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If the circumference of a circular sheet is $154$ m. Find its radius. Also find the area of the sheet.

Which of the following is the conjugate surd of $-3-\sqrt{8}$?

Explain the meaning of each of the following terms.
(i) Variate
(ii) Class interval
(iii) Class size
(iv) Class mark
(v) Class limint
(vi) True class limits
(vii) Frequency of a class
(viii) Cumulative frequency of a class

ABCD is a trapezium with AB $\parallel$ DC. A line parallel to AC intersects AB at X and BC at Y.
Prove that ar ($△$ADX) = ar ($△$ACY). [3 MARKS]

Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both two-wheeler and credit card, 30 had both credit card and mobile phone and 60 had both two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?

The perimeter of a square is 4x + 20 cm. Then find the length of diagonal

If (x+1) and (x-1) are factors of mx³ +x² - 2x +n find the value of m and n

The time taken by the earth to complete one revolution is –

If $(x^{\frac{1}{3}}+y^{\frac{1}{3}}+z^{\frac{1}{3}}=0)$, then

If $z=5x+2y$ subject to the following constraints : $x-2y\le 2,3x+2y\le 12,-3x+2y\le 3,x\ge 0,y\ge 0,$ then which of the following is/are true?

A die is thrown 300 times and the outcomes are noted as given below:

$\begin{array}{ccccccc}\text{Outcome}& 1& 2& 3& 4& 5& 6\\ \text{Frequency}& 60& 72& 54& 42& 39& 33\end{array}$

When a die is thrown at random, what is the probability of getting a

(i) 3?

(ii) 6?

(iii) 5?

(iv) 1?

To construct a parallelogram given its length of diagonals, which of the following additional information is required?

(ii) $-6x^2$

In the adjoining figure, $OD$ is perpendicular to the chord $AB$ of a circle with centre $O$. If $BC$ is a diameter, show that $AC||DO$ and $AC=2\times OD$.

What is the name of the geometric instrument used to draw arcs?

In quadrilateral ABCD, the bisectors of angle A and angle B meet in a point P. If $\angle C={105}^{\circ }$ and $\angle D={55}^{\circ }$, find the measure of angle APB.

If y = 2x+3 and y = 5, what does x equal to?

A sum of money invested at compound interest amounts to ₹16500 in 1 year and to ₹19965 in 3 years. Find the rate per cent and the original sum of money invested

If ABCD is a parallelogram with AC = 20x ,then AE equals

In the figure, EF $\parallel$ AB and E is the mid-point of FG. Find the ratio of area (ABCDO) to the sum of area (BAFGO) and area (AEB).

If x = $\sqrt{a}tan\alpha$ and y = $\sqrt{a}sec\alpha$. Find the value of $y^2$ – $x^2$ .

In the figure, the bisector of B and C meet at O. Then $\angle$ BOC is:

How many m³ of soil has to be excavated from a rectangular well 28 m deep and whose base dimensions are 10 m and 8 m. Also find the cost of plastering its vertical walls at the rate of Rs 15/m².

Draw a triangle ABC where vertices A, B and C are (0, 2), (2, -2), and (-2, 2) respectively.

How many rational numbers exist between 1 and 2?

Which of following points lies on the line, $2x+3y=11?$