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What is the area of the blue part as a fraction of the whole regular hexagon?

In the given figure, ABCD is a parallelogram, M is the midpoint of BD and BD bisects $\angle B$ as well as $\angle D$. Then, $\angle AMB=$ ?

(a) ${45}^{\circ }$

(b) ${60}^{\circ }$

(c) ${90}^{\circ }$

(d) ${30}^{\circ }$

If $a^2+b^2+c^2=1$, then what could be the value of (ab + bc + ac)?

Chords AB & CD of a circle are parallel to each other and lie on opposite sides of the centre of the circle. If AB = 36 cm, CD = 48 cm and the distance between the chords is 42 cm. Find the radius of the circle.

If triangle ABC is an isosceles triangle in which AB = AC = 13 cm then find the value of $\frac{\text{area of}\Delta ADC}{\text{area of}\Delta EFB}.$

Express 2.5434343..... In the form of p/q where p and q are integers and q is not equal to zero.

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

Question 120

What's the error? Ramu evaluated the expression - 7 - (- 3) and came up with the answer - 10. What did Ramu do wrong?

1. 90

The surface area of a sphere is 32π cm${}^2$. Find the radius and volume of this sphere?

In the square ABCD below, what is the measure of $\angle AOB$?

Match the two columns;



$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{(A) C is a point on the minor arc AB of the circle with centre O.}& {\text{(P) 60}}^{\circ }\\ \text{Given}\angle \text{ACB = x. Calculate}\angle \text{x if ACBO is a parallelogram.}& \\ \text{(B) Chord ED is parallel to the diameter AC of the circle.}& {\text{(q) 120}}^{\circ }\\ \text{Given}\angle {\text{CBE = 55}}^{\circ }\text{, calculate}\angle \text{DEC.}& \end{array}$



$\begin{array}{cc}\text{(C) In the given figure,O is the centre of the circle.}& {\text{(r) 35}}^{\circ }\\ \text{If}\angle {\text{ACB = 60}}^{\circ }\text{find}\angle \text{OAB.}& \end{array}$







$\begin{array}{cc}\text{(D) In the given figure, O is the centre of a circle.}& {\text{(s) 30}}^{\circ }\\ \angle \text{AOB = 400 and}\angle \text{BDC = 1000. Find}\angle \text{OBC}& .\end{array}$

Choose the Correct option;

Question 1 (iv)

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

$4u^2+8u$

If we take a circle and a hemisphere of the same radius, then the total surface area of the hemisphere is___ times the area of the circle.

If 2 is a zero of the polynomial $p\left(x\right)$ and one zero is half of the other zero. Which of the following expressions can $p\left(x\right)$ be?

Question 68

In the given figure. How many line segments are there? Name them.

The number that should be multiplied with $(\sqrt[3]{381}-\sqrt[3]{39}+1)$ to make it rational is

Question 62

In the following question, fill in the blanks to make the statements true.

By solving $(6^0-7^0)\times (6^0+7^0)$, we get ___ .

Let $x=\frac{p}{q}$ be a rational number, such that the prime factorisation of $q$ is not of the form $2^m{5}^n$, where $n,m$ are non-negative integers. Then, $x$ has a decimal expansion which is

Find the roots of the equation, $x-5=0$

Factorise: $\sqrt{ab}(x^2+1)+x(a+b)$

Question 71

State whether the following statement is true or false:

If $a^2$ ends in 9, then $a^3$ ends in 7.

In the parallelogram AMKR, KA is equal to

In the following, the set of measures which can form a triangle

If two similar triangles have a scale factor of a : b, then the ratio of their areas is

Factorize:

$x^2+5\sqrt{5}x+30$

How many irrational numbers lie between $2$ and $3$? Find any three irrational numbers lying between $2$ and $3$.

One angle of a parallelogram is twice the adjacent angle. Angles of the parallelogram are:

If the angles of a hexagon are of measures xo, (x-5)^o,(x-5)^o, (2x-5)^o, (2x-5)^o and (2x+10), then the value of x is

The marks obtained by 12 students in a mathematics examination are given below.

48, 78, 93, 90, 66, 54, 83, 58, 60, 75, 89, 84.

Find (i) the mean of the marks; (ii) the mean mark of the students if each student is given 4 grace marks.

Two solutions of this equation 2x + y = 1 are

If a sphere of radius $9cm$ is cut into 27 smaller spheres then, the radius of each smaller sphere is .

Match the given expressions with their resultants.

1. 2

ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
MD $\perp$ AC .

Choose the correct answer in each of the following :

If the volumes of two cones be in the ratio 1:4 and the radii of their bases be in the ratio 4:5 then ratio of their heights is

(a) 1:5 (b) 5:4 (c) 25:16 (d) 25:64