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Which of the following options is equal to the given expresssion?

$\frac{cot({90}^{\circ }-\theta )}{cose{c}^2\theta }$ $\times$ $\frac{sec\theta .co{t}^3\theta }{si{n}^2({90}^{\circ }-\theta )}$

Class size for the following distribution: 0 – 0.25, 0.25 – 0.50, 0.50 – 0.75 is

The graph y = 1/x lies in

All the integers are

Find three different irrational numbers between the rational numbers 5/7 and 9/11

In the adjoining figure, chords AC and BD of a circle with centre O, intersect at right angles at E. If $\angle OAB={25}^{\circ },\text{calculate}\angle EBC.$

$In\Delta ABC,\text{AB = AC and}\angle B={50}^{\circ }.Then\angle A=?\left(a\right){40}^{\circ }\left(b\right){50}^{\circ }\left(c\right){80}^{\circ }\left(d\right){130}^{\circ }$

Factorize:

$y^3+125$

Factorise:
$x^2+6\sqrt{6}x+48$

If $x+\frac{1}{x}=3$, find the value $x^6+\frac{1}{x^6}$.

The angle in a semicircle measures

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

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

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

(d) ${36}^{\circ }$

If two interior angles on the same side of a transversal intersecting two parallel lines are in the ratio 2 : 3, then the measure of the larger angle is

If the $\angle$A, $\angle$B and $\angle$C of $\Delta ABC$ satisfy the relation $\angle$B - $\angle$A = $\angle$C - $\angle$B, then find the measure of $\angle B.$

Below given figure shows map of a village. A denotes the location of temple and B represents location of school. A and B in mathematical terms are called __.

In a circus, a motorcyclist performs stunts in a hollow sphere. The thickness of the sphere is negligible. If the diameter of the hollow sphere is $14m,$ then find the area available for the motorcyclist to perform stunts. [Take $\pi =\frac{22}{7}$]

Choose the correct answer in each of the following questions:
In the class intervals 10-20, 20-30, the number 20 is included in
(a) 10-20
(b) 20-30
(c) in each of 10-20 and 20-30
(d) in none of 10-20 and 20-30

If the point (2, 5) lies on the graph of 3y = ax + 7, then find the value of a

Factorise:
$40+3x-x^2$

Calculate the value of x in each of the following figures.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

If $\overline{x_1},\overline{x_2}\dots ,\overline{x_n}$ are the means of n groups with $n_1,n_2,\dots ,n_n$ number of observations respectively then the mean $\overline{x}$ of all the groups taken together is
(a) ${\sum }_n^{i=1}n,\overline{x_i}$

(b) $\frac{{\sum }_{i=1}^n{n}_i\overline{x_i}}{n^2}$

(c) $\frac{{\sum }_{i=1}^n{n}_i\overline{x_i}}{{\sum }_{i=1}^n{n}_i}$

(d) $\frac{{\sum }_{i=1}^n{n}_i{\overline{x}}_i}{2n}$

$\text{In the given figure, D is a point on side BC of a}\Delta ABC\text{and E is a point such that CD = DE.}\text{Prove that AB + AC}>BE.$

what are the zeroes of polynomial equal to

Question 57
In the following question, state whether the given statement is true (T) or false (F).
The predecessor of a two-digit number is always a two-digit number.

The relation "less than” in the set of natural numbers is

Without actually calculating the cubes, find the value of each of the following:
(i) ${(-12)}^3+{\left(7\right)}^3+{\left(5\right)}^3$
(ii) ${\left(28\right)}^3+{(-15)}^3+{(-13)}^3$

Simplify:
$\frac{3^{-5}\times {10}^{-5}\times 125}{5^{-7}\times 6^{-5}}$

The number $0.\overline{35}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, is __________.

P, Q, and R are 3 points on a straight line. QP = 5 cm, PR = 10 cm and QR = 15 cm.
Which of the following is true?

Information is ___ data.

What will you substitute to make the following equation a linear equation

$\frac{1}{x}$ + $\frac{3}{y}$ = 1

Ratio of height to base radius of a cylinder is 1:2. The ratio of total surface of cylinder to curved surface of cylinder is__

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Point (-3, 5) lies in which quadrant?

Find the sum of all multiples of 9lying between 300 and 500?

Identify the type of coordinating conjunction used in the sentence.

The wind blew, the rain fell and the lightning flashed.

Factorise 4x^2-1-6y-9y^2

Andy spent ₹ 450 in fencing the parallelogram shaped land (leaving 1 m for the gate).. If Andy starts from a point 5 m away from A (on side AB) and take the shortest possible path to the opposite side, he would reach D. Andy restructured his land to be a rectangle having the same base and same height. Find the cost of fencing the new land in at ₹ 6 / m.

Two parallel lines l and m are such that A, C are the points on l and B, D are the points on m. AB and CD are perpendicular to both l and m. If AB = 4 cm, then CD =

If $|x-2|+|x-6|=3$ then the value of $x$ is

If the area of a triangle is 48 $c{m}^2$ and its base is 8cm.Then find the height of the triangle.

Check whether the polynomial f (x) = 4x^3+4x^2 -x -1 is a multiple of 2x +1