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When two dice are thrown , what is the probability of getting a sum of 6?

In a right angled triangle $△ABC,$ the right angle is at $B.$ Which of the following is true about the other two angles $A$ and $C?$

If $x_1,x_{2}and{x}_3$ as well as $y_1,y_{2}and{y}_3$ are in GP with the same common ratio, the points
$P(x_1,y_1),Q(x_2,y_2)andR(x_3,y_3)$

Both roots of the equation are 0 if

If two tangents inclined at an angle of ${60}^o$ are drawn to a circle radius 3 cm then the length of each tangent is

(a) 3 cm (b) $\frac{3\sqrt{3}}{2}$ cm (c) $3\sqrt{3}$ cm (d) 6 cm

17 cards numbered 1, 2, 3, 4, ... 17 are put in a box and mixed throughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an odd number (ii) a number divisible by 5.

A car travels first half distance between two places with uniform speed of $60\text{km/hr}$. What should be its uniform speed (in $\text{km/hr}$) for the second half of the distance so that its average speed over the entire journey becomes $90\text{km/hr}$.

If A, B and C are interior angles of a triangle ABC, and
$\sin \left(\frac{B+C}{2}\right)=\cos \left(x\right),$
then find thevalue of x.

A child puts one five rupee coin from her saving in the piggy bank on the first day. She increases her saving by one five - rupee coin daily. If the piggy bank can hold 190 coins of five rupees in all, find the number of days she can contribute to putting the five rupees of into it and find the total money she saved.

If the equation $x^2+4x-k=0$ has real and distinct roots, then :

One card is drawn at random from a well - shuffled deck of 52 cards.
What is the probability of getting a face card?
(a) $\frac{1}{26}$ (b) $\frac{3}{26}$ (c) $\frac{3}{13}$ (d) $\frac{4}{13}$

If α, β are zeroes of the polynomial f(x) = x² + 5x + 8, then value of (α + β) is

If $\sin {90}^{\circ }-(A+B)=\cos x=\cos y,$

find the value of $x$ and $y$; if $y$ is the angle $C$ of triangle $ABC.$ (In triangle $ABC,\angle A+\angle B={90}^{\circ }$)

If $\frac{a}{b}$ = $\frac{8}{3}$ then find the ratio $\frac{a+4b}{4b}$ ?

Draw a circle of radius 3 cm. Draw a tangent to the circle making an angle of ${30}^{\circ }$ with a line passing through the centre.

The equation of the circle having $(4,2)$ and $(2,-12)$ as the end points of its diameter is

Solve the following systems of equations:

$\frac{5}{x+y}-\frac{2}{x-y}=-1$

$\frac{15}{x+y}+\frac{7}{x-y}=10$

Find the point on x- axis which is equidistant from the points (-2, 5) and (2, -3).

A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?

Complete the following table :

Point Transformation Image

(a) (5, -7)-------------------------------(-5, 7)

(b) (4, 2) Reflection x-axis ---------

(c) --------- Reflection in y-axis (0, 6)

(d) (6, -6) ----------------- (-6, 6)

(e) (4, -8) ------------------ (-4, -8)

Draw a circle of diameter 9 cm. Mark a point at a distance of 7.5 cm from the centre of the circle. Draw tangents to the given cirlce from this exterior point. Measure the length of each tangent.

A pair of unbiased dice are rolled together till a sum of either 5 or 7 is obtained. Probability that 5 comes before 7 is

A statue 1.6 m tall stands on the top of pedestal. From a point on the ground, the angle of elevation of the top of the statue is ${60}^{\circ }$ and from the same point the angle of elevation of the top of the pedestal is ${45}^{\circ }$. Find the height of the pedestal.

Find the point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3).

The sum of first 20 terms of the sequence 0.3, 0.33, 0.333, ....., is

Find the probability of getting an even sum when you toss two dice simultaneously.

A model of an aeroplane is made to a scale of 1 : 400. Calculate : (i) the length, in cm, of the model; if the length of the aeroplane is 40 m. (ii) the length, in m, of the aeroplane, if length of its model is 16 cm.

The marks scored by Rohit in two tests were 65 and 70.Find the minimum marks he should score in the third test to have an average of at least 65 marks.

In $\Delta$ ABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that:
(i) CB: BA =CP: PA
(ii)AB $\times$ BC = BP $\times$ CA

The total surface area of a cuboid with length 'l', breadth 'b' and height 'h' is .

A wholesaler buys a TV from the manufacturer for Rs 25,000. He marks the price of the TV $20\%$ above his cost price and sells it to a retailer at a $10\%$ discount on the marked price. If the rate of VAT is $8\%$, find the :
(i) Marked price
(ii) Retailer's cost price inclusive of tax
(iii) VAT paid by the wholesaler.
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In the given triangle ABC, the point P is the intersection of all the medians. The length of AP is 10 cm. Then what is the length of PE?

Solve the following systems of inequalities graphically:

$4x+3y\le 60,y\ge 2x,x\ge 3,x,y\ge 0$

Which of the following are correct?

Mr.Parekh invested Rs.52,000 on Rs.100 shares at a discount of Rs.20 paying 8% dividend. At the end of 1 year he sells the shares at a premium of Rs.20.

Find the profit earned including his dividend.

Rushil and Bhanu jointly started a business with a capital of Rs. 40,000 and Rs. 20,000 respectively. After 6 months, Rushil invested Rs. 20,000 more in the business, but Bhanu withdrew Rs. 10,000. At the end of the year, the profit earned by the business is Rs. 65,000. What is the profit earned by Bhanu?

hey dear i have doubt in word problems of this chapter real numbers

i have to know hole concept of HCF and LCM which is used in word problem.

A person sells an item for Rs56 and earns as many percent of profit as CP numerically is?

Find CP and profit%

√(3+2√2)

√(3 -2√2)

x=3+2√2

then find the value of √x-√1/x

If x-1by x = half then find tge value of 4x square +4 by x square

A bucket contains 10 brown balls, 8 green balls, and 12 red balls. A ball is drawn. What is the probability that the ball will be brown?