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3 chairs and 2 tables cost 700 and 5 chairs and 3 tables cost 1100 find the cost of 2 chair and 2 table

The points P (4, 1) and Q (-2, 4) are reflected in line y = 3. Find the co-ordinates of P', the imae of P and Q', the image of Q.

A certain number of metallic cones, each of radius 2 cm and height 3 cm, are melted and recast into a solid sphere of radius 6 cm. Find the number of cones used.

A factory manufactures 120000 pencils daily. The pencils are cylindrical in shape each of length 25 cm and circumference of base as 1.5 cm. Determine the cost of colouring the curved surfaces of the pencils manufactured in one day at $Rs0.05perd{m}^2$.

Question 1 (i)

Find the roots of the quadratic equations by using the quadratic formula in the following question$2x^2-3x-5=0$.

Question 4 (iii)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(iii) -1.2, -3.2, -5.2, -7.2 …

'Global Foods' supplies groceries. On some grocery items the rate of GST is $18\%$, then what is the rate of CGST and SGST?

A rectangular paper is folded into a cylinder. The length and breadth of the paper are L and B respectively. What is the outer surface area of the cylinder?

For the AP: $x-7,x-2,x+3,....$ the ${15}^{th}$ term is ____.

The remainder when we divide $x^2+x+7$ by x - 7 is

In an equilateral triangle, a perpendicular drawn from one of the vertices to the opposite side as shown.The value of $Sin\theta$ is equal to

Question 11
If x = a and y = b is the solution of the equations x – y = 2 and x + y = 4, then the values of a and b are respectively:
(A) 3 and 5
(B) 5 and 3
(C) 3 and 1
(D) –1 and –3

If AB is the tangent to the circle with center O what is $\angle OCP$? Given that OP= PC

In the figure, the pair of tangents AP and AQ drawn form an external point A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm. Then the radius of the circle is:

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions $6cm\times 42cm\times 21cm$.

Show that the mid-point of the line segment joining the points (5, 7) and (3, 9) is also the mid-point of the line segment joining the points (8, 6) and (0, 10).

Find $a_{30}-a_{20}$ for the A.P.
(i) -9,-14,-19,-24,... (ii)a,a+d,a+2d,a+3d,...

The sum of two numbers is 137 and their difference is 43.Find the numbers.

AB is a line segment which is inclined to line XY, such that they intersect at point O. A line PQ is drawn which intersects line XY at point P at the same angle of inclination as AB. Line PQ is __ to line segment AB.

In the given figure, O is the centre of a circle; PQL adn PRM are the tangents at the points Q and R respectively and S is a point on the circle such that $\angle$ SQL = ${50}^o$ and $\angle$ SRM = ${60}^o$ Then, $\angle$ QSR = ?

(a) ${40}^o$ (b) ${50}^o$ (c) ${60}^o$ (d) ${70}^o$

PQRS is a cyclic quadrilateral whose diagonals intersect at A. If $\angle SQR={80}^{\circ }$ and $\angle QPR={30}^{\circ },$ then find $\angle SRQ.$

The areas of two similar triangles are $100c{m}^2$ and $49c{m}^2$ respectively. if the altitude of the ingle is 5cm, find the corresponding altitude of the other.

The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.

In a $△ABC,\angle A={60}^{\circ },\angle B={30}^{\circ }and\angle C={90}^{\circ }.$
Then the ratio of the sides AC: BC: AB = _____

If $\Delta \text{XYZ}$ and $\Delta \text{ABC}$ are congruent, then which of the following is true?

In triangle $ABC,\angle A={60}^{\circ },\angle B={45}^{\circ }$ and AB=20cm. Then the area of the triangle is equal to

If two events A and B are such that P(A) > 0 and $P\left(B\right)\ne 1$, then $P\left(\frac{\overline{A}}{\overline{B}}\right)$ is equal to

$(cosec\theta -cot\theta {)}^2$ = ?

(a) $\frac{1+cos\theta }{1-cos\theta }$ (b) $\frac{1-cos\theta }{1+cos\theta }$ (c) $\frac{1+sin\theta }{1-sin\theta }$ (d) none of these

cos $1^o$ cos $2^o$ cos $3^o$ ..... cos ${180}^o$ = ?

(a) -1 (b) 1 (c) 0 (d) $\frac{1}{2}$

If $\alpha ,\beta$ are the zeros of the polynomial $x^2$ - px + 36 and ${\alpha }^2$+${\beta }^2$ = 9, then what is the value of p?

In $\Delta ABC$, P divides the side AB such that AP : PB =1 : 2. Q is a point in AC sucht that PQ||BC. Find the ratio of the areas of $\Delta APQ$ and trapezium BPQC.

In the given diagram , $△$ PQO is congruent to which triangle ?

Find the factors of $x^2+8x+15$ by splitting the middle term.

As observed from the top of a 150 m high lighthouse from the sea-level, the angles of depression of two ships are ${30}^{\circ }$ and ${45}^{\circ }$. If one ship is exactly behind the other on the same side of the lighthouse, find the distance between the two ships.

Subba Rao started work in 1995 at an annual salary of Rs 5000 and received an increment of Rs 200 each year. After how many years did his income reach Rs 7000?

In $△$ABC, if $\angle B={90}^{\circ },tanA=\frac{1}{\sqrt{3}}$, then $sinAcosC+cosAsinC$=

If $7si{n}^2\theta +3co{s}^2\theta =4$, then $sec\theta +cosec\theta$ is equal to

In $\Delta ABC$ what is the relationship between the sides, if AC is the largest side?

In the formula for finding mode of a grouped data,

Mode = $X+\left(\frac{A-B}{2A-B-C}\right)\times h$

$$\begin{array}{cc}i)X& a)frequencyoftheclassprecedingthemodalclass\\ ii)A& b)Lowerlimitofthemodalclass\\ iii)B& \text{c) frequency of the class succeeding the modal class}\\ iv)C& d)frequencyofthemodalclass\end{array}$$

Match the options.

In the figure, AC=10cm, PC= 15cm, PQ=12cm, find PB?

The figure given alongside shows two straight lines AB and CD intersecting each other at point P (3, 4). Find the equations of AB and CD.

Find the HCF of 96 and 404 by prime factorisation method. Thereafter, find their L.C.M.