Explore topic-wise InterviewSolutions in Current Affairs.

In Fig. 7.137, AB || QR. Find the length of PB.

A die is rolled twice, find the probability that
(i) 5 will not come up either time,
(ii) 5 will come up exactly one time,
(iii) 5 will come up both the times.

The perpendicular from A on side BC of a ΔABC intersect BC at D such that DB = 3 CD. Prove that 2 AB² = 2 AC² + BC²

The sum total of the ages of father and son is 55yrs.if the father was to live till his son's age equal his present age,the total of their ages would be 93 yrs .find present ages

Are there numbers x and y for which?

If the nth term of the A.P. 9,7,5,... is same as the nth term of the A.P. 15,12,9,... find n.

Let a line meet a circle at A and B. This line is rotated about point A in clockwise direction such that B always remains on the circumference of the circle until point B coincides with A. What is the resulting line called?

The circle in the figure below touches all the three lines.

Prove that the perimeter of the right angle triangle is equal to the diameter of the circle.

$ABC$ is an isosceles triangle right angled at $C$. Prove that $A{B}^2=2A{C}^2$

The equation $x^2+ax-a^2$ - 1 = 0 will have roots of opposite signs if :

Which of the following equations is a solution of x = 7, y = 3?

Which is the correct relation of radius and diameter?

Visualizing Euclid’s division algorithm, find the values of $a,b$ and $c.$

Cards marked with numbers 1, 2, 3, 4……… 20 are well shuffled and a card is drawn at random. What is the probability that the number on the card is:

i) a prime number

ii) divisible by 3

iii) a perfect square

Question 63

The buying price of 5 kg of flour with the rate Rs 20 per kg, when 5% sales tax is added on the purchase, is Rs 21.

Prove that:

(i) $sin({70}^{\circ }+\theta )-cos({20}^{\circ }-\theta )=0$

(ii) $tan({55}^{\circ }-\theta )-cot({35}^{\circ }+\theta )=0$

(iii) $cosec({67}^{\circ }+\theta )-sec({23}^{\circ }-\theta )=0$

(iv) $cosec({65}^{\circ }+\theta )-sec({25}^{\circ }-\theta )-tan({55}^{\circ }-\theta )+cot({35}^{\circ }+\theta )=0$

(v) $sin({50}^{\circ }+\theta )-cos({40}^{\circ }-\theta )+tan{1}^{\circ }tan{10}^{\circ }tan{80}^{\circ }tan{89}^{\circ }=1$

In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.

Two towers are 40m apart. The angle of elevation of the top of the taller tower from the base and top of the shorter tower is ${70}^{\circ }$ and ${40}^{\circ }$ respectively. Find the height of the shorter tower. $[Tan{40}^{\circ }=0.83,Tan{70}^{\circ }=2.74]$

If $sec\theta +tan\theta =p$ , prove that

(i) $sec\theta =\frac{1}{2}(p+\frac{1}{p})$

(ii) $tan\theta =\frac{1}{2}(p-\frac{1}{p})$

(iii) $sin\theta =\frac{p^2-1}{p^2+1}$

What is the range of 6, 3, 9, 12, 0, 1?