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Two adjacent sides of a parallelogram are 5 cm and 3.5 cm and one of its diagonals is 6.5 cm. The area of the parallelogram is

In a triangle ABC,
cosA- cosB=

What is the factor form of the expression x2 + ax + bx + cx + bc + ac?

Which of the following angle construction is not possible with a ruler and a compass?

Question 8

Zero of the zero polynomial is



A) 0

B) 1

C) Any real number

D) Not defined

Question 5: Draw a rough figure and label suitably in the following case:

(a) $\overleftrightarrow{OP}$, and $\overleftrightarrow{OQ}$, meet at O

The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining number is 78. The value of discarded number is

If x=2+√3 then find x^{​​​​​​2}+1÷x²

The expression $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ when simplified reduces to a-b$\sqrt{15}$.

Then a + b is __________.

The following data gives the amount of manure (in thousand tones) manufactured by a company during some years:

Choose the correct alternative: The consecutive years during which there was maximum decrease in manure production are

Rationalise the denominator of $\frac{2+\sqrt{5}}{2-\sqrt{5}}$

Choose the major sector in the given figure.

If the dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its total surface area is 88 $m^2$, then the volume of the cuboid is :

Isabella had $\$9$ before she started shopping. She spent ${\left(\frac{1}{20}\right)}^{th}$ of the money in buying some commodities. How much money did she spend?

In a histogram the area of each rectangle is proportional to

(a) the class mark of the corresponding class interval

(b) the class size of the corresponding class tnterval

(c) frequency of the corresponding class interval

(d) cumulative frequency of the corresponding class interval

If a>0, b>0, c>0 are in G.P., then $lo{g}_{a}x,lo{g}_{b}x,lo{g}_{c}x$ are in

Find the remainder when $x^3+3x^2+3x+1$ is divided by

(i)$x+1$
(ii) $x-\frac{1}{2}$
(iii) $x$

(iv) $x+\pi$
(v) $5+2x$

In the figure, E is the mid-point of side AD of a trapezium ABCD with AB || CD. A line through E parallel to AB meets

BC in F.



Then find which of the option is correct.

$\text{If}{x}^3+\frac{1}{x^3}=110,\text{then}x+\frac{1}{x}=$ ?

Question 70

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

XYZ is an equilateral triangle and PQRS is a square. The figure has been cut and re-arranged in the form of a trapezium.

What is the length of the path ADCB in the trapezium ABEF?

(i) If $log(a+1)=log(4a-3)-log3$; find a.

(ii) If $2logy-logx-3=0$, express x in terms of y.

(iii) Prove that : $lo{g}_{10}125=3(1-lo{g}_{10}2)$.

If $P=\{2,4,6,8,10,12\},Q=\{4,6,8\}$ and $R=\{4,6\}$, then which of the following statements is not correct?

$\text{In the given figure, the sides CB and BA of}\Delta ABC\text{hs been produced to D and E respectively such that}\angle ABD={110}^{\circ }and\angle CAE={135}^{\circ }.Then,\angle ACB=?$

$\left(a\right){65}^{\circ }\left(b\right){45}^{\circ }\left(c\right){55}^{\circ }\left(d\right){35}^{\circ }$

Question 10

A point lies on positive direction of x-axis at a distance of 7 units from the y-axis. What are its Coordinates, if this lies in the negative direction of y-axis at a distance of 7 units from x-axis?

4 focus lights are to be fixed on a square aluminum plate with side length, l = 28 inch. Circles are cut in the plate to accommodate the lights. After the required alterations the aluminum plate looks similar to the figure shown. What would be the area of the aluminum plate after alterations?

Prove that in any triangle, cash external angle is equal to the sum of the internal angles at the other two vertices.

The angle between the vectors $\overline{u}=<3,0>and\overline{v}=<5,5>$ is ___

If arc AXB and arc AYB are corresponding arcs and m(arc AXB) = 120${}^{\circ }$ then m(arc AYB) =

The frequency polygon below shows marks obtained by students of a class.

From the graph, it can be said that the maximum number of student has scored ____

A road-roller is of diameter 80 centimetres and length 1.2 metres. What is the area of ground levelled, as it rolls once?

2.50505050... in $\frac{p}{q}$ form is .