$ is
(where $c$ is a constant of integration)

The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola $y^2=4ax$ is the curve

The number of ways in which $5$ girls and $2$ boys can sit in row such that the boys are not together.

Let $x=my+c$ is normal to $x^2=4y$, if $k^2+mk+m=0$ has only one real value of $k$,then value(s) of $c$ is/are

Evaluate : ${\int }_0^{\frac{\pi }{4}}\frac{sinx+cosx}{16+9sin2x}dx.$
OR
Evaluate ${\int }_1^3(x^2+3x+e^x)dx$, as the limit of the sum.

Bag I contains 3 red and 4 black balls and bag II contains 4 red and 5 black balls. One ball is transferred from bag I to bag II and then is drawn from bag II. The ball so drawn is found to be red in colour. Find the probability that the transferred ball is black.

An experiment succeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.

Show that the given differential equation is homogeneous and then solve it.

$x\frac{dy}{dx}-y+xsin\left(\frac{y}{x}\right)=0$

The order of the differential equation
$2x^2\frac{d^{2}y}{d{x}^2}-3\frac{dy}{dx}+y=0$ is
(a) 2
(b) 1
(c) zero
(d) None of these

The locus of point of intersection of two tangents to $y^2=4ax$ at $t$ and $2t$ on the parabola is

Find the transpose of the following matrix.
$$\left[\begin{array}{ccc}-1& 5& 6\\ \sqrt{3}& 5& 6\\ 2& 3& -1\end{array}\right]$$

State whether each of the following statements is true or false. Justify your answer.

(i) {2, 3, 4, 5} and (3, 6} are disjoint sets.

(ii) {a, e, i, o, u} and {a, b, c, d} are disjoint sets.

(iii) {2, 6, 10, 14} and {3, 7, 11, 15} are disjoint sets.

(iv) {2, 6, 10} and {3, 7, 11} are disjoint sets.

Which of the following pair is twin prime numbers ?

The normal at a point $P$ on the ellipse $x^2+4y^2=16$ meets the $x-$ axis at $Q$. If $M$ is the midpoint of the line segment $PQ$, then the locus of $M$ intersects the latus rectum of the given ellipse at the points

assuming that a person of a normal sight can read print at such a distance that the letters subtend an angle of 5' at his eye,find the height of letter that he can read a distance of 12m

if f:(1,∞)–(2,∞) is given by f(x)= x+(1/x) then find f inverse

If $\frac{si{n}^{4}A}{a}+\frac{co{s}^{4}A}{b}=\frac{1}{a+b},$ then the value of $\frac{si{n}^{8}A}{a^3}+\frac{co{s}^{8}A}{b^3}$ is equal to

Let $f_1:R\to R;f_2:[0,\infty )\to f_3:R\to R$ and $f_4:R\to [0,\infty )$ be defined by
$f_1\left(x\right)=|x|ifx<0=e^{x}ifx\ge 0f_2\left(x\right)=x^2{f}_3\left(x\right)=sinxifx<0=xifx\ge 0$
and $f_4\left(x\right)=f_2\left(f_1\right(x\left)\right),ifx<0f_2\left(f_1\right(x\left)\right)-1,ifx\ge 0$

$\begin{array}{cccc}& List-I& & List-II\\ P.& f_{2}is& 1.& \text{Onto but not one-one}\\ Q.& f_{3}is& 2.& \text{Neither continuous nor one-one}\\ R.& f_{4}is& 3.& \text{Differentiable but not one-one}\\ S.& f_{2}o{f}_{1}is& 4.& \text{Continuous and one-one}\end{array}$

Let $f:[2,3]\to B$ be a function defined by $f\left(x\right)=\left[{\log }_2\right[x^2+2x-1\left]\right]$, where $[.]$ represents the greatest integer function. If range of $f$ is $B$, then

Input: the in cot as he mum me

Which of the following will be the third step for this input?

If a, b, c are in A.P, then the equation $(a-b)X^2+(c-a)X+(b-c)=0$ has two roots which are

If the magnet is suspended at an angle 30^o to the magnetic meridian, the dip needle makes an angle 60^o with the horizontal. What is the true dip?

The letters of the word COCHIN are permuted and all the permutations are arranged in alphabetical order as in English dictionary. The number of words that appear before the word COCHIN is

Two systems of rectangular axes have the same origin. If a plane cuts the two sets of axes at distances a, b, c and a', b', c' from the origin, then:

Let f(x) be a function defined by f(x) = x - [x], 0 $\ne$ x $ϵ$ R where [x] is the greatest integer less than or equal to x. Then the number of solutions of $f\left(x\right)+f\left(\frac{1}{x}\right)=1$ are :

He was normally entirely ____________but in the embarrassing situation in which he found himself he felt compelled to ______________.

The equation of the common tangent to the curves $y^2=8x\text{and}xy=-1$ is

If $z$ is a complex number of unit modulus and argument $\theta$, then arg$\left(\frac{1+z}{1+\overline{z}}\right)$ is equal to