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Question 1 (ii)

Without actually performing the long division, state whether $\frac{17}{8}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

A car's number plate was to be painted equally in blue and red as shown in the figure. What will be the total cost of painting the car's number plate if red paint costs Rs. 2 per $c{m}^2$ and blue paint costs Rs. 1 per $c{m}^2$?

If $\left[\overrightarrow{a}\overrightarrow{b}\overrightarrow{c}\right]=-4,$ then the Volume (in cubic units) of the parallelopiped with coterminous edges $\overrightarrow{a}+2\overrightarrow{b},2\overrightarrow{b}+\overrightarrow{c},3\overrightarrow{c}+\overrightarrow{a}$ is

In the figure, DE || BC, name the quadrilateral BCED.

The slant height and base diameter of a conical tomb are $25m$ and $14m$ respectively. Find the cost of white-washing its curved surface at the rate of $Rs.210$ per $100m^2$.

A part of monthly hostel charges is fixed and the remaining depends on the number of days one has taken food in the mess. When a student A took food for 27 days she had to pay Rs 1210 as hostel charges whereas a student B, who took food for 15 days, paid Rs 850 as hostel charges. Find the fixed charges and the cost of food per day. [4 MARKS]

The pairs of linear equations which have the unique solution $x=2,y=–3$ are,

In the following question out of the four options only one is correct, write the correct answer.

If $\frac{-4}{3}y=-\frac{3}{4},$ then y is equal to:

(a) ${\left(\frac{-3}{4}\right)}^2$

(b) ${\left(\frac{-4}{3}\right)}^2$

(c) ${\left(\frac{3}{4}\right)}^2$

(d) ${\left(\frac{4}{3}\right)}^2$

The following histogram shows the monthly profits (in rupees) of 100 shops. How many shops have profit more than Rs. 200?

The equation of a straight line parallel to x-axis and passing through (0, 5) is

If $x-\frac{1}{x}=5$, find the value of $x^3-\frac{1}{x^3}$.

Find the total surface area of a hemisphere of radius $10cm$.

Question 6 (ii)

Given the linear equation 2x + 3y - 8 = 0, write another linear equation in two variables such that the geometrical representation of the pair so formed is:

(ii) Parallel lines

Use the following information to answer the next question.

The given figure shows two triangles.

Which of the following statements is correct?

Factorise:
$8a{b}^2-18a^3$

Question 6: Consider the following figure of line $\overleftrightarrow{MN}$. Say whether following statement is true or false in the context of the given figure



(a) M is point on ray $\overrightarrow{OP}$.

For positive integer n, ${10}^{n-2}$ > 81n, if

The angle of elevation of the top of a tower from a point A due south of the tower is $\alpha$ and from B due east of th tower is $\beta$. If AB = d, show that the height of the tower is $\frac{d}{\sqrt{co{t}^2\alpha +co{t}^2\beta }}$ [3 MARKS]

Let $F_1$ be the set of all parallelograms, $F_2$ the set of rectangles, $F_3$ the set of rhombuses, $F_4$ the set of squares and $F_5$ the set of trapeziums in a plane, then $F_1$ is equal to

Question 5 (iii)

Rationalize the denominators of the following:

$\frac{1}{(\sqrt{5}+\sqrt{2})}$

Find the smaller of the fraction $\frac{3}{5}$ and $\frac{8}{13}$

Pick a rational number greater than $\frac{6}{7}$.

Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reasons for your answer.

ABC and BDE are two equilateral triangles such that D is the mid point of BC. AE intersects BC in F. Then ar (BDE) is equal to

Raghu had to make a cylindrical tube with an aluminium cover. What is the area of the aluminium sheet he needs to cover the tube if the tube has a length of 1 m and base radius 3.5 cm?
(Take π=22/7)

A weather station recorded the temperatures of a place over a period of 7 days as follows:

In Fig. two circles with centres A and B touch each other at the point C. If AC = 8 cm and AB = 3 cm, find the area of the shaded region.

The equation 2x + 5y = 7 has a unique solution, if x and y are

(a) natural numbers

(b) rational numbers

(c) positive real numbers

(d) real numbers

Identify polynomials in the following :

(i) f(x) = $4x^3-x^2$ - 3x + 7

(ii) g(x) = $2x^3-3x^2+\sqrt{x}-1$

(iii) p(x) = $\frac{2}{7}{x}^2-\frac{7}{4}x+9$

(iv) q(x) = $2x^2-3x+\frac{4}{x}+2$

(v) h(x) = $x^4-x^{\frac{3}{2}}+x-1$

(vi) f(x) = 2 +$\frac{3}{x}+4x$

Universal set $\text{U}=\{x:x\text{is an even natural number and}$$x<15\}$

If $\text{A}=\{x:x=4n,x\le 12\text{and}n\in \text{N}\}$, then ${\text{A}}^{\prime }$ is:

Construct a frequency table for the following ages (in years) of 30 students using equal class intervals, one of them being 9-12, where 12 is not included.
18, 12, 7, 6, 11, 15, 21, 9, 8, 13, 15, 17, 22, 19, 14, 21, 23, 8, 12, 17,15, 6, 18, 23, 22, 16, 9, 21, 11, 16.