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Find the measure of the complement of an angle 37degree 42'34".

Prove that the right bisector of a chord of a circle, bisects the corresponding arc of the circle.

Write the rationalisation factor of $\sqrt{5}-2$.

In the following figure, ABC and BDE are two equilateral triangles such that D is the mid-point of BC. If AE intersects BC at F, show that

(i)

(ii)

(iii)

(iv)

(v)

(vi)

[Hint: Join EC and AD. Show that BE || AC and DE || AB, etc.]

ABCD is a trapezium with $AB\parallel DC$. E and F are points on non-parallel sides AD and BC respectively such that $EF\parallel AB$. Show that $\frac{AE}{ED}=\frac{BF}{FC}$.

The distance between the tops of two trees 20 m and 28 m high is 17 m. The horizontal distance between the trees is:

Among the following, the terminating rational number is .

If one angle of a parallelogram is ${90}^0$ and its adjacent sides are equal, it is a

ABCD is a rectangle in which OB = x + 2 and AC = 5x - 2. Find the measure of AC.

ABCD is a cyclic quadrilateral whose diagonals intersect at a point E. If $\angle DBC={70}^{\circ }$ and $\angle BAC={30}^{\circ }$, then $\angle BCD$= ___. Further, if AB = BC, then $\angle ECD$ = ___.

Match the following identities with their correct answers.

$(\sqrt{a}-\sqrt{b})\times (\sqrt{a}+\sqrt{b})=$

In the pair of equations $a_{1}x+b_{1}y+c_1=0$ and $a_{2}x+b_{2}y+c_2=0$,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

Statement 1 : This is an inconsistent pair of linear equations.

Statement 2 : There exists infinitely many solutions.

Statement 3 : The lines representing these linese are parallel.

Which of the above statements is/are true?

If $A=\left[\begin{array}{cc}2& -1\\ -1& 2\end{array}\right]$ and $I$ is the unit matrix of order $2,$ then $A^2$ is equal to

Total revenue of a firm rises from Rs. 400 to Rs. 500 when the price of its product rises from Rs. 8 per unit to Rs. 10 per unit. Calculate the price elasticity of supply.

Which of the following statements is correct with respect to the movement of the line PQ horizontally towards the right?

1. 3

The blood groups of 30 students of a class are recorded as under
A, B, O, O, AB, O, A, O, A, B, O, B, A, O, O, A, AB, O, A, A, O, AB, B, A, O, B, A, B, O.
(i) Represent this data in the form of a frequency distribution table.

(ii) Find out which is the most common and which is the rarest blood group among these students.

1. 7.3

In the figure, O is the centre of the circle and $\angle BDC={42}^o$. The measure of $\angle ACB$ is

Parth went to Coorg on a holiday. He wanted to make a tent using a canvas cloth and a few bamboo sticks as support. Initially, he made a sketch of the tent as shown in the figure. He wanted to make the tent as an exact replica of the sketch. So, he placed the bamboo stick DE parallel to the ground BC and AG perpendicular to the ground. Let’s analyse his sketch.





In order to replicate the sketch, Parth wanted to find out the ratio in which DE divides AC. The ratio $\frac{AE}{EC}=$



[ 1 mark]

For real values of $x$, the minimum value of the fuction $f\left(x\right)=exp\left(x\right)+exp(-x)$ is

The perpendicular distance of the point P (4,3) from y-axis is

Given, $\sqrt{2}=1.4141and\sqrt{6}=2.449,findthevalueof\frac{1}{\sqrt{3}-\sqrt{2}-1}$ correct to 3 places of decimal.