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A computer producing factory has only two plants $T_1$ and $T_2$. Plant $T_1$ produces $20\%$ and plant $T_2$ produces $80\%$ of the total computers produced. $7\%$ of computers produced in the factory turn out to be defective. It is known that $P$(computer turns out to be defective given that it is produced in plant $T_1$)=$10P$(computer turns out to be defective given that it is produced in plant $T_2$).
Where $P\left(E\right)$ denotes the probability of an event $E$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_2$ is

If $5^{th}$ term of a H.P. is $\frac{1}{45}$ and ${11}^{th}$ term is $\frac{1}{69}$, then its ${16}^{th}$ term will be

The graph of the quadratic polynomial $y=a{x}^2+bx+c$ has its vertex at $(4,-5)$ and two $x$ intercepts, one positive and one negative. Which of the following hold(s) good?

10 bulbs out of a sample of 100 bulbs manufactured by a company are defective. The probability that 3 out of 4 bulbs, bought by a customer will not be defective, is

x and y are the sides of two squares such that $y=x-x^2$. The rate of change of area of the second square with respect to that of the first square is

A box contains 15 transistors, 5 of which are defective. An inspector takes out one transistor at random, examines it for defects, and replaces it. After it has been replaced another inspector does the same things, and then so does a third inspector. The probability that atleast one of the inspectors finds a defective transistor, is equal to

The degree of the differential equation is

[Pb. CET 2004]

The equation of the plane which is parallel to 2x – 3y + 5z + 7 = 0 and passing through the point (3, 4, -1) is

${\sum }_{r=1}^{n}si{n}^{-1}\left(\frac{\sqrt{r}-\sqrt{r-1}}{\sqrt{r(r+1)}}\right)$ is equal to

The $n^{th}$ term of a sequence is given by $a_n=2n+7$. Show that it is an A.P. Also, find its $7^{th}$ term.

If a>0 and the equation $a{x}^2+bx+c=0$ has two real roots $\alpha$ and $\beta$ such that $\left|\alpha \right|\le 1,\left|\beta \right|\le 1,$ then

In throwing a fair die find the probability of the event 'a number less than or equal to 4 turns up'

Write the number of ways in which 7 men and 7 women can sit on a round table such that no two women sit together.

The value of E = sin${}^2$ 60${}^0$ cos${}^2$ 45${}^0$ + 8 tan${}^2$ 60${}^0$ + $\frac{1}{4}$cot${}^2$ 60${}^0$ is

Calculate the mean deviation from the mean for the following data :

(i) 4, 7, 8, 9, 10, 12, 13, 17

(ii) 13,17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

(v) 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

PQR is a right angle. What is the size of the larger of the two angles?

If a chord joining $P(aSec\theta ,atan\theta ),Q(aSec\alpha ,atan\alpha )$ on the hyperbola $x^2-y^2=a^2$ is the normal at P,then $Tan\alpha$

If $k>0,|z|=k$ and $w=\frac{z-k}{z+k}$, then $Re\left(w\right)$ equals

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are $A\times B,$ write A and B.

If P(5,r) = P (6,r-1), find r.

The equation of a plane passing through $\overline{r}.(\hat{i}+\hat{j}+\hat{k})=1$ and $\overline{r}.(2\hat{i}+\hat{k})=2$ can be given by

For every positive integer n, $2^n<n!$ when

A circle of radius 2 has centre at (2, 0) another circle of radius 1 has centre at (5, 0). A line is tangent to the two circles at points in the quadrant. which of the following is the y-intercept of the line?

If A1, B1, C1 … are the cofactors of the elements a1, b1, c1... of the matrix

$\left[\begin{array}{ccc}a1& b1& c1\\ a2& b2& c2\\ a3& b3& c3\end{array}\right]$ then $\left|\begin{array}{cc}B2& C2\\ B3& C3\end{array}\right|=$

Find the area bounded by y=x|sinx| and the x-axis between x=0, x=2$\pi$

${lim}_{x\to 0}\frac{ax+xcosx}{bsinx}$

$\mathrm{If}A=\left(\begin{array}{cc}1& 0\\ 1& 1\end{array}\right]\mathrm{and}I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right],\mathrm{then}\mathrm{which}\mathrm{of}\mathrm{the}\mathrm{following}\mathrm{holds}\mathrm{for}\mathrm{all}n\in N?$

The value of $tan[co{s}^{-1}\left(\frac{-2}{7}\right)-\frac{\pi }{2}]$ is

If tan (A + B) = p, tan (A - B) = q, then the value of tan 2A in terms of p and q is

The remainder when $1+2^1+2^2+2^3...........{.2}^{1999}$ is divided by 5 is:

If x = a cos t, y = a sin t, then $\frac{d^{2}y}{d{x}^2}$at t = $\frac{\pi }{4}$ is

If the real valued function $f\left(x\right)=\frac{a^x-1}{x^n(a^x+1)}$ is even, then $n$ is equal to

If odds against solving a question by three students are 2 : 1, respectively, then probability that the question is solved only by one student is [RPET 1999]

If ${\log }_{0.5}\left(\frac{3-x}{x+2}\right)<0$, then $x$ can be

The differential equation of the family of curves $v=\frac{A}{r}+B$ where A and B are arbitrary constants, is

The value of the definite integral ${\int }_0^1\frac{xdx}{x^3+16}$ lies in the interval [a, b]. The smallest such interval is.

If $z$ and $\omega$ be two non-zero compex numbers such that $|z|=|\omega |$ and $arg\left(z\right)+arg\left(\omega \right)=\pi$, then $z$ equals

Write the area of the figure formed by the lines $a|x|+b|y|+c=0$.

The equation $\frac{x^2}{2-r}+\frac{y^2}{r-5}+1=0$ represent an ellipse if

A compound $M{X}_2$ has observed and normal molar masses of 65.6 and 164 respectively. Calculate the apparent degree of dissociation.

If $y=c{e}^{si{n}^{-1}x},$ then corresponding to this the differential equation is

If the sides of a triangle are in G.P., and its larger angle is twice the smallest, then the common ratio r stisfies the inequality

From the prices of shares X and Y given below : find out which is more stable in value :

$\begin{array}{ccccccccccc}X:& 35& 54& 52& 53& 56& 58& 52& 50& 51& 49\\ Y:& 108& 107& 105& 105& 106& 107& 104& 103& 104& 101\end{array}$