List of top Mathematics Questions

A ray of light coming from (3, 1) incident on 2x + y = 6 and deflected ray passing through (7, 2). If equation of incident ray is ax + by + 1 = 0, then a² + b² + 3ab =

If \(\frac{1}{(1+d)(1+2d)}+\frac{1}{(1+2d)(1+3d)}+...+\frac{1}{(1+9d)(1+10d)}=1,\) then the value of 50d is____. (d > 0)

A ray of light passing through (1, 2) after reflecting on x-axis at point Q passes through R(3, 4). If S(h, k) is such that PQRS is a parallelogram, then find the value of hk².

Use the figure to name :

Line containing point E

(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.

A line segment has length 63 and direction ratios, <3, -2, 6>. If the line makes an obtuse angle with x-axis, then the components of the line vector are

Classify each one of the following angles as right, straight, acute, obtuse or reflex:

angles as right, straight, acute, obtuse or reflex:

Let 'd' be the perpendicular distance from the centre of the ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}}

= 1 to the tangent drawn at a point P on the ellipse. If F1 and F are two foci of the ellipse, then (PF1 - PF)²is equal to;

Add without using number line :
(a) 11 + (– 7)
(b) (– 13) + (+ 18)
(c) (– 10) + (+ 19)
(d) (– 250) + (+ 150)
(e) (– 380) + (– 270)
(f) (– 217) + (– 100)

The value of $\frac{1\times 2^2+2\times3^2+...+100\times (101)^2}{1^2 \times 2\times2^2 \times3+...+100^2 \times 101}$

For 8^2x - 16.8^x + 48 = 0, the sum of values of x is equal to:

Evaluate each of the following:

(–30) ÷ 10
50 ÷ (–5)
(–36) ÷ (–9)
(– 49) ÷ (49)
13 ÷ [(–2) + 1]
0 ÷ (–12)
(–31) ÷ [(–30) + (–1)]
[(–36) ÷ 12] ÷ 3
[(– 6) + 5)] ÷ [(–2) + 1]

Set up equations and solve them to find the unknown numbers in the following cases:
(a) Add 4 to eight times a number; you get 60.
(b) One-fifth of a number minus 4 gives 3.
(c) If I take three-fourths of a number and add 3 to it, I get 21.
(d) When I subtracted 11 from twice a number, the result was 15.
(e) Munna subtracts thrice the number of notebooks he has from 50, he finds the result to be 8.
(f) Ibenhal thinks of a number. If she adds 19 to it and divides the sum by 5, she will get 8.
(g) Anwar thinks of a number.If he takes away 7 from \(\frac{5}{2}\) of the number,the result is 23.

Name the types of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) \(∆ABC\) with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.
(c) \(∆PQR\) such that PQ = QR = PR = 5 cm.
(d) \( ∆DEF\) with m\(∠\) D = 90°
(e) \(∆XYZ\) with m \(∠\)Y = 90° and XY = YZ.
(f) \(∆LMN\) with m \(∠\)L = 30°, m \(∠\)M = 70° and m \(∠\)N = 80°.

Let,\(f(\theta)=\frac{sin^4\theta+3cos^2\theta}{sin^4\theta+cos^2\theta},\)then range of f(θ) ∈ [a, b]. The sum of infinite G.P., where first term is 64 and common ratio is a/b is equal to:

If $\begin{vmatrix}a&5x&p\\ b&10y&5\\ c&15z&15\end{vmatrix} = 125$, then find the value of $\begin{vmatrix}3a&3b&c\\ x&2y&z\\ p&5&5\end{vmatrix}$

The cost of 4 kg onion,3 kg wheat and 2kg rice is Rs 60.The cost of 2 kg onion,4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

Add the following. a – b + ab, b – c + bc, c – a + ac.

Evaluate\(\begin{vmatrix} 1 & x & y\\ 1 & x+y & y\\1&x&x+y \end{vmatrix}\)

Investigate:
In the given figure, the angle measure 30º. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?

magnifying glass

The following table gives the distribution of students of two sections according to the marks obtained by him:

Section A		Section B
Marks	Frequency	Marks	Frequency
0 − 10	3	0 − 10	5
10 − 20	9	10 − 20	19
20 − 30	17	20 − 30	15
30 − 40	12	30 − 40	10
40 − 50	9	40 − 50	1

Represent the marks of the students of both the sections on the same graph by two frequency polygons. From the two polygons compare the performance of the two sections.

The resultant of two vectors of magnitudes \(2A\) and \(\sqrt2A\) acting at an angle θ is \(\sqrt10 A\). The correct value of \(θ\) is?

What is the period of the function sin 4x + tan 2x?

Show that the function given by f(x)=\(\frac{logx}{x}\) has maximum at x=e

ABC and DBC are two isosceles triangles on the same base BC (see Fig). Show that ∠ABD = ∠ACD.

ABC and DBC are two isosceles triangles on the same base BC

If $X=\{1,2,3, \ldots, 10\}$ and $A=\{1,2,3,4,5\}$. Then, the number of subsets $B$ of $X$ such that $A-B=\{4\}$ is