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On January 1, 2011 a company issued 15% debentures of Rs. 10,00,000 at par. The debentures were redeemable at par after three years on December 31, 2011. A sinking fund was set up to raise funds for redemption of debentures. The amount for the purpose was invested in 6% Government securities of Rs. 100 each available at par. The sinking fund table shows that if investments earn 6% per annum, to get Rs. 1 at the end of 3 years, one has to invest Rs. 0.31411 every year together with interest that will be earned. On December 31, 2013, all the Government securities were sold at a total loss of Rs. 6,000 and the debentures were redeemed at par.
Prepare Debentures Account, Sinking Fund Account, Sinking Fund Investment Account and Interest on Sinking Fund Investment Company closes its books of accounts every year on December 31.

If $a^2+b^2=23ab$, show that :

$log\frac{a+b}{5}=\frac{1}{2}(loga+logb)$

Find x if ${\log }_2(x-5)>3$

Factorise:
$4a^2-9b^2-2a-3b$

Euclid's which axiom illustrates the statement that when x+y=15,then x+y+z=15+z ?

(a) first

(b) second

(c) third

(d) four

A ball is thrown from point A and it reaches point B which is 7m away. There is another point C which lies somewhere on the line AB. Given that the ball follows a straight path, and AC = 9m, BC = 2m. Which is the point that lies in between other two? Draw the path of the ball. [1 MARK]

In the adjoining figure,the diagonals AC and BD of a quadrilateral ABCD intersect at O.If BO=OD,prove that $ar\left(△ABC\right)=ar\left(△ADC\right)$.

The upper limit of a class interval is 450 and the lower limit is half of it. What is the mid value of this interval?

$(104\times 96)$ = ?
(a) 9894 (b) 9984 (c) 9684 (d) 9884

the blood groups of 30 students of class VIII are recorded as follows:

A, B, O, O, AB, O, A, O, B, A,

O, B, A, O, O, A, AB, O, A, A,

O, O, AB, B, A, O, B, A, B, O

Represent this data in the form of a frequency distribution table. Find out which is the most common and which is the rarest blood group among these students

The coefficient of x in the expansion of $(x+3{)}^3$ is
(a) 1 (b) 9 (c) 18 (d) 27

Two lines AB and CD intersect at O. If $\angle AOC={50}^{\circ }$, find $\angle AOD,\angle BOD$ and $\angle BOC$.

In a $\Delta ABC,$ $D$ is the midpoint of side $AC$ such that $BD=\frac{1}{2}AC.$ Show that $\angle ABC$ is a right angle.

We know that Probability of an event E, written as
P(E)
$=\frac{\text{Number of outcomes favourable to E(m)}}{\text{Number of all possible outcomes of the experiment (n)}}$.

Which of the following options correctly explains the relationship between m and n?

Find the area of a wall which is in the shape of a parallelogram ABCD in which AB = 6 cm and BC = 11 cm and AC = 15 cm using heron's formula.
[3 MARKS]

In a $△$ ABC, if $\angle$ A = 55 $\circ$, $\angle$ B = 40 $\circ$, find $\angle$ C.

Factorize:

$1-27a^3$

If one of the pair of vertically opposite angles is ${105}^o$, what is the other angle?

The area of a playground is 4800m² . Find the cost of covering it with gravel 1 cm deep if the gravel cost ₹260 per cubic meter .

If a + b + c = 9 and ab + bc + ca = 23, then $a^3+b^3+c^3-3abc=$

$ABCD$ is a trapezium in which $AB\parallel CD$ and $AD=BC$ show that
I) $\angle A=\angle B$
II) $\angle C=\angle D$
III) triangle $ABC$ congruent to triangle $BAD$
IV) diagonal $AC$ =diagonal $BD$
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If two triangles $△ABC$ and $△PQR$ are such that AB = QR, BC = RP and CA = PQ, then ___.

The opposite sides of a quadrilateral have

Plot the points A (4, 0), B (4, 4) and C (0, 4) on the graph. Join OA, AB, BC, and CO, where O is the origin. Name the figure so formed and measure its sides.

Draw a line parallel to the x-axis at a distance of 2 units below the x-axis. [2 MARKS]

Find the value of k, if 2x + 3y = 13 passes through the point (2k,3k)

If two chords of a circle are equally inclined to the diameter through their point of intersection, prove that the chords are equal.

X³_ax²+2x-a is divided by (x-a)

An isosceles triangle is one in which __ sides are equal. (Write a number)

Give the factorization of 64a³-343b³ ?

Which of the following is a linear polynomial ?

x = 7, y = 3 is a solution of which of the following?

Which of the following is the value of $\sin \theta$ in a right angled triangle?

if x=root 5 + 2 / root 5 + 2 , find x + 1 / x

If $f\left(x\right)=x^2-5x+7$, evaluate $f\left(2\right)-f(-1)+f\left(\frac{1}{3}\right)$

Find the ratio of areas of two similar right triangles whose scale factor is 3 : 4.

Question 2 (ii)
AD is an altitude of an isosceles triangles ABC in which AB = AC.
Show that AD bisects $\angle A$.

Rain water fills a tub of dimensions 11 m × 7 m × 2 m. The capacity of the tub is

Area of a sector of angle p (in degrees) of a circle with radius r is

In the trapezium $ABCD,AB=10$ units, $DC=6$ units and $CE=5$ units. Find the area of the trapezium.

The height of a cone is 8 cm and its base radius is 6 cm. The curved surface area the cone is (Use $\pi$ = 3.14).