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Solve:-

b/a*x + a/b*y = a² + b^{2 ;}

^{x + y = 2ab}

If three parallel lines cut a line 8.5 cm in the ratio 1:2:3 then they will cut a line measuring 10 cm in the ratio_____

Consider the following functions:
1. Issue of bank notes of all denominations.
2. Lender of the last resort
3. Underwrite the loans of state and central governments.
4. Periodic inspection of commercial banks
Which of the above are functions of the Reserve Bank of India?

Area of a trapezium is 160 sq cm and the height is 10 cm . Find the sum of its two parallel sides.

The area of a circle whose circumference is equal to the difference of the circumference of the two circles of diameters $36\text{cm}$ and $22\text{cm}$ is

The coordinates of some pairs of points are given below. Without drawing the axes of coordinates, mark these points with the left-right, up-down positions correct. Draw rectangle with these as opposite vertices. Find the coordinates of the other two vertices and the lengths of the sides of these rectangles:

(i) (3, 5), (7, 8)

(ii) (−3, 5), (−7, 1)

(iii) (6, 2), (5, 4)

(iv) (−1, −2), (−5, −4)

A coin is tossed three times. Find the probability that heads and tails will appear alternatively. Give the answer up to 2 decimal places

__

A container in the shape of a frustum of a cone having diameters of its two circular faces as 35 cm and 30 cm and vertical height 14 cm, is completely filled with oil. If each $c{m}^3$ of oil has mass 1.2 g then find the cost of oil in the container if it costs Rs 40 per kg.

Question 55

The common factor method of factorisation for a polynomial is based on ___ property.

The mean proportional of the line segment of lengths 4 cm and 2 cm is _____.

p = $2^2$.$3^2$.$q^2$ (where q is a prime $<$ 7) is the prime factorisation representation of ‘p’. What is the value of p?

The figure given below have been constructed by following the steps given below.

I: Draw line segment AB of length 16.9 cm and draw a ray AX making an acute angle with line segment AB.

II: Mark points Alf A₂, A₃, A₄........A₁₃, on AX such that AA₁ = A₁A₂ = A₂A₃ and

so on.

III: Join BA₁₃. Through the point A₅, draw a line parallel to BA₁₃ intersecting AB at point C.

Find two consecutive positive even integers whose product is 288.

Question 4 (i)

Which of the following pairs of linear equations are consistent/ inconsistent? If consistent, obtain the solution graphically:

x + y = 5, 2x + 2y = 10

Rangaji deposited Rs. 6050 in his saving account. His amount increases by $\frac{1}{5}$ times of itself after two years. What is the maturity amount (in Rs.)after two years?

Find out the wrong number in the series given below :

$4,5,9,18,34,59,93$

The prodcut of Shikha's age five years ago and her age 8 years later is 30, her age at both times being given in years. Find her present age.

In the given figure, AB = CF, EF = BD, and $\angle$AFE = $\angle$DBC.

Is $△AFE\cong △CBD$? If yes, then by which criterion?

If $\alpha$ and $\beta$ are roots of quadratic equation $x^2-1=0$, then find the equation whose roots are $\frac{2\alpha }{\beta }$ and $\frac{2\beta }{\alpha }$

Given below is a cumulative frequency distribution showing the marks secured by 50 students of a class
$\begin{array}{cccccc}Marks& Below20& Below40& Below60& Below80& Below100\\ Numberofstudents& 17& 22& 29& 37& 50\end{array}$
Form the frequency distribution table for the data.

Figure shows a sector of a circle of radius r cm containing an angle $\theta {}^{\circ }$. The area of the sector is A $c{m}^2$ and perimeter of the sector is 50 cm. Prove that

(i) $\theta =\frac{360}{\pi }(\frac{25}{r}-1)$

(ii) $A=25r-r^2$

What will be the cost of the product in rupees after adding 10% sales tax on Rs 400?

The construction of triangle ΔA'C'B similar to triangle ΔACB is shown in the figure below. Then

A merchant has 120 litres of oil of one kind, 180 litres of another kind and 240 litres of the third kind. He wants to sell the oil by filling the three kinds of oil in tins of equal capacity. What should be the greatest capacity of such a tin? [4 MARKS]