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In the following figure, PQ and PR are tangents to the circle, with centre O. If $\angle QPR={60}^{\circ }$. Select the statements that are true,

A body falls 8m in the 1^st second of the motion, 24 meters in the 2^nd ,40 meters in the 3^rd and so on.How long will it take to fall 2048 meters?

In the figure above, M is the centre of the circle. EA and ED are tangents from point E. FB anf FC are tangents through point F. Also, $\angle AEM={24}^{\circ },\angle MFC={30}^{\circ }$

What is the value of (x + y )?

A manufacturer X sells a refrigerator to a trader Y for ₹ 22500. The trader Y sells it to a trader Z at a profit of ₹ 1250 and trader Z sell it to a consumer at a profit of

₹ 1000. If the rate of value added tax (VAT) is $4\%$, find the total amount of tax (under VAT ) received by the government on the scale of the refrigerator.

What is the conjugate of $\sqrt{6}-\sqrt{5}$?

The roots of the equation (x+5)(x-5) = 39 are

Prove the following trigonometric identities:

$\frac{cotA-cosA}{cotA+cosA}=\frac{cosecA-1}{cosecA+1}$

A window of a house in h meter above the ground. From the window, the angles of elevation and depression of the top and bottom of another house situated on the opposite side of the lane are found to be $\alpha$ and $\beta$ respectively. Prove that the height of the house is h(1+tan~\alpha~tan~\beta) metres.

Solve each of the following equations by using the method of completing the square:
$2x^2+5x-3=0$

$△$ABC is a right angled triangle with ∠B = ${90}^{\circ }$. D is a point on AC such that BD is perpendicular to AC. If AC = 2AB, what is the area of $△$ABD, given, area of $△$ABC = 5 sq units.

If the coordinates of a triangle ABC is A(3,1), B(5,1) and C(5,8) then find the side of the triangle which is parallel to the Y-axis.

A solid cone of base radius 10 cm is cut into two parts through the mid-point of its height, by a plane parallel to its base. Find the ratio in the volumes of two parts of the cone.

Find the roots of each of the following equations, if they exist, by applying the quadratic formula:
$2x^2+x-4=0$

In linear equations inequalities portion is not available

Find the sum of terms of the AP: $34+32+30+\dots \dots +10$

The circumference of the front wheel of the cart is 30 feet long and that of the back wheel is 36 feet long . What is the distance travelled by the cart , when the front wheel has done five more revolutions than the rear wheel

The sum of two numbers is 9. If the sum of their reciprocals is $\frac{1}{2}$, find the numbers.

ABCD is a rectangle in which length is double of its breadth ,two eqilataral triangle are drawn on each length ,find the ratio of their areas.

D, E, F are the midpoints of the sides BC, CA and AB respectively of an equilateral $△ABC.$ Then $△AEF$ is congruent to triangle –

Calculate the percentage of Boron ($B$) in $N{a}_2{B}_4{O}_7.10H_{2}O$. Answer correct to 1 decimal place. [H = 1, B = 11, O = 16, Na = 23].

Please let me get this sum solved!!!!

The sum of first 100 natural numbers is greater than the sum of the even numbers between 1 and 100 by _____________

As it is said that even numbers between 1 and 100 so, should I consider 100 or 98 ?????

Draw an equilateral triangle of side 8 cm and its circumscribed circle. Find the length of the radius.

cos A - 2cos³ A/ 2sin³ A - sin A = cot A

Solve

$3x^2-4x+\frac{20}{3}=0$

Solve the following systems of the equation:

X+Y=2XY, X-Y/XY=6

A shopkeeper buys some books to Rs.80. If he had bought 4 more books for the same amount each book would have cost Re.1 less. Find the number of books he bought

If the length of tangent drawn from the point (5,3) to the circle $x^2+y^2+2x+ky+17=0$ be 7, then k =

An isosceles right angled triangle is reflected about its hypotenuse. The figure formed by the triangle and its reflection is

If -1 and 3 are the roots of $x^2+px+q=0,$ find the values of p and q.

Which of the following is rational?

In the figure, AP and AQ are tangents to the circle with centre O, from an external point A. If ∠PAQ = 70^o then APQ is equal to:

Mr. Manan purchased 100 shares in a company at Rs 150 each. The company issues one bonus share for every two shares held by him. When the price of the shares fell to Rs 120 he sold the shares. Find his percentage gain.

If A(7,5) , B(4,3) and C(-2,-3) are vertices of a triangle, then find the difference between the slope of Side AC and slope of Side AB.

The value of x in the system x - 3y = 7; 3x - 3y = 15 is:

1. 8

In $\Delta ABC,AB=18cm,\angle A={45}^{\circ },\angle B={60}^{\circ }.$ Then the area of the triangle ABC is

In the given figure, $DE||BC$ such that AD = x cm, DB = (3x + 4) cm, AE = (x + 3) cm and EC = (3x + 19) cm. Find the value of x.

Show that the points$O(0,0),A(3,\sqrt{3})andB(3,-\sqrt{3})$ are the vertices of an equilateral triangle. Find the area of this triangle.

Solve the following quadratic equation by factorization.
$\frac{3}{x+1}+\frac{4}{x-1}=\frac{29}{4x-1};x\ne 1,-1,\frac{1}{4}$

Question 56

What happens to the value of a fraction, if the denominator of the fraction is decreased while numerator is kept unchanged?

(i) $1+\frac{co{t}^2\theta }{(1+cosec\theta )}=cosec\theta$
(ii) $1+\frac{ta{n}^2\theta }{(1+sec\theta )}=sec\theta$

In the given figure, PQR is a tangent to the circle at Q, whose centre is O and AB is a chord parallel to PR such that $\angle$ BQR = ${70}^o$, Then $\angle$ AQB = ?

(a) ${20}^o$ (b) ${35}^o$ (c) ${40}^o$ (d) ${45}^o$