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For universal set $\cup$, and sets A, B which are subsets of $\cup$, the following information is given

n(U) = 47

n(A) = 18

n(B) = 11, n(A $\cap$ B) = 10

Then, the number of elements that are neither in A nor B is_____

Bank cheques and bank drafts are useful for trading in

The circumference of a circle exceeds the diameter by 16.8 cm. Find the circumference of the circle.

Find the focal length.

How many solutions are possible for the following pair of equation?
2 x + 4 y -12= 0 and x + 2y- 4 =0

In the given figure, ∆ ABC, DE || BC, AD: DB = 3: 2. Find AD: AB, DE: BC. Find ratio of areas of ∆ DEF & ∆ BFC

A two- digit is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places. Find the number.

If the point P (m , 3) lies on the line segment joining the points $A(-\frac{2}{5},6)$ and B (2, 8), find the value of m.

Choose the correct option.

10. Sandhya and Ragini have same weight. With the help of proper exercise and strict diet regime they each lost weight by 8kg. How will their new weights be compared? Write the Euclid’saxiom that best supports your answer. Why is exercise important to us?

What can you tell about the ratio of coefficients of the lines $a_1$x + $b_1$y + $c_1$ = 0 and $a_2$x + $b_2$y + $c_2$ = 0 from the graph ?

Let $T_r$ be the $r^{th}$ term of an A.P, for r=1, 2, 3,-------. If for some positive integers m,n we have $T_m=\frac{1}{n}$ and $T_n=\frac{1}{m}$, then $T_{mn}$ =

Two AP 's have the same common difference.The first term of one AP is 2,and that of the other is 7.The difference between their 10th trms is the same difference between the 21th terms which is the same as the difference between any two corresponding terms. Why?

If cos theta - sin theta = √2 sin theta then prove that cos theta + sin theta = √2 cos theta

In a quadrilateral ABCD, $\angle B={90}^{\circ },A{D}^2=A{B}^2+B{C}^2+C{D}^2$, prove that $\angle ACD={90}^{\circ }$

There is a circle on the co- ordinate plane for which there are 2 tangent lines. These are x - y = 3 and x - y = 0. The meeting points of the circle with the 2 lines are ($\frac{3}{2}$,$\frac{3}{2}$) and (0,3). Find the radius and the centre of the circle.

two vertices of isosceles triangle are 2, 8 and 10,2. find the third vertex if the length of equal sides is 10 units

Question 2 (i)
Write whether the given statement is true or false. Justify your answer.
Every quadratic equation has exactly one root.

A right circular cylinder just encloses a sphere of radius r (see figure). Find the curved surface area of the cylinder.

In $\Delta$ ABC $\sim$ $\Delta$ PQR by AAA criteria and $\angle B=\angle R={60}^{\circ }$. Find $\angle$ RPQ.

If the radius of a right circular cone is halved and height is doubled, then the volume will remain unchanged.

If (x-9): (3x+6) is the triplicate ratio of 4:9. Find X.

Without using tables, show that (cos ${35}^{\circ }cos{55}^{\circ }-sin{35}^{\circ }sin{55}^{\circ }$) = 0

Given that sin A= $\frac{1}{2}$ and cosB =$\frac{1}{\sqrt{2}}$, then find the value of (A+B) (where A and B are acute angles).

Simplify : $\frac{1+2sinxcosx}{(sinx+cosx{)}^2}$

Let $S$ be the standard deviation of $n$ observations. Each of the $n$ observations is multiplied by a constant $C$. Then the standard deviation of the resulting number is

Any line segment which touches a circle at exactly one point is called the __ to the circle at that point.

A circus artist is climbing a 20 m long rope, which is tightly stretched and tied from the top of a vertical pole to the ground. Find the height of the pole if the angle made by the rope with the ground level is ${30}^{\circ }$.

If the $4^{\text{th}},7^{\text{th}}$ and ${10}^{\text{th}}$ terms of a G.P. are $a,b$ and $c$ respectively, then the relation between $a,b$ and $c$ is ___.

In the given right angled isosceles triangle ABC, if $AC=10cm$ then the area of triangle is ___ $c{m}^2$

A tree $12m$ high, is broken by the wind in such a way that its top touches the ground and makes an angle ${60}^{\circ }$ with the ground. At what height from the bottom, the tree is broken by the wind?

Meenakshee cycles to her school at an average speed of 12 km/hr and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be:

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 42 cm, find the area in $c{m}^2$ between the two consecutive ribs of the umbrella.

Find the locus of the position of a person at the same distance from a tower.

The cost of levelling a square ground at Rs 1.80 per meter square is 91936.80. Find the cost of fencing at rs 2.25 per meter.

Metallic spheres of radii 6 cm,8 cm and 10 cm respectively are melted and recasted into a single solid sphere.Taking $\pi$=3.1,find the surface area of solid sphere formed.

Find the value of k if k+1,2k+1 and 13 are 3 consecutive terms of an arithmetic sequence ?

Find zeros of f(x)= x³ - 5x² - 16x + 80 , if it’s two zeros are equal in magnitude but opposite in sign

Mrs Mathew opened a Recurring Deposit Account in a certain bank and deposited Rs 640 per month for $4\frac{1}{2}$ years. Find the maturity value of this account, if the bank pays interest at the rate of 12 % per year.

Which among the following is the correct histogram for the following data:

$\begin{array}{cccccc}\text{Class interval}& 30-39& 40-49& 50-59& 60-69& 70-79\\ \text{Frequency}& 24& 16& 9& 15& 20\end{array}$

Given are the steps to construct tangents from an external point P to a circle with centre O. Order the steps correctly.
STEPS:
i) Join PM and PN.

ii) Draw a circle with centre as L and radius LO. Let it cut the given circle at points M and N.

iii) Bisect the segment OP, at L.

iv) Join OP.

ABC is an isosceles triangle right-angled at B. Similar triangles ACD and ABE are constructed on sides AC and AB. Find the ratio between the areas of $\Delta ABE$ and $\Delta ACD$. [4 MARKS]

Which among the following is the midpoint of the line segment AB, where A (-6, 11) and B (10, -3)?