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Two complementary angles are such that twice the measure of the one is equal to three times the measure of the other. The larger of the two measures

(a) ${72}^{\circ }$

(b) ${54}^{\circ }$

(c) ${63}^{\circ }$

(d) ${36}^{\circ }$

Find the values of x in each of the following:

$\left(i\right)2^{5x}÷2^x=\sqrt[5]{52^{20}}$

$\left(ii\right)(2^3{)}^4=(2^2{)}^x$

$\left(iii\right){\left(\frac{3}{5}\right)}^x{\left(\frac{5}{3}\right)}^{2x}=\frac{125}{27}$

$\left(iv\right)5^{x-2}\times 3^{2x-3}=135$

$\left(v\right)2^{x-7}\times 5^{x-4}=1250$

$\left(vi\right)(\sqrt[3]{34}{)}^{2x+\frac{1}{2}}=\frac{1}{32}$

$\left(vii\right)5^{2x+3}=1$

$\left(viii\right)(13{)}^{\sqrt{x}}=4^4-3^4-6$

$\left(ix\right){\left(\sqrt{\frac{3}{5}}\right)}^{x+1}=\frac{125}{27}$

If $a=\sqrt{2}+1$, then find the value of $a-\frac{1}{a}$.

ABCD is a parallelogram. DK is perpendicular to BA produced at K and DM is perpendicular to BC produced at M. Find the measure of $\angle KDM.$

Solve for x

( ³√4)^2x+1/2 = 1/32

Why did we plot 2/9 in between 0 and 1 whereas 5/2 in between 2 and 3

Factorise the polynomial x²ⁿ+ 5xⁿ + 6

Which of the given statements is incorrect

1.Diagonals of the parallelogram bisect each other.
2.If the Diagonals of a quadrilateral bisect each other,it is a parallelogram.
3.Diagonals of a parallelogram are equal.
4.Diagonals of the parallelogram are perpendicular to each other

Measure of the four angles ∠A, ∠B, ∠C and ∠D in the given parallelogram will be

Expression of 2.2323… in the form of ^a/_b is ________.

$A,B$ and $C$ are three points on a circle such that the angles subtended by the chords $AB$ and $AC$ at the centre $O$ are ${90}^{\circ }$ and ${110}^{\circ }$ respectively. Then the measure of angle $BAC$ is

If a sheet measuring 1m² costs Rs 15. The cost of sheet required for making a cuboidal box of dimension 5 m × 6.5m × 6 m is

In the given figure, QR and PQ are the tangents for the inner circle through A and B respectively. If OP = 10 cm and OB = 8 cm, what is the length of QR?

Which of the following points is wrongly plotted in the graph shown below?

Find the area of a quadrilateral ABCD in which diagonal AC is 10 cm & lengths of perpendiculars from the vertices B & D on it are 5 cm & 6 cm respectively.

The angles of a quadrilateral are (5x)^o, (3x + 10)^o, (6x – 20)^o and (x + 25)^o. Now, the measure of each angle of the quadrilateral will be

Factorise :

$20a^2-45b^2$

In figure, ∠POR = 3x and ∠QOR = 2x + 10 . The value of x for which POQ is a straight line, is

Which of the following lines contain the point (1, 2)?

To clear his doubt, John decided to take help of Byjus classes videos. While going through the video, He found that some of the fractions can be written as combination of whole number and a proper fraction. Which of the following represents 13/3 in that form?

$\text{Each side of an equilateral triangle measures 8 cm. The area of the triangle is}\left(a\right)8\sqrt{3}c{m}^2\left(b\right)16\sqrt{3}c{m}^2\left(c\right)32\sqrt{3}c{m}^2\left(d\right)48c{m}^2$

$\text{A spherical ball of radius 3cm is melted and recast into three spherical balls.The radii of two of these balls are 1.5cm and 2cm.The radius of the third ball is}\left(a\right)1cm\left(b\right)1.5cm\left(c\right)2.5cm\left(d\right)0.5cm$

$\text{How many planks of dimensions}5m\times 25cm\times 10m.\text{can be stored in a pit which is 20 m long, 6 m wide and 80cm deep?}$

In a parallelogram ABCD, If $\angle DAB={75}^{\circ }$ and $\angle DBC={60}^{\circ },then\angle BDC=$

Show that (p -1) is a factor of $(p^{10}-1)$ and also of $(p^{11}-1)$.

ABCD is a cyclic quadrilateral whose side AB is a diameter of the circle through A, B, C and D. If $\angle ADC={130}^{\circ }$, then find $\angle BAC$.

IF a + b + c = 9 and ab + bc + ca = 40, Find $a^2+b^2+c^2.$

Which of the following statements is false?

(a) Through a given point, only one staright line can be drawn.

(b) Through two given point, it is possible to draw one and only one straight line.

(c) Two straight lines can intersect only at one point.

(d) A line segment can intersect only at one point.

1. 32

In the given figure, quadrilateral ABCD is circumscribed and AD $\perp$ AB. If the radius of incircle is 10 cm, find the value of x.

Which of the following statements is true about the figure given below?

Given : $\angle$ ABD = 110${}^{\circ }$

The standard deviation of the first n natural numbers is

The mean of the following distribution is:

$$\begin{array}{ccccc}{x}_i& 15& 10& 12& 20\\ f_i& 2& 5& 7& 6\end{array}$$

If the class Mark in a frequency distribution are 19.5,26.5,33.5,40.5,47.5,54.5,61.5, then the class size of distribution is

factorize: 2√2a³+16√2b³+c³-12abc

If $a+b+c=0$ then find value of $\frac{a^2}{bc}+\frac{b^2}{ac}+\frac{c^2}{ab}$

Temperature in Fahrenheit is given as,

$\frac{C}{5}=\frac{F-32}{9}$

Where C and F are temperatures in Celsius and Fahrenheit respectively.

What is the temperature in Fahrenheit if it is 45 degrees Celsius?

If $\frac{a}{b+c}$ = $\frac{b}{c+a}$ = $\frac{c}{a+b}$ and $a+b+c\ne$ 0, value of $a$ is .

Find the volume of a cuboid whose length is 24 cm , breadth is 12 cm and height is 13 cm.

Find the value of (12m – 15n)²

The above table depicts the age group of people living in an apartment. Since the group width is unequal find the length of rectangle with respect to age group width 5 per interval.

$\begin{array}{cc}agegroup& numberofpeople\\ 10-19& 12\\ 20-24& 13\\ 25-29& 36\\ 30-34& 15\end{array}$
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Statement 1: The value of the polynomial \({x}^{5} + 2{x}^{4} + 3{x}^{3}+ {x}^{2}– 7x + 8\) at x = -1 is 14.

Statement 2: The polynomial \({x}^{5} + 2{x}^{4} + 3{x}^{3}+ {x}^{2}– 7x + 8\) when divided by x + 1, gives 14 as remainder.