Explore topic-wise InterviewSolutions in Current Affairs.

$\frac{\text{sec}{17}^{\circ }}{\text{cosec}{73}^{\circ }}+\frac{\text{tan}{68}^{\circ }}{\text{cot}{22}^{\circ }}-[{\text{cos}}^2{44}^{\circ }+{\text{cos}}^2{46}^{\circ }]=$___.

Two people working together can finish the work in $\frac{22}{55}$ minutes. If one person takes 8 minutes more than the other person to finish it, find the second degree equation from which we can find time in which the faster person would finish the work.

A survey was conducted on 20 families in a locality by a group of students .What will be the mode of the data?

$$\begin{array}{cccccc}\text{Age of family member}& 0-20& 20-40& 40-60& 60-80& 80-100\\ \text{Number of students}& 7& 8& 2& 2& 1\end{array}$$

In an equilateral triangle, prove that the centroid and the centre of the circumcircle (circumcentre) coincide. [4 MARKS]

Compare the area of regions I and II.

Write the arithmetic progression when first then a and common difference d are as follows:
(i) $a=4,d=-3$
(ii) $a=-1,d=\frac{1}{2}$
(iii) $a=-1.5,d=-0.5$

5 chairs and 4 tables together cost Rs.5600,while 4 chairs and 3 tables together cost Rs.4340.Find the cost of a chair and that of a table.

Can two numbers have 16 as their HCF and 380 as their LCM? Give reason.

The points A(-4, 0), B(4, 0) and C(0, 3) are the vertices of a triangle, which is

(a) isosceles (b) equilateral (c) scalene (d) right angled

The area of a rhombus is 480 $c{m}^2$, and one of its diagonals measures 48 cm. Find (i) the length of the other diagonal, (ii) the length of each of its sides, and (iii) its perimeter.

A vertical tower stands on a horizontal plane and is surmounted by a vertical flag-staff. At a point on the plane 70 metres away from the tower, an observer notices that the angles of elevation of the top and the bottom of the flag-staff are respectively ${60}^{\circ }and{45}^{\circ }$. Find the height of the flag-staff and that of the tower.

Prove the following trigonometric identities:

$(sec\theta +cos\theta )(sec\theta -cos\theta )=ta{n}^2\theta +si{n}^2\theta$

2. (i)Which term of the A.P. 3,8,13,...is 248?
(ii) Which term of the A.P. 84,80,76,... is 0?
(iii) Which term of the A.P. 4,9,14,... is 254?
(iv) Which term of the A.P. 21,42,63,84,...is 420?
(v) Which term of the A.P. 121,117,113,... is its first negative term?

What is the importance of finding areas and perimeters of circular shapes?

Find the values of k for which the given quadratic equation has real and distinct roots:

(i) $k{x}^2+6x+1=0$

(ii) $x^2-kx+9=0$

(iii) $9x^2+3kx+4=0$

(iv) $5x^2-kx+1=0$

The internal and external diameters of a hollow hemispherical shell are $6cm$ and $10cm$ respectively. It is melted and recast into a solid cone of base diameter $14cm$. Find the height of the cone so formed.

If you jumble up the following words randomly, what is the probability that the jumbled words start with the letter E?
(i) EERIE (ii) DEEP (iii) SHARK (iv) VEHEMENT

A wheat hut is in the form of a cone has a radius of 3m and height of 14m. Find the capacity of the hut to store the wheat. [2 MARKS]

Solve for x and y:

$\frac{5}{x}-\frac{3}{y}=1,\frac{3}{2x}+\frac{2}{3y}=5(x\ne 0,y\ne 0).$

From a well-shuffled pack of 52 cards, a card is drawn at random, find the probability that it is a spade.

Euclid's division lemma states that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy

(a) 1 < r < b (b) $0<r\le b$ (c) $0\le r<b$ (d) 0 < r < b

Question 18
The weight of coffee in 70 packets are shown in the following table

Determine the model weight.

Question 92

For the celebrating children's day, students of class VII bought sweets for Rs 740.36 and cold drink for Rs 70. If 35 students contributed equally what amount was contributed by each student?

Evaluate:
$8\frac{1}{2}-3\frac{5}{8}$

State the co-ordinates of the following points under reflection in the line y - 0;

(i) (-3, 0) (ii) (8, -5) (iii) (-1, -3)

P and Q have co-ordinates (-2, 3) and (5, 4) respectively. Reflect P in the x-axis to P' and Q in the y-axis to Q'. State the co-ordinates of P' and Q'.

Is (5,2) a solution of x+y-7= 0?

Which of the following is a polynomial in 1 variable?

The product of 2 consecutive natural numbers is 56. Solve this problem using completing the square method of quadratic equation. Write the equation obtained after completing the square and also write the smaller of the 2 numbers.

The areas of two similar triangles are 100 $c{m}^2$ and 64 $c{m}^2$ respectively, If a median of the smaller triangle is 5.6 cm, find the corresponding median of the other.

1. 5082

Using quadratic formula find the roots of the quadratic equation $2x^2-7x+3=0$ .

A ladder 15 m long just reaches the top of a vertical wall. If the ladder makes an angle of ${60}^{\circ }$ with the wall, then find the height of the wall.

The cost of 5 oranges and 3 apples is Rs. 35 and the cost of 2 oranges and 4 apples is Rs. 28. Find the cost of an orange and an apple by cross multiplication method.

Simplify $\frac{x+2}{x+3}+\frac{x-1}{x-2}.$

In the given figure, $△ABC$ ~ $△BDC$. Identify the equal angles in the triangles.

$\begin{array}{cc}1.\angle DBC=\square & A:\angle BCA\\ 2.\angle BDC=\square & B:\angle BAC\\ 3.\angle DCB=\square & C:\angle ABC\end{array}$​

When two dice are thrown simultaneously, the probability of getting a sum of 12 is___

If sin(A+B)=√3/2 and cos(A-B)=√3/2, then find A and B. Hence find the value of tan(A+B)+tan(A-B).

$\text{ABC is a right angled triangle with}\angle B={90}^0,a=6\text{cm}.\text{If the radius of the circumcircle is 5 cm, then the area of}\Delta ABCis$

Why is a pair of rectangles are not said to be similar

Find equation of the line parallel to the line 3x - 4y + 2 = 0 and passing through the point (-2, 3).

If ABC is an equilateral triangle of side a, prove that its altitude $=\frac{\sqrt{3}}{2}a$ [3 MARKS]