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Question 2
Write down the decimal expansions of
(i) $\frac{13}{3125}$
(ii) $\frac{17}{8}$
(iii) $\frac{15}{1600}$
(iv) $\frac{23}{2^3{5}^2}$
(v) $\frac{6}{15}$
(vi) $\frac{35}{50}$

Find the medians of following data sets.

Set I -- {3, 7, 2, 11, 8}

Set II -- {-1, 0, 1, 7, 11, 4}

Find the equation of the line passing through the points (2, 3) and the point of intersection of the lines $4x-3y=7$ and $3x+4y+1=0$.

From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area of the remaining solid.

If $(10{)}^9+2(11{)}^1(10{)}^8+3(11{)}^2(10{)}^7+...+10(11{)}^9=k(10{)}^9,$ then k is equals to:

In the figure given below CD is the median and DB = 3 cm , CD = 4 cm. The lenght of BC is :

Two numbers are respectively 20$\%$ and 50$\%$ more than a third number. The ratio of the first two numbers is

If one zero of the polynomial (ax^2 + 9)x^2+13x+6a is reciprocal of other. Find the value of a

If $\alpha ,\beta$ are the roots of equation x2 +px +q =0, then -$\alpha$-1 -$\beta$-1 are the roots of which of the following equations?

If in a question which we are solving by step deviation, if we take assumed mean to be 60 instead of 70 (which is given in ncert solution) will our answer be wrong??

If $A=\left[\begin{array}{cc}3& 7\\ 2& 4\end{array}\right],B=\left[\begin{array}{cc}0& 2\\ 5& 3\end{array}\right]$ and $C=\left[\begin{array}{cc}1& -5\\ -4& 6\end{array}\right]$
Find: AB - 5C

RS.17 is in the form of 50 paise coins,25 paise coins, and 20 paise coins. The number of 25 paise coins is double the number of 20 paise coins but half the number of 50 paise coins. Find the number of coins of each type.

Find the greatest of 6 digit exactly divisible by 24 15 and 36

Find the zeros of the polynomial p(x)=x^2+2√2-6

If tangents are drawn from any point on the circle x²+y²=25 to the ellipse x²/16 +y²/9=1, then the angle between the tangents is

The point is its own image if the point is __

If two sides of a $△$ ABC are equal in length and the third side has a different length, then the triangle is a/an:

P is the centre of a circle. the diameter AB bisects chord CD at E. AE is bigger than EB. If EC = 8cm and EB = 4cm, find the radius of the circle.

ABCD is a parallelogram. If the radius of the circle passing through all the vertices of a parallelogram is 4cm, then the length of the diagonal AC is ___.

The vertices of a triangle are A(–2, 8), B(1, 2) and C(7, –1).

i) Find the equation of the median AD.

ii) Find the equation of the altitude BE.

A rational number between and √3 is:

The relation shown in the arrow diagram in set builder form is

Prove that the points (a, b + c), (b, c + a) and (c, a + b) are collinear.

Find the sum of all odd numbers between
(i) 0 and 50 (ii) 100 and 200.

1. 3

A vessel in the form of an inverted cone is filled with water to the brim. Its height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, 1/3 of the water in the original cone overflows. What is the volume of each of the solid cones submerged?

The distance between the points $(x_1,-y_1)and(-x_2,y_2)$ is ___ units.

The angle of elevation of the top point P of the vertical tower PQ of height h from a point A on the ground is ${45}^{\circ }$ and from a point B, the angle of elevation is ${60}^{\circ }$, where B is a point at a distance d from the point A, measured along the line AB, which makes an angle ${30}^{\circ }$ with AQ. prove that d = $h(\sqrt{3}-1)$

If the sum of an terms of an A.P. is $3n^2+5n$ and its $m^{th}$term is 164, find the value of m.

The following are the marks obtained in Science by students in class X.
The mean of the given data is 63.33.
Is this mean an appropriate representation of the average marks obtained?
If no, what would be the most appropriate measure of central tendency for the correct representation of the marks distribution?
What is the value of this measure of central tendency for the given data?

$\begin{array}{cc}\text{Marks}& \text{Frequency}\\ 10-20& 1\\ 20-30& 0\\ 30-40& 0\\ 40-50& 0\\ 50-60& 1\\ 60-70& 5\\ 70-80& 15\\ 80-90& 20\\ 90-100& 3\end{array}$

Without using tables, evaluate: 3 cos 80⁰ cosec 10⁰ + 2 cos59⁰ cosec 31⁰

You ask a friend to think of a number from 5 to 40. What is the probability that his number will be multiple of 10?

What is the remainder obtained when the polynomial P(x) = $x^7$ + 9$x^5$ + 5$x^3$ + x -1 is divided by x – 1, and what is the value of P (1).

Two dice are rolled simultaneously. Find the probability of getting the sum of the numbers as 13.

If the numerator of a fraction is increased by 25% and the denominator is doubled the resultant fraction thus obtained is $\frac{15}{32}$ What is the original fraction? (Andhra bank SO)

The 4th term of an A.P. is three times the first and the 7th term exceeds twice the third term by 1. Find the first term and the common difference.

If 10 times the 10th term of an A.P. is equal to 15 times the 15th term, show that 25th term of the A.P. is zero.

A chord 10 cm long is drawn in a circle whose radius is $5\sqrt{2}cm$. Find the area of both the segments. (Take $\pi =3.14$)

How many number lie between $10$ and $300$, which when divided by $4$ leave a remainder $3$?

An elastic belt is placed around the rim of a pulley of radius 5 cm. One point on the belt is pulled directly away from the Centre O of the pulley until it is at P, 10cm from O. Find the length of the belt that is in contact with the rim of the pulley. Also, find the shaded area.

A trader bought a number of articles for Rs. 1,200. Ten were damaged and he sold each of the remaining articles at Rs. 2 more than what he paid for it, thus getting a profit of Rs. 60 on the whole transaction ?

Taking the number of articles he bought as x, form an equation in x and solve it.

Which of the following cannot be the probability of an event?
(a) $\frac{1}{3}$ (b) 0.3 (c) 33 (d) $\frac{7}{6}$