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Area of a sector of a circle is 1/6 the area of the circle . Find the degree measure of its minor arc.

If the radius of a sphere is 12 cm, then its surface area will be .
(Take $\pi =3.14)$

The water in a rectangular reservoir has a base 80 m × 60 m and is 6.5 m deep. In what time(in hours) can the water be emptied by a pipe having a cross section in the form of a square of side 20 cm, if water runs through the pipe at the rate of 15 km/ hr?

P(3, 4), Q(7, -2) and R(-2, -1) are the vertices of triangle PQR. Write down the equation of the median of the triangle through R.

Find the lengths of the medians of a triangle ABC whose vertices are A(7, –3), B(5, 3) and C(3, –1).

The total price paid by a customer for a PC is Rs 31104, including 8% sales tax. If the list price of the PC were Rs 32000, what discount percentage was given to the customer for the PC?

What is the largest area of rectangle formed by two perpendicular diameters and a point on the circle of diameter $20\sqrt{2}$ cm?

What is the sufficient condition for a two digit number to be divisible by 3?

Find the equation of a line whose $x$ intercept is 8 and passing through the point (4, -8).

A : What is the radius of circle whose area is 38.5 $c{m}^2$? ( Take $\pi =\frac{22}{7}$)
B : What is the perimeter of circle of above circle?
1) 11cm
2) 3.5 cm
3) 7 cm
4) 22 cm
5) 38.5 cm
Choose the correct matching

Find two numbers such that the sum of thrice the first and the second is 142,and four times the first exceeds the second by 138.

In the given figure, the Distance D(P,Q) is:

The radius of a circle is 7 cm and it forms a sector by rotating through 60${}^{\circ }$. Then, the radius gets doubled and further moves 30${}^{\circ }$ to form another sector. What is the area of the total region covered by the radius? ( Take π= $\frac{22}{7}$)

Construct a $3\times 3$ matrix whose elements $a_{ij}$ are given by $a_{ij}=0$ if $i\ne j$ and $a_{ij}=i\times j$ if $i=j$

A tank is in the shape of a right circular cylinder whose radius and height are 7 cm and 14 cm respectively. The capacity of the tank is ___ $\times {10}^{-4}{m}^3$.

Construct a triangle with sides $5cm,6cm$ and $7cm$ and then another triangle whose sides are $\frac{7}{5}$ of the corresponding sides of the first triangle.

Question 2 (ii)

E and F are points on the sides PQ and PR respectively of a $\Delta PQR$. For the following case, state whether EF || QR.

(ii) PE = 4 cm, QE = 4.5 cm, PF = 8 cm and RF = 9 cm

A train travels from place A to place B which is nearly 150 km . Give the speed time formula for it and draw the graph. Find the number of hours it takes to travel with a speed of 25 km/hr.

If the pth term of an AP is q and its qth term is p then show that its (p+q)th term is zero.

A vessel is a hollow cylinder fitted with a hemispherical bottom of the same base. The depth of the cylinder is $\frac{14}{3}$m and the diameter of hemisphere is 3.5 cm.Calculate the volume and the internal surface area of the solid.

The given figure shows a trapezium in which AB || DC and diagonal AC and BD intersect at point P. If AP : CP = 3:5 and area of $△APB$ is $27m^2$, Find the area of $△CPD$ .

On 1st April, 2013, X, Y and Z started business sharing profit and losses in the ratio of 3 : 2 : 1 respectively. They contributed Rs. 1,00,000, Rs. 80,000 and Rs. 40,000 respectively as their capital which was deposited into bank. Each partner withdrew Rs. 15,000 during the year. The firm was dissolved on 31st March, 2014. X took up the stock at an agreed price of Rs. 25,000. Y took up furniture at Rs. 5,000 and Z took up debtors at Rs. 18,500. Creditors were paid off and then remained a balance of Rs. 14,000 in the bank account.

Prepare the necessary accounts to show the distribution of cash at bank and of the further cash brought in by any of the partners.

Question 7

A number is divisible by 12. By what other numbers will that number be divisible?

Let 'a' and 'b' be positive integers. Show that root 2 lies between a/b and a+2b/a+b .

With full detailed solution of every step.

Spherical marbles of diameter 1.4 cm are dropped into beaker containing some water and are fully submerged. The diameter of the beaker is 7 cm. Find how many marbles have been dropped in it if the water rises by 5.6 cm ?

Using Euclid's division algorithm, find the HCF of 1650 and 847.

Prepare a bank reconciliation statement from the following information:
1. Overdraft balance as per cash book is Rs. 1,20,000.
2. Cheque deposited Rs. 30,000 but no entry was passed in cash book.
3. Bill discounted dishonoured for Rs. 20,000.
4. Bank charges of Rs. 50 entered in cash book twice.

If $f\left(x\right)=\text{sgn}(x^2-ax+1)$ has maximum number of points of non differentiability, then

An arithmetic sequence has

$6^{th}$ term as 52 and ${15}^{th}$ term as 142. Find a & d .

If you take a random 4 digit number, what is the probability that (i)the ten's place digit is greater than the unit's place digit

(ii) that the leftmost digit is a multiple of 3 (iii) the rightmost digit is a multiple of 3. [4 MARKS]

A drain cover is made from a square metal plate of side 40 cm by having 441 holes of radius 1 cm each drilled in it. Find the area in $c{m}^2$ of the remaining square plate. $Use\pi =\frac{22}{7}$