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Write the remainder when the polynomial

f(x) = $x^3+x^2$ -3x + 2 is divided by x + 1,

The length of medians of a $\Delta ABC$ are $6,8,10$ then its area is:

If $D,E,F$ are respectively the mid points of $\overrightarrow{AB},\overrightarrow{AC}$ and $\overrightarrow{BC}$ in $\Delta ABC,$ then $\overrightarrow{BE}+\overrightarrow{AF}=$

List - II gives the coordinates of a point P that divides the line segment AB joining the points given in List -I. Match them correctly.
$\begin{array}{cccc}& List-I& & ListII\\ \left(P\right)& A(-1,3)andB(-5,6)Internallyintheratio1:2& \left(1\right)& (7,3)\\ \left(Q\right)& A(-2,1)andB(1,4)internallyintheratio2:1& \left(2\right)& (0,3)\\ \left(R\right)& A(1,7)andB(3,4)internallyintheratio3:2& \left(3\right)& (\frac{11}{5},\frac{26}{5})\\ \left(S\right)& a(4,-3)andB(8,5)internallyintheratio3:1& \left(4\right)& (-\frac{7}{3},4)\end{array}$

$\text{If LM || AB, AL = 2x - 4, AC = 4x,}\text{BM = x - 2 and BC = 2x + 3 with x >0,}\text{then x is:}$

If x^(2)+y^(2)=89 and xy=40,then find the value of x^(3)+y^(3).

In the figure given, what are the values of a, b and c respectively?

The value of $\frac{\left(2^5\right)}{\left(2^8\right)}\times \left(2^{-7}\right)$ is

If the side of the square is x = 6 cm. then find the area of the square.

Write the following cubes in expanded form:

(i) $(2x+1{)}^3$

(ii)$(2a-3b{)}^3$

(iii) $(\frac{3}{2}x+1{)}^3$

(iv) $(x-\frac{2}{3}y{)}^3$

Question 11

In the following question out of the four options only one is correct, write the correct answer.

The value of S in $\frac{1}{3}+S=\frac{2}{5}$ is :

(a) $\frac{4}{5}$

(b) $\frac{1}{15}$

(c) 10

(d) 0

A proof is required for:

. O is any point in the interior of a triangle ABC. Prove that

1. AB + AC > OB + OC

2.AB + BC + CA > OA + OB + OC

3.OA + OB + OC > 1/2(AB + AC + BC)

The difference between two numbers is 45 and one number is six times the other. Find them.

Two fair dice are thrown together. The probability that the number 5 does not appear on any of them is:

In the figure given below, ABC is a right triangle right-angled at B such that BC = 6 cm and AB = 8 cm. Find the radius of its incircle.

One of the angles of a triangle is 75^o. If the difference of the other two angles is 35^o, then the larger angle of the other two angles of the triangle has a measure of:

In which quadrant of the x-y plane would you plot the point (3,1)?

Question 7 (ii)

AB is a line segment and P is its mid-point. D and E are points on the same side of

AB such that $\angle BAD=\angle ABE\text{and}\angle EPA=\angle DPB$ (See the given figure). Show that

AD = BE

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P(x) is equal to cx+d, c is not equal to 0, c, d are real numbers

In the given figure, AP $\parallel$ BQ $\parallel$ CR. Prove that ar ($△$AQC) = ar ($△$PBR).

[2 MARKS]

Four different positions of the same die are shown. Which number will be at the bottom if $5$ is at the top?

A regular hexagon has a side 6 cm. Its area is:

If $x=9-4\sqrt{5}$, find the value of $x^2+\frac{1}{x^2}$

The distance between the points $2\frac{1}{2}$ and $5\frac{1}{4}$ on the number line is

The total surface area of a hemisphere of radius r is

Among the given options, is a non-terminating and repeating decimal.

The sides of a right-angled triangle are p, p+1 and 5. Find the area of triangle, if the longest side measures 5 cm.