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If $D=0$ and at least one of $D_1,D_2,D_3$ is not 0 then according to Cramer's rule the system of linear equations will have

In $△$ABC, the ratio of altitudes BE and CF is equal to one. What can be said about the nature of $△$ABC?

If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200km. Find the speed of the aeroplane.

A Cuboid has length, breadth and height of 6cm, 4 cm and 2 cm respectively. The total surface area of Cuboid is

P and Q started a business and invested for the same period of time. If the ratio of their investment is 4: 5, then, their profit distribution would also in the ratio of 4: 5. Is this statement true?

Question 1 (x)
Without actually performing the long division, state whether$\frac{77}{210}$ will have a terminating decimal expansion or a non-terminating repeating decimal expansion.

Question 52

Fill in the blanks to make the statement true.

23 $\times$ (-99) = ___ $\times$ (-100 + ___) = 23 $\times$ ___ + 23 $\times$ ___ .

If $\left|x\right|<1$ and $\left|y\right|<1,$ find the sum to infinity of the series

$(x+y)+(x^2+xy+y^2)+(x^3+x^{2}y+x{y}^2+y^3)+....$

Or

Find the sum to n terms of the series $\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....$

If A and B are 2 sets such that A $\cup$ B has 40 elements, A has 18 elements and B has 29 elements, how many elements does A $\cap$ B have? _______

The market value of a $10.5\%$ stock, in which an income of Rs. 756 is derived by investing Rs. 9000, brokerage being $1/4\%$ is:

In an AP, the first term is 7 and the common difference is 4. Which term of the AP will be five times the first term?

This is out of syllabus.

I want a help in doing my maths project on the topic "various types of cryptarithm".

Please send your reply in detail.!!!

Please Use the Components of Proportion like Componendo and dividends etc

If (a+3b+2c+6d)(a-3b-2c+6d)=(a+3b-2c-6d)(a-3b-2c+2c-6d)

Prove that a:b::c:d

Express 140 as the product of its prime factors:

Sale price of a pair of shoes is ₹ 540. If Amit paid ₹ 45 as sales tax for it, find the rate of sales tax.

The locus of a point equidistant from two parallel lines is

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

$\begin{array}{cccccc}\text{Number of mangoes}& 50-52& 53-55& 56-58& 59-61& 62-64\\ \text{Number of boxes}& 15& 110& 135& 115& 25\end{array}$

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

A man invests Rs 11,200 in a company paying 6 percent per annum when its Rs 100 shares can be bought for Rs 140. Find :

(i) his annual dividend.

(ii) his percentage return on his investment.

Progressive taxation in direct taxes ensures equality in the

Question 12
A milk container of height 16 cm is made of metal sheet in the form of a frustum of a cone with radii of its lower and upper ends as 8 cm and 20 cm respectively. Find the cost of milk at the rate of ₹ 22 per litre which the container can hold.

Points A (-8,0), B (-16,0) are invariant points when reflected in the line $L_1$ . Find the image of the points C (-15,6) and D(8, 19) in the line $L_1$.

The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.

Find the $n^{th}$ term of the AP with ‘a’ as first term and ‘d’ as common difference.

There are 20 cards numbered from 1 to 20. Krishna selects a card at random from these cards. What is the probability that this card selected at random is a multiple of 3?

Sam is looking at the roof of the adjacent building from the top of his flat. His height is 5 feet. He knows that the height of his building and the distance between the two buildings is 50 feet. Sam measures the angle of elevation of his line of sight of the tip of the other building to be ${30}^{\circ }$. Based on the information in the question, find the height of the adjacent building.

A car started at a speed of 10 km/hr and increasing its speed by 5 km/hr for every 1 hour. If the car has travelled for 4 hours then find its average speed.

If $S_1,S_2,S_3\cdots S_p$ are the sums of infinite geometric series whose first terms are $1,2,3,...p$ and whose common
ratios are $\frac{1}{2},\frac{1}{3},\frac{1}{4},\cdots \frac{1}{p+1}respectively,$ then $S_1+S_2+S_3+\cdots +S_p=$ ___.

A small disk rolls on a cylindrical surface of radius R without slipping. The time period of oscillations will be?

Find the next number in the sequence 6, 24, 60, 120 ___

What is the relation between n (A), n( B), n(A intersection B)

and n(A union B)

Step 3: With r as radius, draw arcs with B and C as centres. The point of intersection of the arcs is point D. $\angle DOA$ is__
Note: Answer in degrees.

The mid-point of the line segment joining P(-2,8) and Q(-6,-4) is

A bag contains $4$ white, $6$ red and $7$ black balls. If four balls are drawn one by one without replacement, then the probability that all balls are black is

In the figure, if PS = 14 cm, the value of tan a is equal to:

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector. $Take\pi =\frac{22}{7}$

The sum of the first n terms is $\frac{1}{2}$ + $\frac{3}{4}$ + $\frac{7}{8}$ + $\frac{15}{16}$ + .......... is

If $cosec\theta -sin\theta =a^3$ and $sec\theta -cos\theta =b^3$, then $a^2{b}^2(a^2+b^2)=$

Without actual division, show that each of the following rational numbers is a nonterminating repeating decimal.

$\left(i\right)\frac{11}{(2^3\times 3)}\left(ii\right)\frac{73}{(2^2\times 3^3\times 5)}\left(iii\right)\frac{129}{(2^2\times 5^3\times 7^2)}\left(iv\right)\frac{9}{35}\left(v\right)\frac{77}{210}\left(vi\right)\frac{32}{147}\left(vii\right)\frac{29}{343}\left(viii\right)\frac{64}{455}$