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Which of the following options holds true for the system of equations,

x + y + z =6

x + 2y + 3z = 12

x + 4y + 7z =30

In the right angled triangle shown below, if AB=3 cm, BC=4 cm then what is the value of cos A?

Question 32

When principal P is compounded semi-annually at r% per annum for t years, then amount = ___

The semi-perimeter of a triangle is 96 cm and its sides are in the ratio of 3 : 4 : 5. The area of the triangle is

In the figure below, $\angle$C=${40}^{\circ }$ and CB=AC. Also, EC is the bisector of AB. $\angle$ACE is equal to _____

An exterior angle of a triangle is ${115}^{\circ }$ and one of the opposite angles is ${35}^{\circ }$. Find the other two angles.

The vertical handle bars in a bus are cylindrical in shape. If each bar has a circular base of radius 5cm and height 5 m, how much iron would be required to build 14 such bars?(Take π = $\frac{22}{7}$) [4 MARKS]

In the given figure, AB is diameter of the circle. CD ‖ AB and ∠BAD = 40^o then ∠ACD is

A survey shows that 63% of the people watch news whereas 76% watch sports. If $x$% of people watch both sports and news, then

Which of the following is the correct expanded form of 0.0504?

There is a slide in a park. One of its side walls has been painted in some colour with a message "Keep the park green and Clean". If sides of the wall are 15m, 11 m and 6 m, the area painted in colour is________.

The diagonals divide the shape into 4 equal triangles. Which shape is it?

Three cubes of metal whose edges are in the ratio 3 : 4 : 5, are melted down into a single cube whose diagonals is $12\sqrt{3}cm.$ Find the edges of three cubes.

ABCD is a parellelogram, E and F are the mid points AB and CD respectively. GH is any line intersecting AD, EF and BC at G, P and H respectively. prove that GP = PH.

1. -7

In a circle of radius 6cm, which of the following cannot be the length of a chord?

Consider the figure given below where $△ABC$ and $△DEF$ are similar. Find the length of the missing side x.

To get the census of the country, the government collected data from hospitals for the number of births and deaths of people. What kind of data is this?

Question 46

Fill in the blanks to make the statements true.

10g of caustic soda dissolved in 100ml of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ___.

If an angle of a parallelogram is four-fifths of the adjacent angle, then the angles of the parallelogram are

Factorise:
$ab(x^2+1)+x(a^2+b^2)$

ABCD is a trapezium in which AB || DC and let E be the midpoint of AD. Let F be a point on BC such that EF || AB. Then MF is

1. 8

Question 8

If A and B are (–2, –2) and (2, –4) respectively, find the coordinates of P such that $AP=\frac{3}{7}AB$ and P lies on the line segment AB.

If $\Delta ABC$ is right angled at C, then cos B = ___.

In the figure, ABC adn BDC are two equilateral triangles such that D is the mid point of BC. Ae intersects BC in F.
$\left(i\right)ar\left(△BDE\right)=\frac{1}{4}ar\left(△ABC\right)\left(ii\right)ar\left(△BDE\right)=\frac{1}{2}ar\left(△BAE\right)\left(iii\right)ar\left(△BFE\right)=ar\left(△AFD\right)\left(iv\right)ar\left(△ABC\right)=2ar\left(△BEC\right)\left(v\right)ar\left(△BFE\right)=2ar\left(EFD\right)\left(vi\right)ar\left(△FED\right)=\frac{1}{8}ar\left(triangleAFC\right)$

The number of surfaces, a cone has, is

P and Q invested Rs. 700 and Rs. 500 respectively. If the loss incurred after one year is Rs. 132, the loss incurred by A is Rs. 79 and the loss incurred by B is Rs. 55. Is this statement True or False?

ABCD is a parallelogram. Find $\angle$ ADC.

Find the negation of the following statement. 'All cats scratch'.