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$\text{If}△ABC\text{is a right triangled with}\angle B={90}^{\circ },\text{and BD is perpendicular to AC,}\text{then AC}\times \text{DC will be equal to:}$

Find the value of $(5x+7y)\times (5x-7y)$.

Question 103

By what number should $(-15{)}^{-1}$ be divided so that quotient may be equal to $(-15{)}^{-1}$?

When $7xy+5yz-3zx,$ $4yz+9zx-4y$ and $-3xz+5x-2xy$ are added, we get ___.

Express the rational number $\frac{19}{37}$ to the lowest form.

Solve $(ab+1{)}^2$ - $(ab{)}^2$ where, b - a = 1.

What is the number of vertices in prism with triangular base?

Find the value of $(3a-\frac{1}{2})(3a-\frac{1}{2})$.

In which of the following quadrilaterals, diagonals bisect each other?

i)Parallelogram

ii)Rhombus

iii)Rectangle

iv)Square

Ronit borrows Rs.86000 from Akshay for 2 years at 5% per annum simple interest He immediately lends out to Akshay at 5% compound interest compounded annually for the same period. Calculate Ronit’s profit in the transaction at the end of 2 years.

Which ratio is smaller among :

13 :27, 17 :33 , 146: 297, 157 : 297 ?

The volume of a glass in the shape of a cylinder whose height is 3 times the radius is $81\pi m^3$.The height of the cylinder is:

A car travelled 60 km towards the north direction from a point A. From there, it travelled 100 km in the south direction. How far is the car from point A now?

A rope is tightly held between the 4 poles making the vertics of the rectangle. The length of the rope is 360m The distance between three consecutive poles is in the ratio 4: 5 .find the length and width of the rectangle.

Which of the following is not equal to ${\left(3^2\right)}^3$ ?

On what sum will the compound interest at $5\%$ p.a. annum for 2 years compounded annually be Rs. 164?

What is the area of the rhombus ABCD below if AC=12 cm and BE= 8 cm?

4 tens + 6 tens = ___

If x varies inversely as y, then

$\begin{array}{ccc}x& \square & 60\\ y& 2& 10\end{array}$

What is the degree of the polynomial $2x+\frac{7x^{\frac{9}{2}}}{x^{\frac{3}{2}}}+5?$

Shalini deposited ₹4,00,000 in a bank where she was promised an interest of 10%. She deposited it for two years. Find the difference between the amounts she would receive in case of interest being compounded annually and simple interest, for the same deposit.

△ABC is an isosceles triangle. If, △ABC and △XYZ are similar triangles, find the value of ∠XZY.

Peter makes ₹12000 a month plus some money by commission rates. He gets 6% commision on the items that he sells. If Peter sold 55000 worth of items this month, what is his salary for the month?

A three-dimensional figure made up of polygonal regions is called a _____.

If A, B, C, D,.........Z represents numbers from 1, 2, 3,...... 26. Key can be anything from 1 to 25. For a key of 2, every letter shifts 2 places. To right A becomes C, Z becomes B and so on. If key is equal to 9, match the normal letters with encrypted letters.

$$\begin{array}{cc}NormalLetter& EncryptedLetter\\ 1A& aY\\ 2F& bD\\ 3P& cO\\ 4U& dI\\ 5Z& eJ\end{array}$$

If b = 10 and h = 7, then the area of the following parallelogram is given by:

Question 2(iii)
Find the product:
$(a^2+b)(a+b^2)$

Which is the greatest 5 digit perfect square number?

Find the cube-roots of:

(i) $\frac{27}{64}$ (ii) $\frac{125}{216}$ (iiii) $\frac{343}{512}$

(iv) $64\times 729$ (v) $64\times 27$ (vi) $729\times 8000$

(vii) $3375\times 512$

If 303 × 297 = (a + b) (a - b), then the respective values of a and b are

What must be subtracted from $2x^3-4x^2+6x-2$ to get $3x^3+2x^2-5x+3$ ?

The standard form of $0.0005361$ is ___.

If the measure of the sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as ∠ ABC = ${75}^{\circ }$, ∠ BCD = ${35}^{\circ }$ and ∠ CDA = ${135}^{\circ }$, can you construct a quadrilateral ABCD?