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How long will it take for an amount of ₹ 450 to yield ₹ 81 as interest at $4.5\%$ per annum of simple interest?

Present age of a grandfather is 72 years while his grandson's age is 12 years. After 8 years, the ratio of grandfather's age to grandson's age will be ____.

The 6-th triangular number is:

A. 6

B. 10

C. 21

D. 28

Draw appropriate graph to depict the runs scored by the Indian team. [2 MARKS]

$\begin{array}{cc}\text{Players}& \text{Score}\\ \text{Rahul}& 90\\ \text{Sachin}& 99\\ \text{Saurav}& 56\\ \text{Sehwag}& 30\\ \text{Gambhir}& 30\\ \text{Yuvraj}& 48\\ \text{Kohli}& 82\\ \text{Zaheer}& 0\\ \text{Nehra}& 1\\ \text{Mishra}& 19\end{array}$

The reduced form of the algebraic expression $\frac{2(a^2-b^2)}{(a+b)}$ is ___

Write 5 rational number between , having the same denominators.

If $2x-3y=10$ and $xy=16$ ; find the value of $8x^3-27y^3$

What is the multiplicative inverse of $-\frac{11}{8}$?

Two alternate sides of a regular polygon, when produced, meet at right angles. Find the number of sides of the polygon.

Arrange the following rational numbers in ascending order : $\frac{8}{10}$ , $\frac{48}{60}$, $\frac{32}{40}$ and $\frac{96}{120}$

Question 8.
A gardener has 1000 plants. He wants to plan these in such a way that the number of rows and number of columns remain same. Find the minimum number of plants he needs more for this.

A bag contains ₹510 in the form of 50 p, 25 p and 20 p coins in the ratio 2 : 3 : 4. Find the number of coins of each type respectively.

In the given figure, ABCD is a quadrilateral and $\angle ADC=a^{\circ },\angle BCD=b^{\circ }.$ AO and BO are bisectors of $\angle DAB$ and $\angle ABC$ respectively meeting at O. Find $\angle AOB$ in terms of $a^{\circ }$ and $b^{\circ }$.

1. 7

If a + 10^o, 3a + 10^o, 5a - 10^o and 3a - 10^o are the angles of a quadrilateral, then what is the value of a?

Which of the following are not true?

i) $3^{\left(\frac{1}{3}\right)}$ = $\sqrt{3^{-3}}$
ii) $3^{\left(\frac{1}{2}\right)}$ = $\sqrt{3^2}$
iii) $3^{-2}$ = $\sqrt{3}$
iv) $3^{\left(\frac{1}{2}\right)}$ = $\sqrt{3}$

Find all integers such thatis also an integer.

In a ΔABC, obtuse angled at B, if AD is perpendicular to CB produced, prove that AC = ${AB}^2$ + ${BC}^2$ + 2BC $\times$ BD [4 MARKS]

Factorise : $49(x-y{)}^2-9(2x+y{)}^2$

If the length of the side of a square is $7xy$, then the area of the square will be .

The set $(A\cup B^{\prime }{)}^{\prime }\cup (B\cap C)$ is equal to

Which of the following correctly explains distributive law?

Express 2352 in exponential form.

To construct an equilateral triangle, the minimum requirement is:

Which of the following function satisfy given mapping diagram.





Given that $x\in \text{Domain}\&y\in \text{Range}$

Krishna and Karan are playing see-saw. Krishna's weight is 60 kg and Karan is 80kg. Who among the following kids can help Krishna balance the see-saw. (All of them can sit at extreme ends only).

Simplify: $(3x-2y)(3x+4y)-(3x+2y)(3x-2y)$

A and B. working together can finish a piece of work in 6 days, while A alone can do it in 9 days. How much lime will B alone take to finish it?

The product of $\frac{-5}{17}$ and $\frac{a}{b}$ = 1 , then $\frac{a}{b}$ = ___ and $\frac{-5}{17}$ are ___of each other.

ABC is the right angled triangle with $\angle$ABC=${90}^{\circ }$, The centre of the circle passing through ABC lies on _______.

Divide the given
polynomial by the given monomial.

(i) (5x²
− 6x) ÷ 3x

(ii) (3y⁸ −
4y⁶ + 5y⁴) ÷ y⁴

(iii) 8(x³y²z²
+ x²y³z² +
x²y²z³) ÷
4x²y²z²

(iv) (x³
+ 2x² + 3x) ÷ 2x

(v) (p³q⁶
− p⁶q³) ÷ p³q³

A solid is formed by taking this shape and stacking it to a height of $10inches$. If the area of the shape is $12inche{s}^2$, what is the volume of the solid?

For which triangle the orthocenter lies on the triangle and not inside the triangle.

The pitch and the number of divisions, on the circular scale for a given screw gauge are $0.5\text{mm}$ and $100$ respectively. When the screw gauge is fully tightened without any object, the zero of its circular scale lies $3$ division below the mean line. The readings of the main scale and the circular scale, for a thin sheet, are $5.5\text{mm}$ and $48$ respectively, the thickness of the sheet is

Question 108(iii)
Verify the property $x\times y=y\times x$ of rational numbers by using
$x=\frac{-5}{7}$ and $y=\frac{14}{15}$