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In a right triangle $△$ ABC with right angle at B, BD is a perpendicular, dropped onto the hypotenuse. Which of the following statements are true?

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Question 4 (xv)
Which of the following are APs? If they form an A.P. find the common difference d and write three more terms.
(xv) $1^2,5^2,7^2,73,\dots$

If x > y ; then which of the following statement holds true for the given inequation

A solid cone of radius 5 cm & height 8cm is melted & made into small spheres of radius 0.5 cm. Find the number of spheres formed.

Area of a quadrant of circle whose circumference is 22 cm is : ( π = 22/7)

The line $\frac{x}{a}+\frac{y}{b}-\frac{1}{ab}=0$, will meet the x- axis at ____.

In a right angled triangle $\Delta$ABC, a perpendicular BD is drawn on to the largest side from the opposite vertex. Which of the following does NOT give the ratios of the areas of $\Delta$ABD and $\Delta$ BCD?

Question 13
If an isosceles $\Delta$ ABC in which AB = AC = 6cm, is inscribed in a circle of radius 9 cm, find the area of the triangle.

$\frac{x}{a}cos\theta$ + $\frac{y}{b}sin\theta$ = 1

$\frac{x}{a}sin\theta$ - $\frac{y}{b}cos\theta$ = 1

From a well-shuffled deck of 52 cards, a card is picked at random. (i) Find the probability of the card being a queen of spades. (ii) If the card drawn at first is a queen of spade and is not replaced, what is the probability of getting a card which is a spade?

A natural number, when decreased by 13, equals 140 times its reciprocal. Find the number.

The equation of the circumcircle of the triangle formed by the lines x = 0, y = 0, 2x + 3y = 5 is

Which among the following will have the largest value?

Question 9
One equation of a pair of dependent linear equations is - 5x + 7y – 2 = 0
(A) 10x + 14y + 4 = 0
(B) –10x – 14y + 4 = 0
(C) –10x + 14y + 4 = 0
(D) 10x – 14y = –4

x = −5 can be written as equation in two variable in which of the following ways

Determine whether the following points are collinear or not: A (3, 1), B (6,4) and C (8,6) [2 MARKS]

Solve for $x$ if $4(2x+3{)}^2-(2x+3)-14=0$.

The points on a line are (-1,1), (3,1) and (5,1). Then the slope of this line is

ABDE is a trapezium​​​​​​ with $AE\parallel BD$ and $ED\perp BD$, and AC is drawn parallel to the side DE.

Find the values of $\text{cot}\theta and\text{cosec}\theta$ respectively, from the given figure.

In the given figure, $\frac{BC}{AC}$ = $\frac{24}{25}$.
Find the value of $cose{c}^{2}A-co{t}^{2}A$ = ___.

Find the probability of finding a head when a coin is tossed in the air?

Ina trapezium ABCD, it is given that AB || CD and AB = 2CD. Its diagonals AC and BD intersect at the point O such that ar $\left(\Delta AOB\right)=84c{m}^2$. Find ar $\left(\Delta COD\right)$.

If $x+1,3x$ and $4x+2$ are the first three terms of an AP, then its $5^{\text{th}}$ term is ___.

If $\Delta ABD$ and$\Delta AMP$ are two right triangles right angled at B and M respectively such that $\angle MAP=\angle BAC$. prove that
(i) $\Delta ABC\sim \Delta AMP$
(ii) $\frac{CA}{PA}=\frac{BC}{MP}$

The time taken to travel 30 km upstream and 44 km downstream is 14 hours. If the distance covered in upstream is doubled and distance covered in downstream is increased by 11 km then the total time taken is 11 hours more than earlier. Find the speed of the stream.

If the sum of first p terms, first q terms and first r terms of an A.P. be a, b and c respectively,then $\frac{a}{p}$(q - r) + $\frac{b}{q}$(r - p) + $\frac{c}{r}$(p - q) is equal to :

The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. Let’s say $x$ toys were produced on a day, what is the total cost of production in terms of $x$?

Question 5
For all real values of c, the pair of equations x – 2y = 8 and 5x – 10y = c have a unique solution. Justify whether it is true or false.

A partner draws Rs 1,000 per month. Under the partnership deed, interest on partners drawings is to be charged 12$\%$ p.a. Calculate interest that should be charged from him if he withdraws :

(i) In the beginning of every quarter.

(ii) Middle of every quarter.

(iii) End of every quarter.

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed. If it takes 3 hours to complete total journey, what is its original average speed?

A circular pond is 17.5 m in diameter. It is surrounded by a 2 m wide path. Find the cost of constructing the path at the rate of Rs. 25 per $m^2$.

If - 5 is a root of the quadratic equation $2x^2+px-15=0$ and the quadratic equation $p(x^2+x)+k=0$ has equal roots, find the value of k.

A man saved Rs. 16500 in ten years. In each year after the first he saved Rs. 100 more than he did in the preceding year. How much did he save in the first year?

The hypotenuse of a right-angled triangle is 1 metre less than twice the shortest side. If the third side is 1 metre more than the shortest side, find the sides of the triangle.

An electronic device makes a beep after every 60 seconds. Another device makes a beep after every 62 seconds. They beeped together at 10 a.m. At what time will they beep together at the earliest ?

A quadrilateral PQRS circumscribes a circle. If PS + QR = 10 cm, what is the perimeter of the quadrilateral?

There are two windows in a house. A window is at a height of 2 m above the ground and the other window is 3 m vertically above the lower window. A balloon is flying near the house. At an instant, angles of elevation of the balloon from these windows are observed as ${45}^{\circ }and{30}^{\circ }$ from lower and upper window respectively. The height of the balloon from the ground is:

In the figure, AB || CD and XY is the transversal.

Which of the following is incorrect?

Which of the following is/are rational number(s) ?