List of top Mathematics Questions

Read the bar graph which shows the number of books sold by a bookstore during five consecutive years and answer the following questions:
(i) About how many books were sold in 1989? 1990? 1992?
(ii) In which year were about 475 books sold? About 225 books sold?
(iii) In which years were fewer than 250 books sold?
(iv) Can you explain how you would estimate the number of books sold in 1989?
The letters of the word MODESTY are written in all possible orders and these words are written out as in a dictionary then the rank of the word MODESTY is
Evaluate the determinants 
(i) \(\begin{vmatrix}3 & -1 & -2\\ 0 & 0 & -1 \\ 3&-5&0\end{vmatrix}\)(iii) \(\begin{vmatrix} 3 & -4 & 5\\ 1 & 2 & -2 \\ 2&3&1\end{vmatrix}\)
(ii)\(\begin{vmatrix} 0 & 1 & 2\\ -1 & 0 & -3 \\ -2&3&0\end{vmatrix}\) (iv)\(\begin{vmatrix} 2 & -1 & -2\\ 0 & 2 & -1\\3&-5&0 \end{vmatrix}\)
\(Let\, z_1=2 – i,z_2 = –2+i.\, Find\, (i) Re(\frac{z_1z_2}{z_1}), (ii) \,Im(\frac{1}{z_1z_1})\)

Let A=\(\begin{bmatrix}3&7\\2&5\end{bmatrix}\)and B=\(\begin{bmatrix}6&8\\7&9\end{bmatrix}\),Verify that (AB)-1=B-1A-1.

Find the intervals in which the function f given by \(f(x)=\frac{4sinx-2x-x}{2+cosx}\) is (i)increasing (ii)decreasing
Evaluate
  1. \(\frac{ (8^{−1}× 5^3)}{2^{−4}} \)
  2. \((5^{−1}× 2^{−1})×6^{−1}\)
The family of curves whose x and y intercepts of a tangent at any point are respectively double the x and y coordinates of that point is
Factorise : (i) 12x 2 – 7x + 1 (ii) 2x 2 + 7x + 3 (iii) 6x 2 + 5x – 6 (iv) 3x 2 – x – 4.
Identify the numerical coefficients of terms (other than constants) in the following expressions: 
(i) 5 – 3t2 
(ii) 1 + t + t2 + t3 
(iii) x + 2xy + 3y 
(iv) 100m + 1000n 
(v) – p2q2 + 7pq 
(vi) 1.2 a + 0.8 b 
(vii) 3.14 r2 
(viii) 2 (l + b) 
(ix) 0.1 y + 0.01 y2

For x ∈ (0, π), the equation sin x + 2sin2x −sin3x = 3 has 

Factorise each of the following: 

(i) 27y 3 + 125z 3 

(ii) 64m3 – 343n 3 

[ Hint : See Question 9. ]

Find the local maximum value and local minimum value (whichever exists) for the function \[ f(x) = 4x^2 + \frac{1}{x}, \quad (x \neq 0). \]
For each of the following numbers, find the smallest whole number by which it should be multiplied so as to get a perfect square number. Also find the square root of the square number so obtained. 
  1. 252 
  2.  180 
  3.  1008 
  4.  2028 
  5.  1458 
  6.  768

Express the given complex number in the form \(a + ib: (1 - i) - (-1 + i6)\)

Consider the following parallelograms. Find the values of the unknowns \(x, y, z\).
parallelograms
If p=–2,find the value of: (i)4p+7 (ii) –3p2+4p+7 (iii)–2p3–3p2+4p+7

Solve system of linear equations, using matrix method.
 x-y+2z=7
 3x+4y-5z=-5
 2x-y+3z=12

The distance of the point (3, 4, 5) from X-axis is
A group of \(360\) people were asked to vote for their favourite season from the three seasons rainy, winter and summer. 
  1. Which season got the most votes? 
  2. Find the central angle of each sector. 
  3. Draw a pie chart to show this information.
SeasonNumber of votes
Summer90
Rainy120
Winter150


 

Prove: \(2\ tan^{-1}(cos\ x)=tan^{-1}(2\ cosec\ x)\)

According to recent research, air turbulence has increased in various regions around the world due to climate change. Turbulence makes flights bumpy and often delays the flights. 
Assume that an airplane observes severe turbulence, moderate turbulence or light turbulence with equal probabilities. Further, the chance of an airplane reaching late to the destination are 55\%, 37\% and 17\% due to severe, moderate and light turbulence respectively. 
On the basis of the above information, answer the following questions: 
Find the probability that an airplane reached its destination late. If the airplane reached its destination late, find the probability that it was due to moderate turbulence.

If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
(i) A = {a, b, c}
(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
(iv) D = {f, g, h, a}
Find the product.
(i) (5 – 2x) (3 + x) 
(ii) (x + 7y) (7x – y) 
(iii) (a2+ b) (a + b2) 
(iv) (p2 – q2) (2p + q)
If $A = \{(x, y) : x^2 + y^2 = 25\}$ and $B = \{(x, y) : x^2 + 16y^2 = 144\}$ then $A \cap B$ contains