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List of top Mathematics Questions

Show that the relation R in R defined as R = {(a, b): a ≤ b}, is reflexive and transitive
but not symmetric.

The lengths of two sides of a triangle are 12 cm and 15 cm. Between what two measures should the length of the third side fall?

Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).

The sum of two consecutive odd numbers is divisible by 4. Verify this statement with the help of some examples.

For the differential equations , find a particular solution satisfying the given condition:$(x^3+x^2+x+1)\frac{dy}{dx}=2x^2+x;y=1$ when $x=0$

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube:

Measure and classify each angle:

Angle	Measure	Type
$∠AOB$
$∠AOC$
$∠BOC$
$∠DOC $
$∠DOA$
$∠DOB$

Express the following numbers in standard form.
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000

What other name can you give to the line of symmetry of

an isosceles triangle?
a circle?

A tower stands at the center of a circular park.

A

and

B

are two points on the boundary of the park such that

A B = a

subtends an angle

60^{\circ}

of at the foot of the tower and the angle of elevation of the top of the tower from

A

B

30^{\circ}

. The height of the tower is

If the angle

θ

between the line

\frac{x + 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{2}

and the plane

2 x - y + \sqrt{λ z} + 4 = 0

is such that

\sin θ = \frac{1}{3},

then value of

λ

$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to

Write all the integers between the given pairs (write them in the increasing order.)
(a) 0 and – 7
(b) – 4 and 4
(c) – 8 and – 15
(d) – 30 and – 23

Two adjacent sides of a parallelogram ABCD are given by

\vec{A B} = 2 \hat{i} + 10 \hat{j} + 11 \hat{k} a n d \vec{A D} = - \hat{i} + 2 \hat{j} + 2 \hat{k}

.The side AD is rotated by an acute angel

α

in the plane of the parallelogram so that AD becomes AD'. If AD' makes a right angle with the side AB, then the cosine of the angle

α

is given by;

From an airplane flying, vertically above a horizontal road, the angles of depression of two consecutive stones on the same side of the airplane are observed to be 30° and 60° respectively. The height at which the airplane is flying in km is :

Let a, b, c be such that b

(a + c) \neq 0 .

| \begin{array}{ccc} a & a + 1 & a - 1 \\ - b & b + 1 & b - 1 \\ c & c - 1 & c + 1 \end{array} | + | \begin{array}{ccc} a + 1 & b + 1 & c - 1 \\ a - 1 & b - 1 & c + 1 \\ (- 1)^{n + 2} a & (- 1)^{n + 1} b & (- 1)^{n} c \end{array} | = 0

Then the value of

n

is?

The general solution of

\cot θ + \tan θ = 2

Find the whole quantity if

5% of it is 600.
12% of it is Rs 1080.
40% of it is 500 km.
70% of it is 14 minutes.
(e) 8% of it is 40 litres

What is the HCF of two consecutive
1. numbers?
2. even numbers?
3. odd numbers?

Let x, y, z be positive real numbers such that x+y+z=12 and $x^3y^4z^5$=$(0.1)(600)^3$. Then, $x^3+y^3+z^3$ is equal to

Which of the following is a finite set ?

Find first three common multiples of :

1) 6 and 8

2) 12 and 18

Let $a, b, c$ be in $AP$. If $ 0 < a,b,c < 1 ,x=\sum\limits_{n=0}^{\infty }{{{a}^{n}}}, $ $ y=\sum\limits_{n=0}^{\infty }{{{b}^{n}}} $ and $ z=\sum\limits_{n=0}^{\infty }{{{c}^{n}}}, $ then

f (x)

and

g (x)

are two probability density functions,

f (x) = {\begin{array}{cc} \frac{x}{a} + 1 & : - a \leq x < 0 \\ - \frac{x}{a} + 1 & 0 \leq x \leq a \\ 0 & otherwise \end{array}

g (x) = {\begin{array}{cc} - \frac{x}{a} & : - a \leq x \leq 0 \\ \frac{x}{a} & : 0 \leq x \leq a \\ 0 & : otherewise \end{array}

Which one of the following statements is true?

Value of

\cos (- 1230^{\circ}) \times \cot (- 315^{\circ})

is:

Angle	Measure	Type
\(∠AOB\)
\(∠AOC\)
\(∠BOC\)
\(∠DOC \)
\(∠DOA\)
\(∠DOB\)