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From an external point P, tangents PA and PB are drawn to a circle with centre O. If CD is the tangent to the circle at a point E and PA = 14 cm, find the perimeter of $\Delta$ PCD.

Prove the following trigonometric identities:

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

$4^{th}$ term of an A. P. is equal to 3 times its first term $7^{th}$ term exceeds twice the $3^{rd}$ term by 1. Find the first term and the common difference.

ABCD is a flower bed. If OA = 21m and OC = 14m. Find the area of the bed in $m^2$.

The table below shows 60 children in a class sorted according to their heights :

$\begin{array}{cc}\text{Height (cm)}& \text{Number of Children}\\ 140-145& 5\\ 145-150& 8\\ 150-155& 12\\ 155-160& 16\\ 160-165& 11\\ 165-170& 5\\ 170-175& 3\end{array}$

From the table , find the Median Height

In the figure below, one angle of a triangle is ${120}^{\circ }$ and its opposite side is 4cm. The diameter of its circumcenter will be equal to

Question 101

A lady bought an air-conditioner for Rs. 15200 and spent Rs. 300 and Rs. 500 on its transportation and repair, respectively. At what price should she sell it to make a gain of 15 %?

If $pcot\theta =\sqrt{q^2-p^2}$, then the value of $sin\theta$ is___.

If an= 5-11n,then find the common difference

Question 163(iii)

Supply the missing information for each diagram.

A point A is reflected in the origin $\left(M_0\right)$ and then in y-axis $\left(M_y\right)$ after which the new point is A'. Which single transformation maps A onto A' ?

Find the value of $x$ if $\Delta ABC\sim \Delta PQR$.

Which is better investment: $7\%$ ₹ 100 shares at ₹ 120 or $8\%$ ₹ 10 shares at ₹ 13.50?

1) ''I am 10cm shorter than my father". Can you write this as an equation?

2) My hieght is 158 cm, then what is my father's hieght?

Consider the circle which is named 'A' and has a radius of 7 cm. Then the locus of a point which is at a distance of 3 cm from this circle is/are the concentric circle(s)

A man on top of a building observes a car at an angle of depression $\alpha$, where $tan\alpha =\frac{1}{\sqrt{5}}$ and sees that it is moving towards the base of the building. Ten minutes later the angle of depression of the car is found to be $\beta$ where tan $\beta =\sqrt{5}$. If the car is moving with an uniform speed, then how much more time will it take to reach the base of the tower?

The length of the shadow of a tower standing on level ground is found to be 2x meters longer when the sun’s altitude is is 30° than when it was 45°. Prove that the height of the tower is x(root3 + 1) meters.

In the right -angles triangle QPR, PM is an altitude. Given that QR=8cm and MQ =3.5 cm, calculate the value of PR.

In the given figure, AP and AQ are the tangents drawn to a circle from a point A outside the circle.
If $\angle$PAQ = ${50}^{\circ }$ then, find $\angle$OPQ.

In the given figure, O is the centre of a circle, PQ is a chord and PT is the tangent at P. If $\angle$ POQ = ${70}^o$, then $\angle$ TPQ is equal to

(a) ${35}^o$ (b) ${45}^o$ (c) ${55}^o$ (d) ${70}^o$

Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. Find the edge of the new cube formed.

If cos $cos\theta =\frac{7}{25}$, find the values of all T-ratios of $\theta$

Find the quatient and the remainder when\

$f\left(x\right)=x^4-3x^2+4x+5$ is divided by $g\left(x\right)=x^2+1-x.$

The sum of first n terms of an A.P. is 5n-$n^2$. Find the nth term of this A.P.

A sector of ${56}^{\circ }$ cut out from a circle contains area $4.4c{m}^2$. Find the radius of the circle.

The radius of the circle is 6cm. The circle touches another circle externally and the distance between their centres is 10cm. What is the radius of the second circle?

A tax is one in which the rate of tax remains the same irrespective of the increase in income level.

The sum of n terms of an AP is 4pn(n+3).The sum of squares of these terms is:

The value of x, for which the points (x,-1), (2,1) and (4,5) lie on a line is

The sum of the digits of a two digit number is 8 and the difference between the number and that formed by reversing the digits is 8. Find the number.

If $2^p{.3}^q{.5}^r=60$, which of the following is true? Given; p, q, r are natural numbers.

If three coins are tossed, find the probability of getting at least one tail.

For the construction of a triangle by the method of Triangle Construction 3, how many pieces of information/data need to be provided?

A point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Prove that: ${OA}^2$ + ${OC}^2$ = ${OB}^2$ + ${OD}^2$.

Anushka starts walking straight towards east. After walking $75$ metres, she turns to the left and walks $25$ metres straight. Again she turns to the left, walks a distance of $40$ metres straight, again she turns to the left and walks a distance of $25$ metres. How far is she from the starting point?

The value of a machinery is Rs.10000, which is depreciating at the rate of 15% annually. What will be the value of the machinery after 2 years in rupees?

Question 68

Solve the following:

$\frac{3t+5}{4}-1=\frac{4t-3}{5}$

In the given diagram O is the center of the circle and CD is a tangent. $\angle$CAB and $\angle$ACD are supplementary to each other $\angle$OAC = ${30}^{\circ }$. Find the value of $\angle$OCB:

Question 187

In the marriage of her daughter, Leela spent Rs. 216766 on food and decoration, Rs. 122322 on jewellery, Rs. 88234 on furniture and Rs. 26780 on kitchen items. Find the total amount spent by her on the above items.