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A bag contains $5$ red and $7$ black balls. If two balls are drawn successively without replacement, then the probability that the first one is red and the second is black is

Find the transaction in which IGST is paid.
[ Different portions are different states ]

Find the LCM and HCF of 198 and 144 and verify HCF and LCM equal to product of numbers

Find the Surface Area(in $c{m}^2$) of :

How many terms of an AP 27, 24, 21, ... are required to get the sum as 0?

The longest sides of a triangle is 3 times the shortest side and the third side is 2cm shorter than the longest side. If the perimeter of the triangle is at least 61 cm. Find the minimum length of the shortest side.

What is the formula for the lateral surface area of the given frustum:

Where,
$R_1$ = radius of the base
$L$ = length of lateral side of the bigger cone of which the frustum is a part
$R_2$ = radius of the top surface
$l$ = length of lateral height of cone - lateral height of frustum(s) (L - s)

Use graph paper for this question.

The table given below shows the monthly wages of some factory workers.

(i) Using the table, calculate the cumalative frequencies of workers.

(ii) Draw a cumulative frequency curve.

Use 2 cm = Rs. 500, starting the origin at Rs. 6500 on x-axis, and 2 cm = 10 workers on thr y -axis.

$\begin{array}{cccccccc}\text{Wages (in Rs.)}& 6500-7000& 7000-7500& 7500-8000& 8000-8500& 8500-9000& 9000-9500& 9500-10000\\ \text{No. of workers}& 10& 18& 22& 25& 17& 10& 8\end{array}$

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16cm\times 8cm\times 8cm$. When 16 spheres are packed, the box is then filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[use\pi =3.14]$

Find the zeroes of the polynomial 3^1/2x² - 8x + 4(3^1/2)

State, with reason, whether the following are true or false. A, B and C are matrices of order
$2\times 2.$
(i) A + B = B + A
(ii) A - B = B - A
(iii) (B. C ) . A = B. (C . A)
(iv) ( A + B ) . C = A . C + B . C
(v) A. (B -C ) = A. B - A . C
(vi) (A - B ) . C = A. C - B . C
(vii) $A^2-B^2=(A+B)(A-B)$
(viii) $(A-B{)}^2=A^2-2A.B+B^2$

If one zero of the polynomial 3x²=8x+2k+1 is seven times the other then find the other zero and the value of k

For each real number x such that $-1<x<1,letA\left(x\right)bethematrix(1-x{)}^{-1}\left[\begin{array}{cc}1& -x\\ -x& 1\end{array}\right]andz=\frac{x+y}{1+xy}Then,$

Ram has ₹ 500 in a savings account at the beginning of a year. He wants to have at least ₹ 200 in his account by the end of the year. He withdraws ₹ 25 each week for his needs. For how many weeks can he withdraw?

The ratio in which the x-axis divides the segment joining A(3,6) and B(12,-3) is

The probabilty of an event that is certain to happen is:-

ABC is an isosceles ∆ with /ABC = 90^o. A semicircle is drawn with AC as diameter. If AB = BC = 7 cm, find the area of the shaded region.

A, B & C are three points on a circle. The tangent at C meets BA produced at T. Given that ∠ATC = 36^o & ∠ACT = 48^o, calculate the angle subtended by AB at the center of the circle.

There is a stream which flows for 15 km. I have a boat with speed 14 $\frac{km}{hr}$ and a stream with speed x $\frac{km}{hr}$. In how much time can I travel upstream and downstream respectively?Write an expression for that.

Find the point equidistant from the points P(1,3) and Q(-5,-5), and which lies on the line y= -1

What is the maximum number of times when the graph of the polynomial y = $p{x}^3+q{x}^2+rx+s$ attain y = 0?

20 A.Ms are inserted between 2 and 86. Find the 19th A.M.

From the top of a building 20m high, the angle of elevation of the top of a monument is ${45}^{\circ }$ and the angle of depression of its foot is ${30}^{\circ }$. Find the height of the monument.

Find the next number in the following sequence: 42.00, 39.50, 37.00, 34.50, ...

Which of the given formulae is the correct one to find out the roots of the quadratic equation $a{x}^2+bx+c=0$?

Define statistics.what arr the central tenfency meadure and what isthe realtion between them???

Choose the correct option and justify your choice.
(iii)$sin2A$ = 2sinA is true when A=

If $cos\theta =\frac{3}{5}$, show that $\frac{(sin\theta -cot\theta )}{2tan\theta }=\frac{3}{160}$

In figure OQ : PQ = 3 : 4 and perimeter of $\Delta$ POQ = 60 cm. Determine PQ, QR and OP.

A motor boat whose speed in still water is 18 km /hr, takes 1 hour more to go 24 km upstream than to return to the same spot. Find the speed of the stream.

A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Three positive numbers are in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$. Find the numbers if the sum iof their squares is 244.

For a triangle ABC, show that sin$\left(\frac{B+C}{2}\right)$ = cos $\left(\frac{A}{2}\right)$ , where A, B and C are interior angles of $△$ ABC.

How many terms of the GP $\frac{8}{9},\frac{8}{18},\frac{8}{36}$..... should be added to get the sum $\frac{31}{18}$?

Solve the following equation for $x$:-
$x^2-3x-10=0$

Meaning of CIRCUMCENTRE, CENTROID, INCENTRE, ORTHOCENTRE along with each's FORMULAS ?

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Find the zero of the polynomial (x-3)(x+2)

Question:

In △ABC, AB = 3 and, AC = 4 cm and AD is the bisector of ∠A. Then, BD : DC is —

Solution:

BD/DC = AB/AC =34

So, BD : DC = 3 : 4.

In did not understand how we proved the similarity and how we are taking the sides proportionality. Plz explain. Thank you.

Which of the following is correct about dividend: