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The mean of the following data $1^2,2^2,3^2,4^2,........n^2$ is

Which of the following are not quadratic polynomials?
(i) $3+4x–7x^2$

(ii) $8x^2–15$

(iii) 6x – 15

(iv) $4x^3–3x$

(v) $x^2–x+1$

Given that LCM of 26 and 169 is equal to 338 find the HCF of 26 and 169

In the given figure, XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of contact C intersects XY at A and X'Y' at B. Then $\angle$ AOB is _____.

The height of a hill is 150 m. From the top of the hill, the angle of depression of two objects lying towards the east of the hill is ${45}^{\circ }and{30}^{\circ }$. Find the distance between the objects.

$\sqrt{3}=1.732$

In figure, $\angle CAB={90}^{o}andAD\perp BC$. if AC =75 cm, AB=1 m and BD=1.25 m,find AD.

Area of a trapezium = $\frac{1}{2}\times \text{height}\times$ sum of ___ sides.

A card is drawn at random from a well- shuffled pack of 52 cards. Find the probability that the drawn card is neither a king nor a queen.

Cosa-sina+1/cosa+sina-1=coseca+cota=using the identity cosec2a=1+cot2a

A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12 m. If the length of the rope is 7 m, find the area of the field which the horse cannot graze. Take $\sqrt{3}$ = 1.732. Write the answer correct to 2 places of decimal.

An experiment consist of recording boy-girl composition of families with 2 children.
(i) What is the sample space if we are interested in knowing whether it is a boy or girl in the order of their births?
(ii) What is the sample space if we are interested in the number of girls in the family?

A man has 300, Rs 50 shares of company paying 20% dividend. Find his net income after paying 3% income tax.

Find the mode of the following data.

$$\begin{array}{cccccc}Classinterval& 0-100& 100-200& 200-300& 300-400& 400-500\\ Frequency& 7& 11& 15& 9& 8\end{array}$$

Define void set.

If sum of the digits of any imteger in between 100 and 1000 is subtracted from that integer , then result is always divisible by

State the AAA - similarity criterion.

An arc AB forms $\angle AOB$ at the centre of the circle. If we draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $\angle AOB$.

If the points (1,-1), (2,1) and (4,x) lie on a line, then x is __

Find the number that must be subtracted from the polynomial $3^3+y^2-22y+15,$ so, that the resulting polynomial is completely divisible by y + 3.

To draw a pair of tangents to a circle which are inclined to each other at an angle of ${60}^{\circ }$, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

Find the 53 Sundays in an leap year

If a function defined on f : R $\to$ R with 6 as the period of the f(x). If f(0) = 13 then find f(96) ?

In the given figure, quadrilateral ABCD circumscribes a circle, as shown. Then, AB + CD = ___.

A rectangular sheet of paper having dimension 14m $\times$ 7m is folded along its length. Find the surface area of the cylinder formed.

In Akshita’s house there is a flower pot. The sum of radii of circular top and bottom of a flowerpot is 140 cm and the difference of their circumference is 88 cm. Find the diameter of the circular top and bottom. [4 MARKS]

A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 $c{m}^2$ and its height 12 cm, determine the radius of any of the spheres.

If the coordinates of one end of a diameter of a circle are (2,3) and the coordinates of its centre are (-2,5), then the coordinates of the other end of the diameter are

(a) (-6,7) (b) (6, -7) (c) (4, 2) (d) (5, 3)

Find the sum of n terms of the series $(4-\frac{1}{n})+(4-\frac{2}{n})+(4-\frac{3}{n})+...$

Find the values of a and b for which each of the following systems of linear equations has an infinite number of equations:

$2x+3y=7,(a+b+1)x+(a+2b+2)y=4(a+b)+1.$

$\frac{ta{n}^2\theta }{(1+ta{n}^2\theta )}+\frac{co{t}^2\theta }{(1+co{t}^2\theta )}=1$

What is one of the roots of the quadratic equation ${2x}^2-7x+3=0$ by the method of completion of the square? Also, what is the equation obtained after completion of the square?

Let `head` means 1 and `tail` means 2 and coefficients of the equation $a{x}^2+bx+c=0$ are chosen by tossing a fair coin. The probability that the roots of the equation are non-real, is equal to

A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).

Question 18
Which of the following is not true?
(A) $(7+8)+9=7+(8+9)$
(B) $(7\times 8)\times 9=7\times (8\times 9)$
(C) $7+8\times 9=(7+8)\times (7+9)$
(D) $7\times (8+9)=(7\times 8)+(7\times 9)$

In the following passage, there are some numbered blanks. Fill in the blanks by selecting the most appropriate word for each blank from the given options.

At markets or at county fairs in the old days, the customer had to be on guard against a dishonest trader. A house wife, for example, wanting (1) ___ buy a live piglet might be (2) ___ a discount if she bought (3) ___ packed one, tied up in a small sack (4) ___ a poke. Anyone who agreed to (5) ___ a pig in a poke was naturally (6) ___ a risk. The pig might be ill (7) ___ even dead: Or it might turn (8) ___ to be not a piglet at all. Which of the following words will be most appropriate for blank (2)?

If three times the larger of two numbers is divided by the smaller,we get 4 as the quotient and 8 as the remainder.If five times the smaller is divided by the larger,we get 3 as the quotient and 5 as the remainder.Find the numbers.

If 3 tan $\theta =4$, show that $\frac{(4cos\theta -sin\theta )}{(2cos\theta +sin\theta )}=\frac{4}{5}$

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm Χ 7cm. Find the area of the remaining cardboard.

The circle $x^2+y^2-6x-4y+9=0$ bisects the circumference of the circle $x^2+y^2-(\lambda +4)x-(\lambda +2)y+(5\lambda +3)=0if\lambda$ is equal to

If $sinA=\frac{9}{41}$, compute cos A and tan A.

A man takes a step forward with probability 0.4 and backward with probability 0.6. Find the probability that at the end of eleven steps, he is one step away from the starting point.

The length of the minute hand of a clock is 14 cm. Find the area swept by the minute hand in 5 minutes.

Question 67

In the following question, state whether the given statements are true (T) or false (F).

The multiplicative inverse of ${\left(\frac{3}{2}\right)}^2$ is not equal to ${\left(\frac{2}{3}\right)}^2$

In the given figure, O is the centre of the circumcircle. Tangents at A and C intersect at P. Given $\angle$ $AOB={140}^{\circ }$ and $\angle$$APC$ = ${80}^{\circ }$; find the $\angle$ $BAC$.