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Question 6

The value of $(tan{1}^{\circ },tan{2}^{\circ },tan{3}^{\circ }\dots \dots tan{89}^{\circ })$ is



(A) 0

(B) 1

(C) 2

(D) $\frac{1}{2}$

If $a_1,a_2,a_3,\dots \dots$ are in a harmonic progression with $a_1=5$ and $a_{20}=25$, then, the least positive integer n for which $a_n<0$, is

If tangents PA and PB from a point P to a circle with centre O are inclined to each other an angle of 80, then ∠POA is equal to

(A) 50 (B) 60

(C) 70 (D) 80

1. 5

A cricket ball of radius $r$ is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the surface area of tin is

An AP has the first term as 2 and the common difference as 4. Which term in the AP is the first multiple of 23 to appear in the AP?

From which point shown below can we draw one tangent to the following circle?

Find the number of natural numbers between 101 and 999 which are divisible by both 2 and 5.

In a right angled triangle ABC in which ∠A = ${90}^{\circ }$, If AD $\perp$ BC.

In a school, students thought of planting saplings in and around the school to reduce air pollution. It was decided that the number of saplings, that each section of each class will plant, will be the same as the class, in which they are studying, e.g, a section of Class I will plant 1 tree, a section of class II will plant two saplings and so on till Class XII. There are three sections of each class. How many saplings will be planted by the students?

The sum of 5th and 9th terms of an A.P. is 30. If its 25th term is three times its 8th term, find the A.P.

Find the number of terms in each of the following APs:
(i)$7,13,\mathrm{19....},205$
(ii) $18,\frac{31}{2},13,...-47$

The area of a circle with diameter 6 m exceeds the combined areas of circles with diameters 4m and 2 m by

The tangent at a point C of a circle and a diameter AB when extended, intersect at P. O is the centre of the circle. If $\angle$PCA = ${120}^0$, then find the value of 2$\angle$PBC.

In fig., there are two concentric circles with center O and of radii 5 cm and 3 cm. From an external point P, tangents PA and PB are drawn to these circles. If AP = 12 cm, find the length of BP [3 MARKS]

The H.C.F. of $x^3-3x^2+x-3$ and $x^4+6x^2+5$ is .

What is the mean of the given data? $f$ = Frequency

$\begin{array}{cc}x& f\\ 4& 10\\ 8& 11\\ 12& 9\\ 16& 13\end{array}$

In the given figure, O is the center of the circle. Tangents at A & B meet at C. If ∠ACO = 30^o, find ∠APB.

Given that $tan\theta =\frac{p}{q}$. Find the value of $\frac{psin\theta -qcos\theta }{psin\theta +qcos\theta }$ [3 MARKS]

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

Find the median length of the leaves.

(Hint: The data needs to be converted to continuous classes for finding the median, since the formula assumes continuous classes. The classes then change to 117.5 − 126.5, 126.5 − 135.5… 171.5 − 180.5)

There are 'a' trees in the village Lat. If the number of tree increase every year by 'b' ,then how many trees will be there be after 'x' year

Three sides of a triangle are, a, 3a, √10 a. Find the measurement of the angle opposite to the largest side

If α, β, γ are the zeros of the polynomial 2x³ + x² - 13x + 6, then the value of αβγ is

If P(A) = 0.2, P(B’) = 0.6 and P(A$\cap$B)= 0.1. Find P(A$\cup$B).

A tower is built on a river of width 100m. One can the top of the tower at an angle of elevation of ${50}^{\circ }$ $\&{40}^{\circ }$ from either bank of the river. Find the distance between the foot of the tower and both the river banks. $[Tan{40}^{\circ }=0.83,Tan{50}^{\circ }=1.91]$