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For finding the mean by using the formula,$\overline{x}=A+h\left(\frac{\sum f_i{u}_i}{\sum f_i}\right),$,we have $u_i=?$

$\left(a\right)\frac{(A-x_i)}{h}\left(b\right)\frac{(x_i-A)}{h}\left(c\right)\frac{(A+x_i)}{h}\left(d\right)h(x_i-A)$

It is known that a box of 200 electric bulbs contains 16 defective bulbs. One bulb is taken out at random from the box. What is the probability that the bulb drawn is (i) defective, (ii) nondefective?

One zero of the polynomial $3x^3+16x^2+15x-18$ is $\frac{2}{3}$. Find the other zeros of the polynomial.

Let $a_n$ be the $n^{th}$ term of an AP. If ${\Sigma }_{r=1}^{50}{a}_{2r}=\alpha$ and ${\Sigma }_{r=1}^{50}{a}_{2r-1}=\beta$, then what is the common difference of the A.P.

If ($sec\theta$ - $tan\theta$) = $\frac{1}{3}$, then value of ($sec\theta$ + $tan\theta$) is:

Classify the following as linear, quadratic and cubic polynomials.

(1)$x^2+x$

(2)$x-x^3$

(3)$y+y^2+4$

(4)1 + x

show that the square of any positive integer cannot be of the form 5m+2 or 5m+3 for any integer m

The length of a rectangular plot is 2 m more than thrice its breadth. The area of the plot is 1240 m${}^2$. Find its length and breadth (approximate the values).

Find the reciprocal ratio of 27:31

Solution

Sam buys shares of a company at ₹ 90 and sells them when the price becomes ₹ 30 below par. What will be his loss if he invested ₹ 4050?

If $(a-b),aand(a+b)$ are zeros of the polynomial $2x^3-6x^2+5x-7$, write the value of a.

Prove that the intecept of a tangent between two parallel tangents to a circle subtends a right angle at the centre.

Solve for x and y:

$x+\frac{6}{y}=6,3x-\frac{8}{y}=5(y\ne 0).$

The length of the minute hand of a clock is 21 cm. The area swept by the minute hand in 10 minutes is

(a) $231c{m}^2$ (b) $210c{m}^2$ (c) $126c{m}^2$ (d) $252c{m}^2$

$Constructa\Delta PQR\text{whose perimeter is 12cm and the lenghs of whose sides are i the ration 3:2:4}$

A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm.Find the radius of the base of the cone.

The mean of a set of 20 observations is 19.3. The mean is reduced by 0.5 when a new observation is added to the set. The new observation is:

A red ant is sitting on one side of the table(point X) and a black ant is sitting on the other side of the table(point Y). They decide on switching places and start walking towards each other in a straight line. On the way both ants meet and after that it takes 20 seconds for the red ant to move to point Y and 5 seconds for the black ant to move to point X . Find the total time taken by the red ant and the black ant individually to make their journey.

How to find coordinates of the polynomial given

The length of a rectangle is 3/4 cm and its breadth is1/2 cm. What is the length of the diagonal of the rectangle?

Which of the following should be the LAST sentence after rearrangement?

If a line intersects sides AB and AC of a $△ABC$ at D and E respectively and is parallel to BC, then $\frac{AD}{AB}$ = $\frac{AE}{x}$ Then $x$ is

Karan has 9 pairs of blue socks and 9 pairs of black socks, all in the same bag. If he picks out three socks at random, then what is the probability that he will get a matching pair?

Find the value of the expression ${\sum }_{i=1}^n{\sum }_{j=1}^i$1

$4(1–{\sin }^2\theta )(1+{\tan }^2\theta )=$

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. Find the number of cones thus obtained.

In the figure chords AB & CD when extended meet at X. Given AB = 4 cm, BX = 6 cm, XD = 5 cm calculate the length of CD.

A man invests Rs 7,770 in a company paying 5 percent dividend when a share of nominal value of Rs 100 sells at a premium of Rs 5. Find :

(i) the number of shares bought;

(ii) annual income ;

(iii) percentage income

If LM $\parallel$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?

The slant height of a frustum of a cone is 4 cm and the perimeter (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum(in $c{m}^2$).

An exhibition tent is in the form of a cylinder surmounted by a cone. The height of the tent above the ground is 85 m and the height of the cylindrical part is 50 m. If the diameter of the base is 168 m, find the quantity of canvas required to make the tent. Allow 20% extra for folds and for stitching. Give your answer to the nearest $m^2$ .

if tanθ + cotθ = 2 then the value of tan²θ + cot²θ is

The first term of an AP is $5$, last term is $45$ and the sum is $400,$ then the number of terms and common difference of the series are respectively :

You are given a circle with radius ‘r’ and centre O. You are asked to draw a pair of tangents which are inclined at an angle of ${60}^{\circ }$ with each other. Refer to the figure and select the option which would lead us to the required construction. d is the distance OE.

state the equation of the line which has the y-intercept -5 and is equally inclined to the axes.

AB is the longest chord of a circle with centre O. P is any point on the circumference of the circle, not coinciding with A or B. Find $\angle APB$ in degrees.

Find x and y when x+y=a-b and ax-by=a^2+b^2 by substitution method.

If $(cosec\theta -sin\theta )=a^3$ and $(sec\theta -cos\theta )=b^3$ , prove that

$a^2{b}^2(a^2+b^2)=1$

The length of a rectangle is twice its breadth .if it's length is decreased by 5 cm and the breadth is increased by 5cm,the area of the rectangle is increased by 75 cm2.the length of the rectangle is:

A man on the deck of ship is 10 m above the water level. He observes that the angle of elevation of the top of a cliff is ${45}^{\circ }$ and the angle of depression of the base is ${30}^{\circ }$. Calculate the distance of the cliff from the ship and the height of the cliff.

The letters of the word AUDIT are rearranged.

What is the probability of (i) A new word starting with a vowel (ii) A new word starting with a consonant?

Are one and two complementary events?

The perimeter of the triangle with vertices (0, 4), (0, 0) and (3,0) is

(a) ( $7+\sqrt{5}$) (b) 5 (c) 10 (d) 12

D and E are points on the sides AB and AC respectively of a $△$ABC such that DE || BC. Which of the following statement is true?

(i) $△$ ADE ~ $△$ ABC

(ii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{D}^2}{A{B}^2}$

(iii) $\frac{areaof△ADE}{areaof△ABC}$ = $\frac{A{B}^2}{A{C}^2}$

Solve the following systems of equations:

$x-y+z=4$

$x+y+z=2$

$2x+y-3z=0$

An urn contains 2 green balls, 9 purples, 18 yellow balls, 10 balls,and 7 balls.what is the probablity of drawing a blue or red ball ?

In the following figure, ABCD to a trapezium with AB||DC. If AB =9 cm, DC =18 cm, CF =13.5 cm, AP =6 cm and BE =15 cm. Calculate:

(i) BC

(ii) AF