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For what value of $m$ is $x^3–2m{x}^2+16$ is divisible by x + 2?

Determine whether the following is a statistical question if data pertaining to internet searches is available.

How many internet searches do residents at Jacque’s retirement home perform each day? (Yes/No)

If a polynomial cuts the x-axis at 3 points and y-axis at 2 points, then the number of zeroes of the polynomial would be ___ .

Simplify $\sqrt[4]{4\sqrt[3]{3x^2}}$ and express the result in the exponential form of x.

Evaluate:

(i) $lo{g}_{10}0.01$

(ii) $lo{g}_2(1÷8)$

If $({5x}^2+14x+2{)}^2$ – $({4x}^2+14x+2{)}^2$ is divided by $(x^2+x+1)$, then quotient q and remainder r are given by -

Factorise:

$(a-b+c{)}^2+(b-c+a{)}^2+2(a-b+c)(a-c+a)$

Rohan has n number of marbles. If the value of n can be expressed as $\sqrt{{\left(15625\right)}^{{\left(\frac{1}{\sqrt{3}}\right)}^2}},$ then the probability of getting a marble is



रोहन के पास n कंचे हैं। यदि n का मान $\sqrt{{\left(15625\right)}^{{}^{{\left(\frac{1}{\sqrt{3}}\right)}^2}}}$ के रूप में व्यक्त किया जा सकता है, तब एक कंचा प्राप्त होने की प्रायिकता है

$\text{Solve for}x\text{in the equation}$ $log\left[log\right(2+lo{g}_2(x+1)\left)\right]=0$

''Census data being used to analyze the impact of education'' is an example for _______________ data

A. Primary

B. Secondary

Four points A, B, C, D are given on a circle. Line segment AB and CD are parallel. Find the area of the figure formed by joining these points (in ${cm}^2$).

Which of the following denotes the length of the curve in red in the given circle?

Solve the given expression, and choose the correct option.



$(6\frac{6}{7}-\frac{2}{7})+(4\frac{4}{7}-\frac{1}{7})$

The sum of the first n terms of a sequence is given by $5^{n+1}-5$. Find the ratio of (m)${}^{th}$ and (m+3)${}^{th}$ term of the sequence.

The average marks of the students in Mathematics of class $8^{th}$ is 45. But most of the students were given 60 out of 100.The Median of the class would be:

1. \N

Two poles of heights 6 m and 11 m stand on a plane ground. If the distance between the feet of the poles is 12 m, then find the distance between their tops.

Why is a first degree polynomial in two variables ax + by + c = 0, called a linear equation?

The internal length, breadth and height of a rectangular box A is 20 cm, 18 cm and 15 cm respectively and that of the box B are 18cm, 12cm and 5 cm respectively. The volume of box A is how many times that of B?

In the given figure, BA and BC are the tangents on a given circle from point B. What is the diameter of the given circle (in cm)?

Question 8

Ashima took a loan of Rs 100000 at 12% per annum compounded half-yearly. She paid Rs 112360. If $(1.06{)}^2$ is equal to 1.1236, then the period for which she took the Loan is

(a) 2 yr

(b) 1 yr

(c) 6 months

(d)$1\frac{1}{2}yr$

Question 11 (ii)
In the given figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that:

(ii) ar(AEDF) = ar(ABCDE)

A solid rectangle has length, breadth and height as 15 cm, 8 cm, and 20 cm, respectively. It is cut into two triangular prisms along the diagonal as shown in the figure. Find the total surface area of each prism.

Amit lent out Rs. 900 on the condition that the loan is payable in 10 months in 10 equal instalments of Rs. 100 each. Find the rate of interest per annum.

The cost of a notebook is twice the cost of a pen. Write a linear equations in two variables to represent this statement.

Factorize $8x^3-125y^3+180xy+216$

Among the following, the terminating rational number is .

The base of a prism is a rectangle of sides 5 cm and 12 cm and its height is 20 cm. It is split vertically along the diagonal of the base into two triangular prisms. What is the lateral surface area of each of these triangular prisms?