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If 2 and 5 are factors of a number, what will be the unit’s digit of that number?

Find the change in surface area of a sphere if its radius is increased 4 times.

In figure, arc AB is congruent to arc AC and O is the centre of the circle. Prove that OA is the perpendicular bisector of BC. [4 MARKS]

Find the mode of the following data.

$$\begin{array}{cccccc}Class& 0-20& 20-40& 40-60& 60-80& 80-100\\ Frequency& 5& 11& 12& 13& 9\end{array}$$

Find the coordinates of the point which divides the line segment joining the points (6, 3) and (–4, 5) in the ratio 3 : 2 internally.

Question 91

The population of a town was decreasing every year due to migration, poverty and unemployment. The present population of the town is 631680. Last year the migration was 4% and the year before last, it was 6%. What was the population two years ago ?

Construct a triangle ABC, in which $\angle$B = 53.13°, $\angle$C = 36.87° and AB + BC+ CA = 24 cm. What type of triangle is this?

250 students of class X of a school appeared in a test of 100 marks and the data about the marks secured is a below

$\begin{array}{cc}Markssecured& Numberofstudents\\ 0-20& 20\\ 20-40& 35\\ 40-60& 65\\ 60-80& 60\\ 80-100& 70\end{array}$

Find the modal vlaue of the above data. [2 MARKS]

Find the equation of the perpendicular bisector of the straight line segment joining the points (3, 4) and (-1, 2).

If the replacement set is the set of real numbers , solve
$-2x\le 6$

Find the value of x which will satisfy the equation:

$x\times cos\left(a\right)\times cos({90}^{\circ }-a)\times tan({90}^{\circ }-a)\times sec\left(a\right)\times cosec\left(a\right)\times tan\left(a\right)=1$

A cylinder is having a volume of 231 cu. cm. If the height of the cylinder is 6 cm, then what is the radius of a ball which will fit inside the cylinder?

If the sum of the length of the legs of a right triangle is 49 cm and the hypotenuse is 41 cm, find its shortest side.

What is the distance between (0,8) and (0,-1)

Ted trades his crayons with his friend for a dozen baseball cards. This is an example of ___ system.

A = {1, 2, 3}, B = {2, 3, 4}, C = {4, 5}. Find (A $\cap$ B) $\times$ C.

If the median of the following data is 50, then find p.
$$\begin{array}{cccccc}Class& \text{0-20}& \text{20-40}& \text{40-60}& \text{60-80}& \text{80-100}\\ Frequency& \text{10}& \text{7}& \text{16}& \text{p}& \text{8}\end{array}$$

Please answer this question

Let N be the greatest number that will divide 1305,4665 and 6905, leaving the same remainder in each case. The sum of digits in N is

Find two consecutive positive odd integers sum of whose squares is 290?

(a) Prove that $\frac{cosA}{1+sinA}+tanA=secA$

(b) Prove the identity $(sin\theta +cos\theta )(tan\theta +cot\theta )=sec\theta +cosec\theta$ [6 MARKS]

A manufacturer produces a good and sells it to a wholesaler at a price of Rs.500 and wholesaler sells it to retailer at a price of Rs.600. The retailer sells it to the customer at a price of Rs.800. If the sales tax charged is $Rs5\%$. Find the total tax charged by the government under VAT.

In the figure given below, O is the centre of the circle and SP is a tangent. If $\angle SRT={65}^0$, select the statements that are true.

Which among the following uses the positive form of the underlined adjective correctly?

The age of father is 3 years more then 3 times the son's age. 3 years hence the, age of father will be 10 years more than twice the age of son. Find their present ages.

On dividing x^3-8x3^2+20x-10 by a polynomial g(n) the quotient and the reminder where x-4 and 6 respectively find g(n)

The $\angle B$ in the given triangle is ___ degree.

Consider a ladder which makes an angle 60^o with a wall of height 10 m and its top just touches the top of the wall. If the ladder is now rotates in such a way that its top now touches the top of the opposite wall which has a height of ¹⁰/_√3 m. What is the angle by which the ladder is rotated?

The sum of three numbers in A.P. is 15 and the sum of the squares of the extreme terms is 58. Find the numbers.

Solve the following pairs of linear (simultaneous) equations using method of elimination by substitution:

$2x-3y=7$

$5x+y=9$

In fig., A, B and C are points on OP, OQ and OR respectively such that AB $\parallel$ PQ and AC$\parallel$ PR. Show that BC $\parallel$ QR.

Let $A=\left[\begin{array}{cc}2& 1\\ 0& -2\end{array}\right],B=\left[\begin{array}{cc}4& 1\\ -3& -2\end{array}\right]$ and $C=\left[\begin{array}{cc}-3& 2\\ -1& 4\end{array}\right]$ Find: $A^2+AC-5B$

Two circles with circumference 44$\pi$ cm and 20$\pi$ cm respectively touch internally. Find the distance between their centres.

D and E are respectively the points on the sides AB and AC of a $\Delta$ABC such that AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm, prove that DE || BC.

A, B, C and D are four points on a circle. AC and BD intersect at a point E such that ∠BEC = 130 and ∠ECD = 20. Find ∠BAC