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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{77}{210}$

If 12th term of an A.P. is -13 and the sum of the first four terms is 24, what is the sum of first 10 terms?

Which of the following is not correct about the function f(x)=0?

Hari took part in a quiz where he is asked to find the area of the given figure with sides marked in centimeters. Since the dimensions marked are not in the integer form, Hari needs your help to solve the problem. Can you help him to find the solution?

Draw a regular hexagon of side 5 cm.

Find the 12th term from the end of the following arithmetic progressions:
(i) 3,5,7,9,...201
(ii) 3,8,13,...,253
(iii) 1,4,7,10,...,88

Each question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

(c) Assertion (A) is true and Reason (R) is false.

(d) Assertion (A) is false and Reason (R) is true.

$\begin{array}{cc}Assertion\left(A\right)& Reason\left(R\right)\\ Ifthevolumesoftwospheresare& Volumeofaspheres=\frac{4}{3}\pi R^3.\\ intheratio27:8thentheirsurface& \\ areasareintheratio3:2& Surfaceareaofasphere=4\pi R^2.\end{array}$

The correct answer is (a) / (b) / (c) / (d).

Calculate the median for the following data:

$\begin{array}{ccccccc}\text{Age(in years)}& \text{19-25}& 26-32& 33-39& 40-46& 47-53& 54-60\\ \text{Frequency}& 35& 96& 68& 102& 35& 4\end{array}$

If $a\in R^{+}\&b\in R$, then the equation $x^2-abx-a^2=0$ has

Show that each of the following systems of equations has a unique solution and solve it:

$\frac{x}{3}+\frac{y}{2}=3,x-2y=2.$

Find the values of p for which the quadratic equation $(2p+1)x^2-(7p+2)x+(7p-3)=0$ has real and equal roots.

Find the equation of a line whose: y-intercept = -1 and inclination = ${45}^{\circ }$.

Three metallic cubes whose edges are 3 cm, 4 cm and 5 cm, are melted and recast into a single large cube. Find the edge of the new cube formed.

HCF of $(2^3\times 3^2\times 5),(2^2\times 3^3\times 5^2)and(2^4\times 3\times 5^3\times 7)$ is

(a) 30 (b) 48 (c) 60 (d)105

If 3 cos $\theta$ = 4, write the value of $\frac{(2cos\theta +sin\theta )}{(4cos\theta -sin\theta )}$

The sides of a right-angled triangle are (x - 1) cm, 3x cm and (3x + 1) cm. Find :

(i) the value of x,

(ii) the lengths of its sides,

(iii) its area.

How to solve think and solve problems fast using tricks or how to divide a decimal large numbers, for quick answers?

Solve for x and y:

$x+y=a+b,ax-by=a^2-b^2.$

Given that Sin(A + B)=Sin A Cos B +CosA SinB, find the value of 75°

A lady standing on the deck of a ship, which is 20 m above water level, observes the angle of the elevation of the top of a mountain as ${60}^{\circ }$ and the angle of depression of the base of the mountain as ${30}^{\circ }$. Calculate the distance of the mountain from the ship.

How much money will be required to buy 250, Rs 15 shares at a discount of Rs 1.50 ?

Words are formed using all the letters A, B, G, S, and E without repetition. If a word is chosen randomly then, what is the probability that the word starts with A?

In a$\Delta$ABC, if $(\sqrt{3}-1)a=2b,A=3B,$ then $C$ is

You have budgeted $66amonthtospendonyogaclasses.Youryogastudiocharges$22 per month membership fee, plus $5 per class attended. Find the possible number of classes you can attend each month.

$\frac{secA-tanA}{secA+tanA}=1-2secAtanA+2ta{n}^{2}A$

The marks obtained by 40 students in mathematics (out of 100) is presented in the table below. Find the mean.

$$\begin{array}{cccccc}ClassInterval& 0-10& 10-20& 20-30& 30-40& 40-50\\ Numberofstudents& 3& 4& 13& 15& 5\end{array}$$

The given figure shows the shape of a toy. The height of the conical part is ⁴/₇th of the total height of the toy.

If is the radius of the hemispherical part, then what is the total surface area of the toy?

p(x) = $x^3$ + 8$x^2$ - 7x + 12 and g(x) = x - 1. If p(x) is divided by g(x), it gives q(x) and r(x) as quotient and remainder respectively. If 'a' is the degree of q(x) and b is the degree of r(x), what is the value of (a - b)?

Which of the following cannot be the lengths of the sides a right triangle?

In a deck of playing cards, 2 new suits are introduced which are red and black in color respectively. If the number and types of cards in the new suits are same as the standard suits. Find the probability that I will get a face card on a random draw of 1 card. Also find the probability if the new suits were not introduced.

A book has pages numbered from 1 to 100. If a page is chosen at random, what is the probability that the sum of the digits on the page is 9?

$\text{In the given figure, O is the centre of a circle. If}\angle AOB={40}^{\circ }and\angle BDC={100}^{\circ }thenfind\angle OBC.$

A manufacturer marks an article at Rs. 5000. He sells the article to a wholesaler at a discount of 25% on the marked price and the wholesaler sells it to a retailer at a discount of 15% on its marked price. If the retailer sells the article without any discount and at each stage, the sales tax is 8%, then the amount of VAT paid by wholesaler and retailer are :

Construct a cyclic quadrilateral PQRS with PQ = 6 cm, $\angle P={105}^{\circ }$ , $\angle PQS={45}^{\circ }$ and $\angle SQR={75}^{\circ }$.

If the difference between the circumference and the radius of a circle is 37 cm, then us $\pi =\frac{22}{7}$, the circumference (in cm) of the circle is:

In the given figure, AB & DE are ⊥ BC, if AB = 9 cm, DE = 3 cm and AC = 24 cm, find AD

In order to obtain an income of Rs. 650 from $10\%$ stock at Rs. 96, one must make an investment of:

Which term of the following A.P. would be 0?
36,33,30,27….

A line that intersects a circle at two points is called a

In reference to the above question, what would be the first thing to determine?

If A is involuntory matrix ($A^2=I$) and I is unit matrix of same order, then (I-A)(I+A) is