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The volumes of two spheres are in the ratio 64:27 and the sum of their radii is 7 cm. What is the difference in their total surface areas?

If a coin is tossed 3 times, what is the probability of getting a tail each time?

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the feet of the trees is –

Two years ago Salim was thrice as his daughter and six years later the he will be four year older than twice her age How are they now?

Let $f\left(x\right)=a{x}^2+bx+c$. Then, match the following :
$\begin{array}{cc}a.\text{Sum of roots of f(x) = 0}& 1.–\frac{b}{a}\\ b.\text{Product of roots of f(x) = 0}& 2.\frac{c}{a}\\ c.\text{Roots of f(x) = 0 are real \& distinct}& 3.b^2–4ac=0\\ d.\text{Roots of f(x) = 0 are real and identical.}& 4.b^2–4ac>0\end{array}$
The correct matching is -

Question 115

A cylindrical tank has a radius of 154 cm. It is filled with water to a height of 3m. If water to a height of 4.5 m is poured into it, what will be the increase in the volume of water in kL?

Look at the given graph and find out the range and domain of the function shown below.

1. 1.5

TanA+cot A

Question 11

A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet?
$(Take\pi =3.14)$

Let a matrix $A=\left[\begin{array}{cc}-1& -5\\ 0& 1\end{array}\right],$ then which of the following statement(s) is(are) correct for natural number $n\in N$

(where $I$ is unit matrix of order $2.$)

Question 3

Show that the square of any positive integer cannot be of the form 5q + 2 or 5q + 3 for any integer q.

The geometric representation of a quadratic equation is shown in the given figure. If the numeric value of $\beta$ is greater than the numeric value of $\alpha$, then the quadratic equation can be

The ratio in which the line segment PQ, where P (-5, 2) and Q (2, 3), is divided by the y-axis is

Construct two circles of radii 2 cm and 3 cm, whose centres are 8 cm apart. Construct a transverse common tangent.

On a square handkerchief of side 50 cm, seven non-intersecting circles designs of each radius 7 cm are made. Find the area of the remaining portion of the handkerchief in $c{m}^2$.

Evaluate the value of the following expression:

$A=\frac{\cos {58}^{\circ }}{\sin {32}^{\circ }}+\frac{\sin {22}^{\circ }}{\cos {68}^{\circ }}-\frac{\cos {38}^{\circ }cosec{52}^{\circ }}{\tan {18}^{\circ }\tan {72}^{\circ }}$

In a school of 100 students, only 2 sports – cricket and football are entertained. 40 play only cricket and 40 play only football. If each of 100 students play at least one of the sports. Find the number of students who play both the sports.

Find the zeroes of the polynomial x^2+1\6x-2

A man invests ₹60,000 in shares of a company which pays 12 % dividend at a time when a ₹100 share costs ₹120. Find :-

a) Number of shares he bought.

b) the annual income from his shares.

In below shown figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ. Then $\Delta$PQR is __ Triangle.

If $a,a+b,a+2b$ are zeroes of the cubic polynomial $x^3-6x^2+3x+10$ , then $a+b=$________.

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

(a) 4953 $c{m}^2$ (b) 4952 $c{m}^2$ (c) 4951 $c{m}^2$ (d) 4950 $c{m}^2$