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The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 cm. The length of the wire is

Find out the mode od the following data:

Is the sequence, whose general term is 5n² + 2n + 3 an AP?

If $f\left(x\right)=x^2+2bx+2c^2$ and $g\left(x\right)=-x^2-2cx+b^2$ such that in $f\left(x\right)>maxg\left(x\right)$, then the relation between $b$ and $c$, is

Solve:
$4[1–si{n}^2\theta ][1+ta{n}^2\theta ][1+cose{c}^2\theta ]$

Which of the following satisfies the equation $a^2{b}^2{x}^2-b^{2}x-a^{2}x+1=0?$

$\frac{sinA-sinB}{cosA+cosB}+\frac{cosA-cosB}{sinA+sinB}=$

Area of rectangle = 12.5 sq cm, What will be the ar(||gram) which lies on the same base and same parallels?

If all corresponding angles of two triangles are equal and the corresponding sides are proportional, then the triangles can be said to be __________.

If Q (0, 1) is equidistant from P (5, - 3) and R (x, 6), find the value of x.

In the above scenario, after drawing the circle with radius R, what is the next thing to be constructed?

The inner radius of a hollow iron sphere of thickness 1 cm is 9 cm. Find the volume of iron used to make the ball.

The nature of roots of $x^2-3x+2=0$ will be:

Let $c_1:x^2+y^2=1;C_2:(x-10{)}^2+y^2=1and{C}_3;x^2+y^2-10x-42y+457=0$ be three circle.A circle C has been drawn to touch circles $C_1$ and $C_2$ externally and $C_3$ internally. Now circles $C_1,C_2$ and $C_3$ start rolling on the circumference of circle C in anticlockwise direction with constant speed. The centroid of the triangle formed by joining the centres of rolling circles $C_1,C_2$ and $C_3$ lies on

Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating decimal expansion : $\frac{64}{455}$ [1 MARK]

The sum of reciprocals of Arjun’s ages $3$ years ago and $5$ years from now is $\frac{1}{3}$. His present age is ___ years.

$A.8$

$B.7$

$C.6$

$D.5$

In order to confirm whether two triangles are similar based on their angles, the values of how many angles are required?

A circular garden of radius 10 m is divided into two parts by a straight line fence. Smaller part is the walking area and flowers are planted in the larger part. The fence is at a distance of 6 m from the centre of the garden. What is the walking area in $m^2$? It is given that cos 53°= $\frac{3}{5}.$

Draw the graph of the equation x = 4 [2 MARKS]

If A, B and C are the angles of a $\Delta ABC,$ prove that $tan\left(\frac{C+A}{2}\right)=cot\frac{B}{2}$.

Draw the graphs of the following equations on the same graph paper:

$2x-y+2=0,2x+y=6.$

Find the coordinates of the vertices of the shape formed by these lines. Also, find the area of the shape.

Find the value of a and b for which the given system of equations has an infinite number of solutions :
4x + 6y = 14 ; (a + b + 1) x + (a + 2b + 2)y = 4 (a + b) + 1

Find the area of $△ABC$ with A(1, -4) and midpoints of sides through A being (2, -1) and (0, -1)

Solve each of the following quadratic equations:
(i) $\frac{1}{x-1}-\frac{1}{x+5}=\frac{6}{7},x\ne 1,-5$
(ii) $\frac{1}{2x-3}-\frac{1}{x-5}=1\frac{1}{9},x\ne \frac{3}{2},5$

The radii of two circles are 19 cm and 9 cm. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

The length of a rectangle is twice its breadth and its area is 288 $c{m}^2$. Find the dimensions of the rectangle.

If A (-3, 5), B (-2, -7), C (1, -8) and D (6, 3) are the vertices of a quadrilateral ABCD, find its area.

Construct a triangle ABC in which BC is 8 cm, Angle B is ${75}^{\circ }$and AB+AC=15cm by using the method of perpendicular bisector.by using the method of perpendicular bisector.

The sides of $\Delta \text{ABC}$ are $6cm,8cm$ and $10cm.$ Find the perimeter of the larger triangle which is similar to $\Delta \text{ABC}$ if the ratio of corresponding sides is 2.

A point P is 25 cm from the centre of a circle. The radius of the circle is 7 cm and length of the tangent drawn from P to the circle is $x$ cm. The value of $x$ is ___ cm.

In an art class, suneha sketched a design using geometrical shapes with the help of colours in the following way:

If in the figure, circles in black and blue are the circumcircle and incircle (of the equilateral $\Delta PQR)$ respectively, Then $\angle BAC$ is equal to

In the following figure, what is $\angle ABD$

Find the harmonic mean of the given numbers

$\frac{1}{2},\frac{1}{4},\frac{1}{6}$

There is a hypothetical 2 dimensional building of height 5h and width h. Each floor of the building is of height $\frac{h}{2}$. From the top of the $4^{th}$ floor of this building, there is a slab of length h protruding out of the building, perpendicularly. There is also an infinitely long pole, erected vertically on the terrace of the building. The foot of this pole is on the other end of the building with respect to the slab. A naughty child from the $4^{th}$ floor crawls onto the slab and tries to see the pole. What is the minimum length of the pole the child cannot see (height measured from the foot of the pole)? Assume that the child is of negligible height and always stays on the slab. The slab is in the same plane as that of the building.

A bag contains 5 red 8 white and 7 black balls.A ball is drawn at random from the baground. Find the probability that the drawn ball is :

1.red or white

2.not black

3.neither white or black.

When X is divided by 237, the remainder is 192. When Y is divided by 117, the quotient is the same but the remainder is 108. The remainder when the sum of X and Y is divided by 118 is ?

If log(a^2+9)base 5=2,then a = __________

Abhay and Beena are partners in a firm. They admit Chetan as a partner with 1/4th share in the profits of the firm. Chetan brings Rs 2,00,000 as his share of capital. The value of the total assets of the firm is Rs 5,40,000 and outside liabilities are valued at Rs 1,00,000 on that date. Give the necessary entry to record goodwill at the time of Chetan's admission. Also show your working notes.

Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:

A Book is to be sent as a gift to a person.

The shopkeeper has to gift wrap the book which is in a box of dimensions 20cm × 10cm × 5cm. The quantity of gift wrap(assuming negligible thickness) required would be___________.

Which of the following is a factor of $x^3-5x^2-2x+24?$

Which of the following is true if $0°\le \theta <90°?$