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Shruti can row downstream 30 km in 3 hours, and upstream 10 km in 5 hours. Find her speed of rowing in still water and the speed of the current.

Find the equation of a line through (–2, 3) and perpendicular to 3 = 2 + 1

If $P(x,y,z)$ is a point on the line segment joining $Q(2,3,4)$ and $R(3,5,6)$ such that the projections of the vector $\overrightarrow{OP}$ on the coordinate axes are $\frac{13}{5},\frac{21}{5},\frac{26}{5}$ respectively, where $O$ denotes the origin, then $P$ divides $QR$ in the ratio

In figure, BC is a tangent to the circle with centre O. OE bisects AP. Prove that $\Delta AEO\sim \Delta ABC$.

Sakshi invests a part of ₹ 12,000 in $12\%$ stock at ₹ 120 and the remainder in $15\%$ stock at ₹ 125. If her total dividend per annum is ₹ 1360, how much does she invest in $12\%$ stock at ₹ 120?

Sum of probabilities of all outcomes in an experiment is__

Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder.

$p\left(x\right)=x^4-5x+6,g\left(x\right)=2-x^2$

Each of A and B opened a recurring deposit account in a bank. If A deposited Rs 1,200 per month for 3 years and B deposited Rs 1,500 per month for $2\frac{1}{2}$ years: find, on maturity, who will get more amount and by how much ? The rate of interest paid by the bank is 10 % per annum.

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

Find the value of x?



x + y = 5

3x - y = 3

Which among the following is the solution of $3x+4y=6?$

______ is a line that touches a circle at only one point, and ______ is a line that intersects a circle at two distinct points.

If $x+1$ is a factor of $2x^3+a{x}^2+2bx+1$, then find the value of a and b given that $2a-3b=4$.

A carton of 26 bulbs contains 6 defective bulbs. One bulb is drawn at random. If the selected bulb is defective, what is the probability that the second bulb drawn is defective?

Samaira heard 3 bells toll together at 10:00 AM. The first bell tolls after every 5 second, the second tolls after every 9 seconds and the third tolls after every 10 seconds. When will they toll together again?

If the area of a circle is $1386{\text{cm}}^2$, then its perimeter is

In the cyclic quadrilateral WXYZ on the circle centred at O, $\angle ZYW={10}^{\circ }$ and $\angle YOW={100}^{\circ }$. What is the measure of $\angle YWZ$?

a forester wants to plant 66 apple trees, 88 banana trees and 110 mango trees in equal rows(in terms of number of trees). also he wants to make distinct rows of trees (i.e. only the type of tree in the row) find the number of minimum rows required

A single card is chosen at random from a standard deck of 52 playing cards. What is the probability that the card will be a club or a king?

The 19th term of an A.P. is equal to three times its sixth term. If its 9th term is 19, find the A.P.

Find the number of non-negative terms of the following sequence: 987, 932, 877,…

How many balls, each of radius 1 cm, can be made from a solid sphere of lead of radius 8 cm ?

Draw the graphs of the equations 5x - y = 5 and 3x - y = 3. Determine the co-ordinates of the vertices of the triangle formed by these lines and y-axis. Calculate the area of the triangle so formed.

Question 9

Which of the following vary inversely with each other?

(a) Speed and distance covered

(b) Distance covered and taxi fare

(c) Distance travelled and time taken

(d) Speed and time taken

Consider the following pair of equations:

$2x+4y-5=0$

$px+qy-12=0$

Find the probability, such that a given pair of equations represent parallel lines, where the value of $p$ and $q$ is decided by rolling a pair of dice simultaneously.

A unit vector along $3\hat{i}+4\hat{j}$ is

The angles of a 9 sided polygon are in AP . Which degree measure is always a term of the series

Find the area of the sector of a circle having radius 6 cm and of angle ${30}^{\circ }$. [Take $\pi$= 3.14 ]