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Which among the following is correct?
Parallelograms on the same base and between the same set of parallel lines:

If $x_1,x_2,x_3,x_4$ are four positive real numbers such that $x_1+\frac{1}{x_2}=4,x_2+\frac{1}{x_3}=1,x_3+\frac{1}{x_4}=4$ and $x_4+\frac{1}{x_1}=1,$ then

In a right angled triangle:

Circum-radius $=\frac{1}{2}\times$ length of the ___.

If the height of the cylinder is doubled, then the ratio of the original cylinder to that of the new one is

An observer 2.25 m tall is 42.75 m away from a chimney. The angle of elevation of the top of the chimney from her eyes is ${45}^{\circ }$. What is the height of the chimney?

The polynomials p(x) = x³ + 2x² – 5x -7 and q(x) = x³ + x² – 12x + 6, when divided by (x + 1) and (x - 2) respectively give the remainders R₁ and R₂. Find 2R₁ + R₂ .

$\text{In the given figure, ABCD is a}\text{parallelogram. From the given options,}\text{select the values of x}$

If X/y+yx=-1 then find the value of x^3-y^3

In the adjoining figure, ABCD is a parallelogram whose diagonals intersect each other at O. A line segment EOF is drawn to meet AB at E and DC at F. Prove that OE = OF.

$Constructa\Delta ABCinwhichBC=6cm,\angle B={30}^{\circ }andAB-AC=3.4cm\text{Justify your constructions.}$

A hemi- spherical dome of a building needs to be painted. If the circumference of the base of the dome is 17.6 m, find the cost of painting it, given the cost of painting is Rs. 5 per $100c{m}^2.$

The curved surface area of a cylinder is 1320 $c{m}^2$ and its base had diameter 21 cm. Find the height and the volume of the cylinder. [Use $\pi$ = 22/7]

A hemispherical bowl of internal radius 9 cm contains a liquid.This liquid is to be filled into cylindrical shaped small bottles of diameter 3 cm and height 4 cm.How many bottels are required to empty the bowl?

Which of the following statements are true (T) and which are fales (F):

(i) Sum of the three angles of a triangle is ${180}^{\circ }$ .

(ii) A triangle can have two right angles .

(iii) All the angles of a triangle can be less than ${60}^{\circ }$ .

(iv) All the angles of a triangle can be greater than ${60}^{\circ }$.

(v) All the angles of a triangle can be equal to ${60}^{\circ }$.

(vi) A triangle can have two obtuse angles .

(vii) A triangle can have at most one obtuse angle.

(viii) If one angle of a triangle is obtuse, then it cannot be a right angled triangle.

(ix) An exterior angle of a triangle is less than either of its interior opposite angles.

(x) An exerior angle of triangle is equal to the sum of the two interior opposite angles.

(xi) An exterior angle of a triangle is greater than the opposite interior angles.

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

If $x=\sqrt{\frac{5+2\sqrt{6}}{5-2\sqrt{6}}},\text{then}{x}^2(x-10{)}^2=$

Solve for x

4^x-1 * (0.5)^3-2x=(1/8)^x

The following scores were obtained in a statistics exam

$$\begin{array}{cccccc}classinterval& [50,60)& [60,70)& [70,80)& [80,90)& [90,100)\\ Classvalue{x}_i& 55& 65& 75& 85& 95\\ Frequency{f}_i& 1& 4& 6& 5& 2\end{array}$$

i) Considering the class value, the average score of the whole class is_____.

ii) Ratio of the no. of students who scored above 80 to the no. of students who scored below 70 is______.

ABC is a triangle in which $\angle B=2\angle C.D$ is a point on BC such that AD bisects $\angle BACandAB=CD.\text{Prove that}\angle BAC={72}^{\circ }.$

Find the missing frequencies in the following frequency distribution whose mean is 34.
$\begin{array}{cccccccc}\text{x}& 10& 20& 30& 40& 50& 60& \text{Total}\\ \text{f}& 4& f_1& 8& f_2& 3& 4& 35\end{array}$

Choose the correct answer in each of the following questions:
If the mean of five observations x, x + 2,x + 4,x + 6 and x + 8 is 11 then the value of x is
(a) 5
(b) 6
(c) 7
(d) 8

How many types/cases of problems are possible in Triangle Construction 2 ?

If one angle of a triangle is equal to the sum of the other two angles, then the triangle is:

Question 32(i)
Cardswith numbers 2 to 101 are placed in a box. A card is selected at random. Find the probability that the card has an even number?

Write the equation of the line that is parallel to x-axis and passing through the point

$\left(i\right)(0,3)$ $\left(ii\right)(-0,-4)$ $\left(iii\right)(2,-5)$ $\left(i\right)(3,4)$

In the figure, AB and CD are diameters of a circle with centre O. If $\angle OBD={50}^{\circ }$, find $\angle AOC$.

Three similar coins were tossed simultaneously for 100 times and the data recorded is as given below :

$\begin{array}{ccccc}\text{No of heads}& 0& 1& 2& 3\\ \text{No of tosses = Frequency}& 10& 35& 40& 15\end{array}$

(i) What is the probability of getting more tails than heads?
(ii) What is the probability of getting more heads than tails?
(iii) Are (i) and (ii) complementary? Will they be complementary if we had 4 coins? [4 MARKS]

If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of transversal is 180${}^{\circ }$, then the lines are__.

Find the measure of each angle of an equilateral triangle.

What is each iteration of an experiment called?

If $a^2=logx,b^3=logy$ and $3a^2-2b^3=6logz$, express y in terms of x and z.

Prove that the tangents at the extremities of any chord make equal angles with the chord.

The radius and height of a right cone are in the ratio $3:4$. The ratio of total surface area to curved surface area of the cone is

Without actually calculating the cubes, find he value of the following: ${\left(28\right)}^3$ + ${(-15)}^3$ + ${(-13)}^3$

The value of $tan{1}^{\circ }\times tan{2}^{\circ }\times tan{3}^{\circ }\times \dots ...\times tan{89}^{\circ }$ is :

In the equation $ax+by+c=0$, if
$y=\frac{cx+d}{b}$ and $a=d$, then .

Rationalize the denominator of 4√3+3√2/√48+√18

$LetA=\left[\begin{array}{cc}0& \alpha \\ 0& 0\end{array}\right]and(A+I{)}^{50}-50A=\left[\begin{array}{cc}a& b\\ c& d\end{array}\right],Then,thevalueofa+b+c+dis$

What is a reflex angle ?

How to find a reflex of a given angle?

Eg reflex of 110°.

A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30m and it's longer diagonal is 48m how much area of the grass field will each cow be getting. ..

Factorize :

(a + b + c)² - ( a- b - c)² + 4b² - 4c²

Which of the below surds are arranged in correct ascending order?

What is the mass of a cylinder of lead that is 2.50 cm in diameter and 5.50 cm long? The density of lead is 11.4 g/ml.