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The number of ways of arranging 6 different rings to 5fingers in a hand

A normal to $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ meets the axes in L and M. The perpendiculars to the axes through L and M intersect at P. Then the equation to the locus of P is

Which of the following is/are singleton sets?

Evaluate $\underset{x\to 2}{lim}\left(\frac{e^{3x}-1}{x}\right)$

The value of $\int \frac{\cos x}{\sin (x-\frac{\pi }{6})\sin (x+\frac{\pi }{6})}dx$ is equal to

$(C$ is a constant of integration$)$

Find the area enclosed between the curve $y=5x-x^{2}andy=x$ .

The function $f\left(x\right)=x^3+a{x}^2+bx+c,a^2\le 3b$ has

If $lo{g}_a\left(ab\right)=x$, then $lo{g}_b\left(ab\right)$ is equal to

Two sets: $X,Y$ such that $X=\{x:x\in N;x^2-5x+6=0\}\&$

$B=\{1,2,5,3\},$ then $A\cap B=$

Prove the there is no term containing $x^{10}$ in the expansion of ${(x^2-\frac{2}{x})}^{18}$

If $f\left(x\right)=\int \sqrt{4x-x^2}dx;x\in [0,\frac{\pi }{2}]$ such that $f\left(0\right)=0,$ then the value of $f\left(1\right)$ is

Solution set of $(x+1)(x-1{)}^2(x-2)\ge 0$ is

A positive number is 5 times another number if 21 is added to both the numbers then one of the new numbers becomes twice the other new number what are the numbers

The minimum value of $2^{\sin x}+2^{\cos x}$ is

There are five students $S_1,S_2,S_3,S_4$ and $S_5$ in a music class and for them there are five seats $R_1,R_2,R_3,R_4$ and $R_5$ arranged in a row, where initially the seat $R_i$ is allotted to the student $S_i,i=1,2,3,4,5$. But, on the examination day, the five students are randomly allotted the five seats.



For $i=1,2,3,4,$ let $T_i$ denote the event that the students $S_i$ and $S_{i+1}$ do $NOT$ sit adjacent to each other on the day of the examination. Then, the probability of the event $T_1\cap T_2\cap T_3\cap T_4$ is

If the range of $2{\sin }^{-1}x+{\cos }^{-1}x$ is $[\alpha ,\beta ]$, then

In a multiple choice question there are four alternative answer, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answer. The candidate decides to tick answer at random, if he is allowed upto three chances the probability that he will get marks for the question, is

If $A$ is a square matrix, then $(adjA{)}^{-1}=adj(A^{-1})=$

Consider the matrix $A=\left[\begin{array}{ccc}2& 6& 8\\ 4& 5& 1\\ 3& 7& 9\end{array}\right].$ The cofactor of element $5$ in matrix $A$ is



[1 mark]

If two normals to a parabola $y^2=4ax$ intersect at right angles, then the chord joining their feet passes through a fixed point whose coordinates are

Question 18

Bulbs are packed in cartons each containing 40 bulbs. Seven hundred cartons were examined for defective bulbs and the results are given in the following table.





$\begin{array}{ccccccccc}\text{Number of}& 0& 1& 2& 3& 4& 5& 6& \text{More}\\ \text{defective}& & & & & & & & \text{than 6}\\ \text{bulbs}& & & & & & & & \\ \text{Frequency}& 400& 180& 48& 41& 18& 8& 3& 2\end{array}$



One carton was selected at random. What is the probability that it has

(i) No defective bulb?



(ii) Defective bulbs from 2 - 6?



(iii) Defective bulbs less than 4?

Let two lines be intersecting at $(4,3)$ and angle between them is ${45}^{\circ }.$ If the slope of one line is $2,$ then the equation of the other line can be

The approximate change in the volume of a cube of side x metre caused by increasing the side by 3% is;

(a) $0.06x^3{m}^3$ (b) $0.6x^3{m}^3$
(c) $0.09x^3{m}^3$ (d) $0.9x^3{m}^3$

The value of $\underset{2}{\overset{4}{\int }}\frac{e^x}{\ln x}(1-\frac{1}{x\ln x})dx$ is

Equation of the ellipse with focus $(3,-2)$,
eccentricity $\frac{3}{4}$ and directrix $2x-y+3=0$ is