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The point A(4, 6) is first reflected in the origin to point A'. Point A' is then reflected in the y-axis to point A".

(i) Write down the co-ordinates of A".

(ii) Write down a single transformation that maps A onto A".

If S_r denotes the sum of the first r terms of an AP . Then find

S_3n : (S_2n - S_n)

Find an arithmetic sequence whose first term is 5 and common difference is 9.

Question 92 (xxvi)

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

$(a-b{)}^2-(b-c{)}^2$

If the probability of an occurrence of an event A is denoted by P(A), then the range of P(A) is

Question 2 (i)

Do the following equations represent a pair of coincident lines? Justify your answer.

$3x+\frac{1}{7}y=3and7x+3y=7$

A contract on construction job specifies a penalty for delay of completion beyond a certain date as follows: ₹ 200 for the first day, ₹ 250 for the second day, ₹ 300 for the third day, etc., the penalty for each succeeding day being ₹ 50 more than for the preceding day. How much money the contractor has to pay as penalty, if he has delayed the work by 30 days?

Question 93

Solve the following:

If $\frac{1}{2}$ is substracted from a number and the difference is multiplied by 4. the result is 5. What is the number?

Consider the following infinite AP: a, a+d, a+2d, …., a + (n - 1)d, …..

If the $m^{th}$ term is negative, then which of the following is true?

Raghu wants to make a closed aluminium cone for his science project. The slant height and radius of the cone should be 10 cm and 7 cm respectively. The area of the aluminium sheet required to make the cone is_____.

$(Use\pi =\frac{22}{7})$

Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?

Draw a circle of radius 3.5 cm. Construct two tangents from a point 8 cm away from the centre.

Meena needs to serve mango juice to her guests in cylindrical tumblers of radius 7 cm up to a height of 10 cm. If she wants to serve 25 guests, how much juice should she prepare?

Solution for the following pair of linear equations is:

2x + 4y = 8

4x + 8y = 0

Solve each of the following quadratic equations:
$x^2+2\sqrt{2}x-6=0$

If A (4, –6), B (3, –2) and C (5, 2) are the vertices of triangle ABC, then verify the fact that a median of a triangle ABC divides it into two triangle of equal areas

$ABCD$ is a parallelogram and $E$ is a point on $BC$. If the diagonal intersects $AE$ at $F$, prove that $AF\times FB=EF\times FD$.

In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle. If $\angle$PQA= ${65}^{\circ }$ then, find $\angle$PAQ.

Locus of foot of the perpendicular drawn from $P(a,2a)$ to a variable line passing through $Q(2a,a)$ is

Fill in the blanks using the correct word given in brackets:
(i) All circles are ___ (conruent, similar).
(ii) All squares are ___ (similar, congruent)
(iii) All ___ triangles are similar (isoscles, equilaterals):
(iv) Two triangles are similar, if their corresponding sides are ___(propotional, equal)
(v) Two traingles are similar, if their corresponding sides are ___(proportional equal)
(vi) Two polygons of the same number of sides are similar, if (a) their corresponding angles are and (b) their corresponding are ___ (equal, proportional)

Solve each of the following systems of equations by the method of cross-multiplication:

$2(ax-by)+a+4b=0$

$2(bx+ay)+b-4a=0$

What is the missing number in this sequence: 13, 10, __, 4, 1?

Write $x^2$ + 2$\sqrt{3}$ x + 3 as $x^2$+ p x+ q x + 3 such that p+q = 2$\sqrt{3}$ and pq = 3

If p=$\sqrt{a}$ , q= $\sqrt{b}$ . What is the value of a + b ?

The angle of elevation of the sun is , when the length of the shadow of a tree is equal to the height of the tree.

What is the distance between the points (0,4) and (-3,0)?

Question 4

Construct a tangent to a circle of radius 4 cm from a point which is at a distance of 6 cm from its centre.

Thinking process

1. Firstly taking the perpendicular bisector of the distance from the centre to the external point. After that taking one half of bisector as radius and draw a circle.

2. Drawing circle intersect the given circle at two points Now, meet these intersecting point to an external point and get the required tangents.

If two dice are rolled simultaneously , then what is the probability that the sum of numbers is a multiple of either 2 or 7?

In a leap year the probability of having 53 Sundays and 53 Monday is
(a) $\frac{1}{7}$
(b) $\frac{3}{7}$
(c) $\frac{4}{7}$
(d) $\frac{5}{7}$

Find the value of m if one zero of the polynomial(m^2+4)x^2+65x+4m