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ABCD is a parallelogram with diagonal AC. If a line XY is drawn such that it cuts the side AD at point Z and $XY\parallel AB$, then $\frac{BX}{XC}=$

Given that sin A = $\frac{1}{2}$ and cos B = $\frac{1}{\sqrt{2}}$, then the value of (A + B) is ____.

$(Here,0<A+B\le {90}^{\circ })$

customers are asked to stand in the lines. if one customer is extra in a line , then there would be two less lines . if one customer is less in line , there would be three more lines . find number of customers

One card is drawn from a well - shuffled deck of 52 cards. Find the probability of getting
(i) a king of red suit (ii) a face card
(iii) a red face card (iv) a queen of black suit
(v) a jack of hearts (vi) a spade.

A man has only 20 paise coin and 25 Paisa coin in his purse if he has 50 coins in all totally rupees 11.25 how many coins of each kind does he have

A spherical shell of lead whose external and internal diameters are respectively 24 cm and 18 cm, is melted and recast into a right circular cylinder 37 cm high. Find the diameter of the base of the cylinder.

A man sold a chair and a table together for Rs.1520, thereby making a profit of 25% on a chair and 10% on the table. By selling them together for Rs.1535, he would have made a profit of 10% on the chair and 25 % on the table. Find the cost price of each.

To draw a pair of tangents to a circle, which are inclined to each other at an angle of 45^o, we have to draw tangents at the end points of those two radii, the angle between which is

(a) ${105}^o$ (a) ${135}^o$ (a) ${140}^o$ (a) ${145}^o$

5x(x+2) = 3

Solve using quadratic formula and give answer correct to 2 decimal places.

The answer is 2.27,0.27 OR 2.26,0.26 ?

I think answer should be 2.27,0.27 after complete rounding off.

(Answer given in book is 2.26,0.26 )

(i) $\frac{cosec\theta +cot\theta }{cosec\theta -cot\theta }=(cosec\theta +cot\theta {)}^2=1+2co{t}^2\theta +2cosec\theta cot\theta$

(ii) $\frac{sec\theta +tan\theta }{sec\theta -tan\theta }=(sec\theta +tan\theta {)}^2=1+2ta{n}^2\theta +2sec\theta tan\theta$

Prove that the points (-2, 5), (0, 1) and (2, -3) are collinear.

AOBC is a rectangle whose three vertices are A(0, 3), O(0, 0) and B(5, 0). The length of each of its diagonals is

(a) 5 units (b) 3 units (c) 4 units (d) $\sqrt{34}$ units

What is the maximum value of $1-x^2-3x$?

The probability of picking the letter K if you pick a random letter from the word TREKKING is $\frac{x}{4}$. Then, x = ___.

In the given set of data which numbers have the frequency 2.

10, 40, 80, 100, 30, 40, 30, 40, 20, 80.

Prove the following trigonometric identities:

$\frac{secA-tanA}{secA+tanA}=\frac{co{s}^{2}A}{(1+sinA{)}^2}$

A kite is flying on a string of 40$\sqrt{3}$m. The string attached to the kite is temporarily tied to a point on the ground. The inclination of the string with the ground is ${60}^{\circ }$. Find the height at which the kite is flying.

Three consecutive positive integers are such that the sum of the square of the first and the product of the other two is 46. Find the integers.

A tree stand svertically on a hill side which makes an angle of ${15}^{\circ }$ with the herizontal. From the same point on the ground , the slant distance of the base of the tree is 35m. Find the height of the tree, if the angle of elevation of the to of the tree is ${60}^{\circ }$.

Write the importance of tree in out life.

Find the sum of n terms of the A.P. whose kth term is 5k + 1.

Question 110

Solve the following

For what value of x is the perimeter of shape 77 cm?

(i) A circle is inscribed in a square. A point inside the square is randomly selected. What is the probability that the point is inside the circle as well?

(ii) If, instead, the square was inscribed in the circle, and a point inside the circle was randomly selected, what is the probability that it is inside the square?

If 16 men can make 320 art pieces in one day, how many men will be needed to make 960 such art pieces in one day?

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,...., is

Rationalise and simplify the expression
$\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{2}-\sqrt{5}}+\frac{2}{\sqrt{5}-\sqrt{3}}$

The sum Of four consecutive numbers in an AP is 32 and the ratio of the product of the first and the last term to the product of two middle terms is 7:15 .How can I find the number ?

Find the value of sgn(-1) + sgn(0) + sgn(1), where sgn(x) is the signum function.

If two circles intersect each other internally or externally, then in how many common tangents can be drawn?

$7^{th}$ term of the sequence $\sqrt{2},\sqrt{10},5\sqrt{2},.........$ is

There are four children A, B, C and D. A has 6 chocolates, B has 7 chocolates, C has 8 chocolates and D has 10 chocolates. Which of these children have the average number of chocolates?

In a right angled triangle, If cot x = 4, then what is the value of tan x

Which of the following statement is TRUE?

The angle of the major sector and the corresponding minor sector of a circle are

Prove that the perpendicular at the point of contact to the tangent of a circle passes through the centre

A garage worker goes to a nearby store to buy nuts and bolts. He has ₹ 40 and he is going to buy nuts for 40 paisa and bolts for ₹ 1.5 each. Write an inequality to describe the possible number of nuts and bolts that he can buy (Take the cost price of each bolt and nut as ₹ x and ₹ y respectively).

Insert4 irrational numbers between 3×root 2 and 2× root3

Two isosceles triangles have equal vertical angles and their areas are in the ratio 16 : 25. Find the ratio of their corresponding heights.

Given two finite sets A and B such that n(A) = 2, n(B) = 3. Then total number of relations from A to B is ___.

A ladder 20 m long is placed against a vertical wall of height 10 metres. Find the distance between the foot of the ladder and the wall and also the inclination of the ladder with the ground.

Question 2

A rectangular piece of dimensions 3 cm x 2 cm was cut from a rectangular sheet of paper of dimensions 6 cm x 5 cm (see the figure). Area of remaining sheet of paper is


(a) $30c{m}^2$
(b) $36c{m}^2$
(c) $24c{m}^2$
(d) $22c{m}^2$

The radii of two circles are 8 cm and 6 cm respectively. Find the radius of the circle in cm having area equal to the sum of the areas of the two circles. [4 MARKS]