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Solve for $x$ : $-3x+5<101$

If a and b are the position vectors of two points A and B and C is a point on AB produced such that AC = 3AB, then position vector of C will be

A straight line $L_1:\frac{x}{a}+\frac{y}{b}=1$ intersects the $x$-axis and $y$-axis at $P$ and $Q$ respectively and a straight line $L_2$ perpendicular to $L_1$ cuts the $x$-axis and $y$-axis at $R$ and $S$ respectively. The locus of the point of intersection of the lines $PS$ and $QR$ is

Find the following integrals.
$\int (2x-3cosx+e^x)dx.$

If $\int \frac{1+\cos x}{\cos x-{\cos }^{2}x}dx=\log |\sec x+\tan x|-2f^{\prime }\left(x\right)+C$, then the function $f\left(x\right)$ is

A divisor of N= 2⁵3⁴5³ is selected at random. The probability that the selected number is divisible by 200 if it is known that it is divisible by 100 is

A) 3/4 B) 1/2 C) 1/4 D) 4/5

Each student in a class of $40$, studies at least one of the subjects English, Mathematics and Physics. $16$ study English, $22$ study Physics and $26$ study Mathematics, $5$ study English and Physics, $14$ Mathematics and Physics and $2$ study all the three subjects. The number of students who study English and Mathematics but not Physics is

Each coefficient in the equation $a{x}^2+bx+c=0$ is determined by throwing an ordinary die. Find the probability that the equation will have equal roots.

Integrate the following functions.
$\int \frac{5x-2}{1+2x+3x^2}dx.$

It is known that 10% of certain articles manufactured are defective, what is the probability that in a random sample of 12 such articles, 9 are defective?

$a+ar+a{r}^2+\cdots +a{r}^{n-1}=\frac{a(r^n-1)}{r-1}$

The range of $k$ for which $|x^2-1|=k$ has exactly two solutions is

If $6^n-5n,n\in N$ is divided by $25$, then the remainder is

In a class of $42$ students, $23$ are studying Mathematics, $24$ are studying Physics, $19$ are studying Chemistry. If $12$ are studying both Mathematics and Physics, $9$ are studying both Mathematics and Chemistry, $7$ are studying both Physics and Chemistry and $4$ are studying all the three subjects, then the number of students studying exactly one subject, is

In a class with $\frac{3}{5}$ women and $\frac{2}{5}$ men, $25\%$ of the women are business majors. Find the probability that a student chosen from the class at random is a female business major.

${lim}_{x\to 0}\frac{sinax+bx}{ax+sinbx}$

If $x^2$+px + q = 0 is the quadratic equation whose roots are a – 2 and b – 2 where a and b are the roots of $x^2$ - 3x + 1 =0, then

The two adjacent sides of a parallelogram are $2\hat{i}-4\hat{j}+5\hat{k}$ and $\hat{i}-2\hat{j}-3\hat{k}$. Find the unit vector parallel to its diagonal. Also, find its area.

A box contains 25 tickets numbered 1, 2, ....... 25. If two tickets are drawn at

random then the probability that the product of their numbers is even, is

From a well shuffled deck of 52 cards, 4 cards are drawn at random. What

is the probability that all the drawn cards are of the same colour.

A particle $P$ starts from the point $z_0=1+2i$ , where $i=\sqrt{-1}$ It moves first horizontally away from origin by $5$ units and then vertically away from origin by $3$ units to reach a point $z_1$. From $z_1$ the particle moves $\sqrt{2}$ units away from origin in the direction of $x=y$ and then it moves through an angle $\pi /2$ in anticlockwise direction on a circle with centre at origin to reach a point $z_2$. Then point $z_2$ is given by

(a) A factory manufactures two types of screws, A and B. Each type of screw requires the use of two machines, an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacturer a package of screw A, while it takes 6 minutes on automatic and 3 minutes on the hand operatedmachines to manufacture a package of screw B. Each machine is available for at the most 4 hours (240minutes) on any day. The manufacturer can sell a package of screws A at a profit of Rs 7 and screws B at a profit of Rs.10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit? Determine the maximum profit.

$\left(b\right)Provethat\left|\begin{array}{ccc}1+a& 1& 1\\ 1& 1+b& 1\\ 1& 1& 1+c\end{array}\right|=abc(1+\frac{1}{a}+\frac{1}{b}+\frac{1}{c})=abc+bc+ca+ab$

The domain of the function $f\left(x\right)=\frac{1}{1-\left\{x\right\}}$ is
(where $\{.\}$ denotes the fractional part of $x$)

The first term of an A.P. is 2 and the last term is 50. The sum of all these terms is 442. Find the common difference.

The value of ${\int }_{-1}^2\frac{|x|}{x}$ dx is

$\frac{4x+3}{2x-3}<6$

If $x=ta{n}^{-1}\frac{1}{7}$ and $y=ta{n}^{-1}\frac{1}{3}$, then

If A lies in second quadrant and 3 and A=4=0, then the value of 2 cot A -5 cos A =sin A is equal to

Plane $ax+by+cz=1$ intersects axes in $A,B,C$ respectively. If $G(\frac{1}{6},-\frac{1}{3},1)$ is a centroid of $\Delta ABC$, then $a+b+3c=$_____

If L || M and M || N, then what can be said about L and N?

If the distance between the points $(5,-2)$ and $(1,a)$ is $5$ units, then the sum of all possible values(s) of $a$ is

The maximum slope of the curve $y=\frac{1}{2}{x}^4-5x^3+18x^2-19x$ occurs at the point :

Let $A\left(\theta \right)$ and $B\left(\varphi \right)$ are the parametric ends of a chord of the hyperbola $\frac{x^2}{144}-\frac{y^2}{25}=1$. If the equation of $AB$ is $2x+3y=1$, then

The complete solution set of $\sin x-\sqrt{3}\cos x=0$ is

If $\frac{{\log }_{10}a}{12}=\frac{{\log }_{10}b}{21}=\frac{{\log }_{10}c}{15},$ then $bc$ is equal to

A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.

Prove that $\frac{9\pi }{8}-\frac{9}{4}si{n}^{-1}\left(\frac{1}{3}\right)=\frac{9}{4}si{n}^{-1}\left(\frac{2\sqrt{2}}{3}\right)$

For the question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

$y=e^x+1$ and y''-y'=0.

If $\alpha +\beta -\gamma =\pi$ then $si{n}^2\alpha +si{n}^2\beta -si{n}^2\gamma$ is equal to

The equation of the circle concentric with $x^2-3x+4y-c=0$ and passing through (-1, -2) is

Prove that
$\left|\begin{array}{ccc}1& 1& 1\\ a& b& c\\ a^3& b^3& c^3\end{array}\right|=(a-b)(b-c)(c-a)(a+b+c)$

The first and last term of an AP are 1 and 11 if the sum of its terms is 36 then a = ______,d=_____,n=_____&a₅=_________