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The remainder when the polynomial p(x)= x³ – 3x² + 2x – 1 is divided by x-2 is

If a transversal intersects two parallel lines, then each pair of corresponding angles is ………

In the following figure, PT is the bisector of ___________.

What should be added to each of the numbers 13, 17 and 22 so that, the resulting numbers are in continued proportion?

Continued proportion means a:b : : b:c

In which of the following equations is x and y in inverse proportion ?

In the given figure, AF is parallel to CD, ED is parallel to FC and AD is parallel to BI. J is the mid point of AI. What will be the ratio of $\frac{\text{Area of trapezium AJCB}}{\text{Area of parallelogram EFCD}}$?

The base of a triangular field is 2.4 times its height. If the cost of levelling the field at the rate of Rs 20 per square meter is Rs 9600, then the height of the field is _______________ m.

1. 61

In the area theorem, triangles between the two parallel lines should have___.

In given figure $△$ ABC and $△$ DEF are similar, BC=4cm, EF=5cm, and area of triangle ABC=32$c{m}^2$ find the area of $△$ DEF

Question 33

$25.4\times 1000=$ ___.

Arrange the following rational numbers in ascending order: $\frac{12}{16}$,$\frac{4}{9}$ and $\frac{6}{10}$

The sums of the deviations of a set of n values $x_1,x_2,....,x_n$measured from 15 and -3 are -90 and 54 respectively.Find the value of n and mean.

Hameed has built a cubical water tank with lid for his house, with each outer edge 1.5m long. He gets the outer surface of the tank excluding the base, covered with square tiles of side 25 cm. Find how much be would spend for the tiles, if the cost of tiles is Rs. 360 per dozen.

Choose the correct answer in each of the following questions:
Let m be the midpoint and u be the upper class limit of a class in a continuous frequency distribution. The lower class limit of the class is
(a) 2m - u
(b) 2m + u
(c) m - u
(d) m + u

Rearrange 4x - 2y + 8 = 0 in the form y = mx + c, and determine the Y intercept of the line. Does this line pass through (1,6). [3 MARKS]

Factorise:

$x^2-y^2-4xz+4z^2$

If a and b are different primes such that $\left(i\right){\left[\frac{a^{-1}{b}^2}{a^2{b}^{-4}}\right]}^7÷\left[\frac{a^3{b}^{-5}}{a^{-2}{b}^3}\right]=a^x{b}^y,findxandy.$

$\left(ii\right)(a+b{)}^{-1}(a^{-1}+b^{-1})=a^x{b}^y,findx+y+2.$

If $a^2+b^2+c^2=16$ and ab + bc + ca = 10, find the value of a + b + c.

Question 70

The largest square that can be drawn in a circle has a side whose length is 0.707 times the diameter of the circle. By this rule, find the length of the side of such a square, when the diameter of the circle is
(a) 14..5 (b) 8.63

If measures opposite angles of a parallelogram are $(60-x{)}^{\circ }and(3x-4{)}^{\circ },$ then find the measures of angles of the parallelogram.

What is the median of the following data: 1, 4, 7, 3, 9, 5, 3, 2, 7.

If a - b = 6 and ab = 20, find the value of $a^3-b^3$.

In a right angled triangle ABC in which ∠A = ${90}^{\circ }$, If AD $\perp$ BC.

If D and E are respectively the midpoints of the sides AB and BC of $\Delta ABC$ in which AB = 7.2 cm, BC = 9.8 cm and AC = 3.6 cm then determine the length of DE.

The heights of 75 stucents in a school are given below:
$\begin{array}{ccccccc}\text{Height (in cm)}& 130-136& 136-142& 142-148& 148-154& 154-160& 160-166\\ \text{Number of students}& 9& 12& 18& 23& 10& 3\end{array}$
Draw a histogram to represent the above data.

In the figure, ABC is an equilateral triangle. Find $\angle BDCand\angle BEC$.

If a, b, c are positive real numbers, then $\sqrt[5]{53125a^{10}{b}^5{c}^{10}}$ is equal to

The factors of $a^3+b^3+c^3-3abc$ are

When $5pq(p^2-q^2)$ is divided by $2p(p+q)$ and substituting $p=3$, $q=1$ the value obtained is _______ .

The table below gives data about the number of homework questions that the math teacher gave in the last 20 days.

$$\begin{array}{ccccc}No.ofQuestionsinaday& 0& 1-5& 6-10& 10+\\ Numberofdays& 2& 10& 5& 3\end{array}$$

Find the probability that on any given day, she will give

(i) More than 5 questions
(ii) No homework
(iii) More than 10 questions
(iv) Comparing (i) and (iii), which is greater, and why?

Two coins are tossed 500 times and the out comes are:
No tail: 130, One tail: 235, Two tails: 135
Find the Probability of getting one tail.

In the figure, ABC is a right triangle right angled at A. BCED, ACFG and ABMN are squares on the sides BC, CA and AB respectively. Line segment $AX\perp DE$ meets BC at Y Show that
$\left(i\right)△MBC\cong △ABD\left(ii\right)ar\left(BYXD\right)=2ar\left(△MBC\right)\left(iii\right)ar\left(BYXD\right)=ar\left(ABMN\right)\left(iv\right)△FCB\cong △ACE\left(v\right)ar\left(CYXE\right)=2ar\left(△FCB\right)\left(vi\right)ar\left(CYXE\right)=ar\left(ACFG\right)\left(vii\right)ar\left(BCED\right)=ar\left(AMBN\right)+ar\left(ACFG\right)$

Factorize:

$x^2-2\sqrt{2}x-30$

Factorise:
$a-b-a^2+b^2$

The marks obtained by a student in different subjects in an exam are given below.

$\begin{array}{cc}\text{Subject}& \text{Marks}\\ \text{English}& 77\\ \text{Hindi}& 90\\ \text{Maths}& 70\\ \text{Physics}& 86\\ \text{Chemistry}& 85\\ \text{Biology}& 97\\ \text{Computer Sci.}& 59\\ \text{History}& 62\\ \text{Geography}& 100\\ \text{Moral Sci.}& 75\end{array}$

Find the probability that in an exam, she will score
(i)100
(ii)80 or more
(iii) less than 60. [4 MARKS]

Three metal cubes with edges 6 cm, 8 cm and 10 cm respectively are melted together and formed into a single cube. Find the volume surface area and diagonal of the new cube.

For what value of c will ax + by + c = 0 pass through the origin?

If the base radius and the height of a right circular cone are increased by 20 %,then the percentage increase in volume is approximately

If any two adjacent angles in a quadrilateral are supplementary, then the quadrilateral is

Difference of any two sides of a triangle is ................... than the third side

Find the remainder when $x^3-4x^2+5x-1$ is divided by $2x+1$.