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Question 10
Which of the following equations has no real roots?
(A) $x^2-4x+3\sqrt{2}=0$
(B) $x^2+4x-3\sqrt{2}=0$
(C) $x^2-4x-3\sqrt{2}=0$
(D) $3x^2-4\sqrt{3}x+4=0$

What is the common difference of the arithmetic progression 10, 5, 0, -5?

The radii of the circular ends of a bucket of height 15 cm are 14 cm and r cm (r < 14). If the volume of bucket is 5390 $c{m}^3$, find the value of r.

A cuboid has volume equal to the polynomial, $p\left(x\right)=x^3+12x^2+47x+60$. It is given that $p(-3)=p(-4)=p(-5)=0$. Choose the possible sides of the cuboid.

If the first term of an AP is 12 and the common difference is -2, then term of the AP will be 0.

If $d_1,d_2(d_2>d_1)$ be the diameters of two concentric circle and c be the length of a chord of a circle which is tangent to the other circle. prove that $d_2^2=c^{+}{d}_1^2$.

A rectangular lawn, 75 m by 60 m, has two roads, each road 4 m wide, running through the middle of the lawsn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the roads at Rs 50 per $m^2.$

If $1+co{t}^2\theta ={(\sqrt{3+2\sqrt{2}}-1)}^2$, find the value of $\frac{1}{tan\theta }+\frac{sin\theta }{1+cos\theta }$

A kite is flying at a height of 75 metres from the ground level, attached to a string inclined at ${60}^{\circ }$ to the horizontal. Find the length of the string to the nearest metre.

The image of the point (1, 5) when reflected in a line
LM is (9, 5). Write down the equation of the line
LM.

(ICSE)

90% and 97% pure acid solutions are mixed to obtain 21 litres of 95% pure acid solution.Find the quantity of each type of acids to be mixed to form the mixture.

A triangle is formed by the line 3x+4y=12, the x-axis and y-axis. The circumradius is

The sum of four consecutive numbers in an AP is 32 and the ratio of the product of the first and last term to the product of two middle terms is 7:15. Find the numbers.

In the given figure, AE and BD are two medians of a $△$ABC meeting at F. The ratio of the area of $△$ ABF and the quadrilateral FDCE is -

Question 94

A public sewer line is being installed along $80\frac{1}{4}$ m of the road. The supervisor says that the labourers will be able to complete 7.5m in one day. How long will the project take to complete?

Define Sector of a Circle

1. 2

Consruct an equilateral triangle ABC of side 5 cm. Draw a circle circumscribing the $△$ABC. Find the length of the circumradius.

The statements given below are the steps that need to be followed in the method of substitution in random order. Arrange them in correct order to solve two equations.

1) Find the value of one variable, say y in terms of the x if x and y are the two variables.

2) Substitute the x we got from step 2 in either of the equation to get y.

3) Substitute this y in the second equation and it will be reduced to an equation in x, find x.

In the following figure, ABCD to a trapezium with AB // DC. If AB = 9 cm, DC = 18 cm, CF= 13.5 cm, AP = 6 cm and BE= 15 cm, Calculate : (i) EC (ii) AF (iii) PE

On a map drawn to a scale of 1:2,50,000; a triangular plot of land has the following measurments : AB= 3 cm, BC= 4 cm and $\angle ABC={90}^{\circ }$.

Calculate the actual lengths of AB and BC in km. Then the area of the plot in sq. km. is

If $A=\left[\begin{array}{ccc}1& 2& 3\\ -2& 3& -1\\ 3& 1& 2\end{array}\right]$ and I is a unit matrix of $3^{rd}$ order, then ​$(A^2+9I)$ equals

Madhav and Rama have feedback forms from 50 participants of a workshop in which participants have commented about different sessions. They want to know how the workshop was. What kind of data are they handling?

Is every polynomial a rational expression?

With reference to the figure given, a man stands on the ground at point A, which is on the same horizontal plane as B, the foot of a vertical pole BC. The height of the pole is 10 m. The man’s eye is 2 m above the ground. He observes the angle of elevation at C, the top of the pole as , where tan = ²/₅. Calculate,

When $x^{200}+1$ is divided by $x^2+1$, the remainder is equal to

Which of the following is a zero polynomial ?
[where, $x\ne 0$]

Rohan's mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. What is Rohan's present age?

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :

Comment on the nature of the roots of the equation $2x^2–6x+8=0$

Find the distance between the following pair of points:

(i) (-6,7) and (-1,-5)

(ii) (a+b,b+c) and (a-b,c-b)

(iii) $(asin\alpha ,-bcos\alpha )and(-acos\alpha ,bsin\alpha )$

(iv) (a,0) and (0,b)

Solve

1+4+7+10.…..….......+x =590

Which is not an important source of revenue to government?

$3tan\theta$ + $cot\theta$ = 5 $cosec\theta$, $0\le \theta$ ≤ ${90}^{\circ }$. Then the value of $\theta$ is __${}^{\circ }$.

___ and ___ are the two main stock exchanges of India.

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel of 10 m deep. If the cost of painting is at the rate of $Rs20per{m}^2$, find the inner curved surface area of the vessel.

$[Assume\pi =\frac{22}{7}]$