Explore topic-wise InterviewSolutions in Current Affairs.

The rario between the interior angle and the exterior angle of a regular polygon is 2 : 1. Find :

(i) each exterior angle of the polygon ;

(ii) number of sides in the polygon.

In each case, find whether the trinomial is a perfect square or not :

$\left(i\right)x^2+14x+49$ $\left(ii\right)a^2-10a+25$

$\left(iii\right)4x^2+4x+1$ $\left(iv\right)9b^2+12b+16$

$\left(v\right)16x^2-16xy+y^2$ $\left(vi\right)x^2-4x+16$

The edges of two cubes are in the ratio 3:4 .So the ratio of their volumes is ______

The number of cube numbers between the numbers 10 and 200 is ______ .

When $5pq(p^2-q^2)$ is divided by $2p(p+q)$ and substituting $p=3,q=1$; the value obtained is:

If $x^2$ is multiplied by its square root,then the cube root of the result = .

Question 08.
Rashmi has a road map with a scale of 1 cm representing 18 km. She drives on a road for 72 km. What would be her distance covered in the map?

Arjun has thrice as many rupees as Prateek, and Shubhendu has half as many as Arjun and Prateek put together. If Arjun has 120 rupees, then how much money do Prateek and Shubhendu have? [3 MARKS]

Expand $(x-8)(x-10)$.

Question 105(ii)

The following histogram shows the frequency distribution of teaching experiences of 30 teachers in various schools :

How many teachers are having the maximum teaching experience and how many have the least teaching experience ?

Which of the following is the property of a square?

${\left(\frac{-1}{2}\right)}^5\times {\left(\frac{-1}{2}\right)}^3$ is equal to

If $n(\cup )=700$, $n\left(A\right)=200$, $n\left(B\right)=300$ , $n(A\cap B)=100$, then $n(A^{{}^{\prime }}\cap B^{{}^{\prime }})$

<Two friends arguing>

Arjun: If a figure can be folded along any line such that one half superimposes the other, it is known as symmetric figure.

Shubh: If you can find a line in the figure which divides it in identical parts, then the figure is always symmetric.

A shopkeeper marks his goods in such a way that after allowing a discount of $25\%$ on the marked price, he still makes a profit of $50\%$. Find the ratio of the C.P to the M.P.

$(2^{-5}÷2^{-2})=?$

$\left(a\right)\frac{1}{128}$

$\left(b\right)\frac{-1}{128}$

$\left(c\right)-\frac{1}{8}$

$\left(d\right)\frac{1}{8}$

$8,780,000,000,000=$ _______.

Question 41

All six faces of a cuboid are ___ in shape and of ___ area.

Find $\angle ABF$ from the given figure.

72 men can build a small house in 30 days, working 8 hours a day. In how many days will 80 men, working 6 hours a day, complete the work?

1,024 trees are planted in a grid fashion such that the number of rows is equal to the number of columns. One row and one column of trees are cut such that the number of rows and columns after cutting remain equal. Find the number of trees that were cut?

In a lottery, there are 10 prizes and 25 blanks. Find the probability of getting a prize.

Use the given diagram to find :

$\left(i\right)A\cup (B\cap C)\left(ii\right)B-(A-C)\left(iii\right)A-B\left(iv\right)A\cap B^{\prime }IsA\cup B^{\prime }=A-B?$

Simplification of $(x+3)(x+3)$ gives

Factorise : $5+3a-14a^2$

Division of two rational numbers is a rational number if denominator is not equal to zero.Justify.

Sum of the digits of a two digit number is 9. When we interchange the digits it is found that the resulting new number is greater than the original number by 27. What is the two digit number

Pls guide me how to do this sum

Use direct method to evaluate :

(i) (x + 1)(x - 1)

(ii) (2 + a)(2 - a)

(iii) (3b - 1)(3b + 1)

(iv) ( 4 + 5x)(4 - 5x)

(v) (2a + 3)(2a - 3)

(vi) (xy + 4)(xy - 4)

(vii) (ab + x^2)(ab - x^2)

(viii) (3x^2 + 5y^2)(3x^2 - 5y^2)

(vi) (xy + 4)(xy - 4)

(ix) $(z-\frac{2}{3})(z+\frac{2}{3})$

(x) $(\frac{3}{5}a+\frac{1}{2})(\frac{3}{5}a-\frac{1}{2})$

(xi) (0.5 - 2a)(0.5 + 2a)

(xii) $(\frac{a}{2}-\frac{b}{2})(\frac{a}{2}+\frac{b}{3})$

Question 89

Solve the following:

Sum of the digits of a two-digit number is 11. The given number is less than the number obtained by interchanging the digits by 9. Find the number.

The number of students in a hostel, speaking different languages is given below. Display the data in a pie chart. [4 MARKS]

$\begin{array}{cc}\text{Language}& \text{No. of Students}\\ \text{Hindi}& 40\\ \text{English}& 12\\ \text{Marathi}& 9\\ \text{Tamil}& 7\\ \text{Bengali}& 4\\ \text{Total}& 72\end{array}$

Factorise:

$3a^5-108a^3$

Expand: ${[\sqrt{3x}-\frac{\sqrt{2}}{5}y]}^2$

Question 37

In the class interval 20-30, the lower class limit is ___.

In ∆ABC and ∆PQR, if AB = AC, ∠C = ∠P and ∠B = ∠Q, then the two triangles are:

The dimensions of a cuboid are in the ratio of 1 : 2 : 3 and its Total surface area is 88 $m^2$. The volume of cuboid is___ $m^3$

If (P + Q + R) can finish 11/97 part of work in 1 day, then (P + Q + R) can together finish the work in

Simplify : $0.005\times {10}^2-5\times {10}^{-1}$

Find the area of given figure, if the diameter BC is 14 cm and AD = 16 cm.

In what time will Rs. 1000 amount to Rs. 1331 at $10\%$ per annum compound interest.

A man can do a piece of work in 5 days. He and his son working together can finish it in 3 days. In how many days can the son do it alone? 1

(a) $6\frac{1}{2}$ days

(b) 7 days

(c) $7\frac{1}{2}$ days

(d) 8 days

Diameter of a circle is 30 cm. If the length of a chord is 20 cm, find the distance of the chord from the centre.

What was the second highest rating given?___

Three prizes are to be distributed in a quiz contest. Total prize is Rs.1000. Second prize will be given $\frac{3}{4}$ of the first prize and third prize will be given $\frac{1}{3}$ of the second prize. Find the money given to each contest. [4 MARKS]