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List of top Mathematics Questions

The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots +\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :

If $\frac{dy}{dx} +2y = sin 2x$ and $y(0) = \frac{3}4$ , then $y (\frac{π}{8})$ is equal to:

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components :

Lifetimes (in hours)	0 - 20	20 - 40	40 - 60	60 - 80	80 - 100	100 - 120
Frequency	10	35	52	61	28	29

Determine the modal lifetimes of the components.

Factorise

$x^ 2 + xy + 8x + 8y$
$15xy - 6x + 5y - 2 $
$ax + bx - ay - by$
$15pq + 15 + 9q + 25p$
$z - 7 + 7xy - xyz$

If p=–2,find the value of: (i)4p+7 (ii) –3p²+4p+7 (iii)–2p³–3p²+4p+7

Simplify these expressions and find their values if x = 3, a = – 1, b = – 2. (i) 3x – 5 – x + 9 (ii) 2 – 8x + 4x + 4 (iii) 3a + 5 – 8a + 1 (iv) 10 – 3b – 4 – 5b (v) 2a – 2b – 4 – 5 + a

Let relation defined as $(x_1, y_1) \,R (x_2, y_2)\, x_1 ≤ x_2,\, y_1 ≤ y_2$ and given that
(a) R is reflexive but not symmetric.
(b) R is transitive. then

Find the value of:
(i) -4÷$\frac{2}{3}$
(ii) -$\frac{3}{5}$÷2
(iii) -$\frac{4}{5}$÷(-3)
(iv) -$\frac{1}{8}$÷$\frac{3}{4}$
(v) -$\frac{2}{13}$÷$\frac{1}{7}$
(vi) -$\frac{7}{12}$÷(-$\frac{2}{13}$)
(vii) $\frac{3}{13}$÷(-$\frac{4}{65}$)

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig). Show that the line segments AF and EC trisect the diagonal BD.

Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

402
1989
3250
825
4000

Classify into monomials, binomials and trinomials.
(i) 4y – 7z (ii) y² (iii) x + y – xy (iv) 100 (v) ab – a – b (vi) 5 – 3t (vii) 4p²q – 4pq² (viii) 7mn (ix) z² – 3z + 8 (x) a² + b²(xi) z²+ z (xii) 1 + x + x²

For each of the following numbers, find the smallest whole number by which it should be divided so as to get a perfect square number. Also find the square root of the square number so obtained.

252
2925
396
2645
2800
1620

$\log ( \tan 18\degree) + \log ( \tan 36\degree) + \log ( \tan 54\degree) + \log (\tan 72\degree) =$

If $ x^{1/3} + y^{1/3} = 1 $, find $ \frac{dy}{dx} $ at the point $ \left( \frac{1}{8}, \frac{1}{8} \right) $.

Integrate the function: $\frac {1}{\sqrt {8+3x-x^2}}$

Write the following equations in statement forms:
(i)p+4=15
(ii)m-7=3
(iii)2m=7
(iv)$\frac{m}{5}$=3
(v)$\frac{3m}{5}$=6
(vi)3p+4=25
(vii)4p-2=18
(viii)$\frac{p}{2}$+2=8

Factorise the expressions

$ax^2 + bx$
$7p^ 2 + 21q^ 2$
$2x^ 3 + 2xy^2 + 2xz^2$
$am^2 + bm^2 + bn^2 + an^2$
$(lm + l) + m + 1$
$y(y + z) + 9(y + z)$
$5y^ 2 - 20y - 8z + 2yz$
$10ab + 4a + 5b + 2$
$6xy - 4y + 6 - 9x$

Find $(x + 1)^6 - (x - 1)^6$. Hence or otherwise evaluate $(\sqrt2 + 1)^6 + (\sqrt2 - 1)^6.$

Find $(a + b)^4 - (a - b)^4$. Hence, evaluate $(\sqrt3 + \sqrt2)^4 - (\sqrt3 - \sqrt2)^4$.

Convert the given fractional numbers to per cents.

$\frac{1}{8 }$
$\frac{5}{4 }$
$\frac{3}{40}$
$\frac{2}{7}$

Find the derivative of
(i) 2x - $\frac{3}{4}$
(ii)(5x³+3x-1)(x-1)
(iii) x-3(5+3x) (iv)x⁵(3-6x-9)
(v) x-4(3-4x-5) (vi)$\frac{2}{x+1}-\frac{x^2}{3x-1}$

Find the direction in which a straight line must be drawn through the point (-1, 2) so that its point of intersection with the line x + y = 4 may be at a distance of 3 units from this point

If a matrix has 36 elements, the number of possible orders it can have, is:

If $ y = (\tan x)^x $, then find $ \frac{dy}{dx} $.

You have to find out what will come in place of the question mark
2154.832 ÷ 16.1514 = ?