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An aeroplane leaves an airport and flies due north at a speed of 1000 km per hour. At the same time, another aeroplane leaves the same airport and flies due west at a speed of 1200 km per hour. How far apart will be the two planes after $1\frac{1}{2}$ hours ?

A box contains 4 white balls and 6 black balls and another one, 3 white and 5 black. We can choose one box and take a ball. If we want a black ball, which box is the better choice?

According to __ theorem, in a right angled triangle, the square of the hypotenuse is equal to the sum of squares of the other two sides.

The volume of hemisphere with total surface area 115.62 cm² is approximately (Take π= 22/7)

What is the largest positive integer that divides 401 , 436 and 542 leaving remainder 10,11 and 15 respectively?

The $6^{th}$ term of an A.P. is 16 and the ${14}^{th}$ term is 32. Determine the ${36}^{th}$ term.

Two APs have the same common difference. If the first terms of these APs be 3 and 8 respectively, find the difference between the sums of their first 50 terms.

If $18,a,(b-3)$ are in AP, then find the value of $(2a-b)$

A 16 m deep well with diameter 3.5 m is dug up and the earth from it is spread evenly to form a platform 27.5 m by 7 m. Find the height of the platform.

Find the value of x in the diagram below.

Question 38

If the diagonal d of a quadrilateral is doubled and the heights $h_1$ and $h_2$ falling on d are halved, then the area of quadrilateral is ___.

Question 13

By actual division, find the quotient and the remainder when the first polynomial $x^4+1$ is divided by the polynomial (x - 1)

The fifth term of the H.P :

$2,2\frac{1}{2},3\frac{1}{3},......,$ will be

In the given figure, $\angle A={70}^{\circ }$ and $\angle ABC={50}^{\circ }$ , find $\angle DPC$ and $\angle BQC$.

Question 13
The radii of the top and bottom of a bucket of slant height 45 cm are 28 cm and 7 cm, respectively. The curved surface area of the bucket is

(A) $4950c{m}^2$
(B) $4951c{m}^2$
(C) $4952c{m}^2$
(D) $4953m^2$

In a $△$ABC, prove that ${\text{cos}}^{2}A+{\text{cos}}^2(A+\frac{\pi }{3})+{\text{cos}}^2(A-\frac{\pi }{3})=\frac{3}{2}$

If a and b are roots of the equation $x^{2}px+q=0,$then write the value of $\frac{1}{a}+\frac{1}{b}$.

Solve the following system of equations graphically:

2x - 3y + 6 = 0

2x + 3y - 18 = 0

Also, find the area of the region bounded by these two lines and y-axis.

An arc AB forms $\angle AOB$ at the centre of the circle. If I draw 2 arcs with A and B as centre and a fixed radius 'r' such that they intersect at point P. The line OP will ___________ the $\angle AOB$.

Given
$P=\{x:6<3x-9<12,x\in R\}Q=\{x:-1\le 3+4x\le 35,x\in I\}$
Write down the elements of $P\cap Q$