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A die is thrown 1000 times with the frequencies for the outcomes 1, 2, 3, 4, 5 and 6 as given in the following table:

$\begin{array}{cc}\text{Outcome}& \text{Frequency}\\ 1& 165\\ 2& 175\\ 3& 180\\ 4& 150\\ 5& 145\\ 6& 185\end{array}$

What is the probability of getting 2 or 4?

Question 33
Find the following products:
(i) $(\frac{x}{2}+2y)(\frac{x^2}{4}-xy+4y^2)$

(ii) $(x^2-1)(x^4+x^2+1)$

Simplify 8√35 + 4√5

If the sum of zeroes of quadratic polynomial is 4 and product of zeroes if 3. What is the quadratic polynomial?

If $a,b,c$ are in continued proportion then the value of $\frac{a^2+ab+b^2}{b^2+bc+c^2}$ is equal to __.

The mean $\overline{x}$ of the data is given by:

Question 5

In the given figure, A, B, C and D are four points on a circle. AC and BD intersect at a point E such that $\angle BEC={130}^{\circ }$ and $\angle ECD={20}^{\circ }$. Find $\angle BAC$.

In the parallelogram ABCD, AB = 6 cm and DC : CB = 2 : 1. Find the perimeter of the parallelogram ABCD.

The ratio between the radius of the base and the height of a cylindrical tank is 3 : 4. If its volume is $4851m^3,$ then the curved surface area of the cylinder is equal to

Find the symmetric difference between the set P and Q.
$P=\{2,3,5,7,11\}$ and $Q=\{1,3,5,11\}$

Question 46

Write down fifteen angles ( less than ${180}^{\circ }$ ) involved in the figure.

Jack has a toy in which half of the cylindrical shape is surmounted on a cuboid as shown in the figure below.



Total volume of the given solid is

If a circle passes through the point (a, b) and cuts the circle $x^2+y^2=4$ orthogonally, then the locus of its centre is

In the figure, given below, $\angle$AOC=${67}^{\circ }$, $\angle$BOC=${113}^{\circ }$ and $\angle$AOB=${123}^{\circ }$. Then which of the given options is correct?

Find the value of 'a' if (x-2) is factor of 2x³ − 6x² + 5x + a.

Solve for y if
$\frac{{\left(\frac{1}{9}\right)}^{2y-1}(.0081{)}^{\frac{1}{3}}}{\sqrt{243}}={\left(\frac{1}{3}\right)}^{2y-5}\sqrt[3]{3\frac{{27}^{y-1}}{10000}}$

1. 2

Einstein, Hemmingway, Van Gogh. These are some of the most gifted and talented minds ever to grace the earth. Were they normal? No, in fact they were far from it. Each had weaknesses of his own. Einstein was known to be a little crazy. Hemmingway enjoyed throwing one back every now and again. And Van Gogh was deeply depressed for years. So can these men still be geniuses despite their conditions? If so, then was the great John Nash brilliant as well or simply insane?

The probability of selecting a vowel from the word CHOCOLATE is .

Question 34

Factorise:

(i) $1+64x^3$



(ii) $a^3-2\sqrt{2}{b}^3$

If $A=\left[\begin{array}{cc}2& -3\\ -4& 1\end{array}\right],\text{then}adj(3A^2+12A)$ is equal to

If one angle of a parallelogram is ${24}^{\circ }$ less than twice the smallest angle then the largest angle of the parallelogram is

(a) ${68}^{\circ }$

(b) ${102}^{\circ }$

(c) ${112}^{\circ }$

(d) ${136}^{\circ }$

Find the cubes of:

(1) (1)³

(2) (−2)³

(3) (3)³

(4) (4)³

(5) (−5)³

(6) (2³)³

43 cubic metre = __litres.

$p\left(x\right)=x^3+8x^2-7x+12$ and $g\left(x\right)=x-1$. If $p\left(x\right)$ is divided by $g\left(x\right)$, it gives $q\left(x\right)$ and $r\left(x\right)$ as quotient and remainder respectively. If $a$ is the degree of $q\left(x\right)$ and $b$ is the degree of $r\left(x\right)$, then, $(a-b)=?$.

Prepare Income and Expenditure Account for the year ended 31st March, 2018,and Balance Sheet as on that date.

When the length of the shadow of a pole is equal to $\frac{1}{\sqrt{3}}$ times the height of the pole, then find the angle of elevation of source of light.

Students of a school staged a rally for cleanliness campaign in two groups. Group A walked through the lanes AB, BC and CA, while Group B walked through AC, CD and DA. They cleaned the area enclosed within their lanes. If $\text{AB = 9m, BC = 40m, CD = 15m, DA = 28m and}\angle \text{B = 90°}$, which group cleaned more area. Also, find the total area cleaned by the students?