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A trader buys an unfinished article for Rs 1800 and spends Rs 600 on its finishing, packing, transportation, etc. He marks the article at such a price that will give him 20% profit. How much will a customer pay for the article including 12% sales tax.

If the sides of a parallelogram touch a circle (refer figure of Q. 7), prove that the parallelogram is a rhombus.

Question 11
How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

The string of a kite is 100m long and it makes an angle of ${60}^{\circ }$ with the horizontal. Find the height of the kite from the ground, assuming that there is no slack in the string.

Find a quadratic polynomial,the sum and product of whose zeros are $-3$ &$2$

Choose the correct choice in the following and justify:
(ii) ${11}^{th}termoftheA.P-3,\frac{-1}{2},2is$

A) 28
B) 22
C) -38
D) 44

Question 2 (ii)
Write whether the given statement is true or false. Justify your answer.
Every quadratic equation has at least one real roots.

A shopkeeper earns a profit of $12\%$ on selling a book at $10\%$ discount on the marked price. The ratio of the cost price and the marked price of the book is

The figure shows nine 1cm $\times$ 1 cm squares and a circe. The circle passes through the centres of the squares in the four corners.

What is the area (in sq. cm) of the shaded region?

Prove the identity: $\sqrt{se{c}^2\theta +cose{c}^2\theta }=sec\theta cosec\theta$ [4 MARKS]

In the figure, O is the center of the circle, PQ is tangent to the circle at A. If $\angle PAB={58}^{\circ }$, find $\angle ABQ$ and $\angle AQB$. [2 MARKS]

Question 92 (xxiv)

Factorise the following using the identity $a^2-b^2=(a+b)(a-b).$

$y^4-81$

In Fig. 7.255, DE || BC, AD = 1 cm, BD = 2 cm. What is the ratio of the area (ΔABC) to the areas (ΔADE)?

Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds, they meet in 5 hours. If they travel towards each other, they meet in 1 hour.What are the speeds of two cars?

Question 4 (xiii)

Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.

(xiii) $\sqrt{3},\sqrt{6},\sqrt{9},\sqrt{12},\dots$

Describe the locus for questions 1 to 13 given below:

The locus of a point P, so that:

$A{B}^2=A{P}^2+B{P}^2$

where A and B are two fixed points.

Let $a_n,n\ge 1,$ be an arithmetic progression with first term $2$ and common difference $4.$ Let $M_n$ be the average of the first $n$ terms. Then the sum $\sum _{n=1}^{10}{M}_n$ is

Look at the following table below.

$$\begin{array}{cc}Classinterval& Classmark\\ 0-5& A\\ 5-10& B\\ 10-15& 12.5\\ 15-20& 17.5\end{array}$$

The value of A & B respectively are:

Find the value of 'k' if (1,3k) lies on kx + 4y = 26.

In the given figure, a circle is circumscribing $\Delta ABC$ where $\angle A={125}^{\circ }$ and side BC=8cm. The diameter of the circumcircle is equal to

$[sin{55}^{\circ }=0.82]$

A cone of base radius 24 cm is cut by a plane parallel to its base exactly in the middle of its vertical height. If the vertical height of the cone is 14 cm, then volume of frustum is equal to

The surface area of a solid metallic sphere is 616 cm². It is melted and recast into smaller spheres of diameter 3.5cm. How many such spheres can be obtained?

Jaya, Seema, Nikhil and Neelesh put in altogether $360000$ rupees to form a partnership, with their investments being in the proportion $3:4:7:6$. What was Jaya’s actual share in the capital ? They made a profit of $12\%$. How much profit did Nikhil make ?

What will be the unit digit of the squares of the following number:

52698

Assertion: Area of the triangle whose

vertices are $A(\frac{-3}{2},3),B(6,-2)$ and $C(-3,4)$ is 0

Reason : The points A, B and C are collinear