List of top Mathematics Questions

The integrating factor of the differential equation.
\((1-y^{2})\frac{dx}{dy}+yx=ay\)\((-1<y<1)\)\(is\)

When a = 0, b = – 1, find the value of the given expressions: (i) 2a+2b (ii) 2a²+b²+1 (iii) 2a²b+2ab²+ab (iv) a²+ab+2

There are 4 letters and 4 directed envelopes. The number of ways in which all the letters can be put in wrong envelope is

How many numbers of 6 digits can be formed from the digits of the number 112233 ?

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD (Fig 9.15). If the area of the parallelogram is \(1470\) \(cm^2\) , AB = \(35\) \(cm\) and AD = \(49\) \(cm\), find the length of BM and DL.

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ  and x sin θ – (1 + cos θ) y + a sin θ = 0 is 

For the function f(x)= e^cosx , Rolle’s theorem is

If $x+\frac{1}{x}=2\cos \theta ,$ then for any integer $n,x^n+\frac{1}{x^n}=$

For the real parameter $t$, the locus of the complex number $z=(1-t^2)+i\sqrt{1+t^2}$

The diagonals of a rhombus are 7.5 cm and 12 cm. Find its area.

A floor is 5 m long and 4 m wide. A square carpet of sides 3 m is laid on the floor. Find the area of the floor that is not carpeted.

Radhika’s mother gave her ₹ 10.50 and her father gave her ₹ 15.80, find the total amount given to Radhika by the parents.

Factorise the expressions and divide them as directed. 

1. \((y^ 2 + 7y + 10) ÷ (y + 5)\) 
2.  \((m^2 – 14m – 32) ÷ (m + 2)\) 
3.  \((5p^ 2 – 25p + 20) ÷ (p – 1)\) 
4.  \(4yz(z ^2 + 6z – 16) ÷ 2y(z + 8)\)
5.  \(5pq(p^ 2 – q^ 2 ) ÷ 2p(p + q)\) 
6.  \(12xy(9x^ 2 – 16y ^2 ) ÷ 4xy(3x + 4y)\) 
7.  \(39y^ 3 (50y ^2 – 98) ÷ 26y ^2 (5y + 7)\)

Raju bought a book for ₹ 35.65. He gave ₹ 50 to the shopkeeper. How much money did he get back from the shopkeeper?

If an ellipse the distance between the foci is 8 and the distance between the directrices is 25. The length of the minor axis is

Two persons could fit new windows in house in 3 days.
(i) One of the persons fell ill before the work started. How long would the job take now?
(ii) How many persons would be needed to fit the windows in one day?

Find the number from each of the following expanded forms:
(a) 8 ×10⁴ + 6 ×10³ + 0×10² + 4×10¹ + 5×10⁰ 
(b) 4 ×10⁵ + 5×10³ + 3×10² + 2×10⁰ 
(c) 3 ×10⁴ + 7×10² + 5×10⁰ 
(d) 9 ×10⁵ + 2×10² + 3×10¹

Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

1. \(\frac{1}{6} [  ]\frac{1}{3}\)
2. \(\frac{3}{4} [  ]\frac{ 2}{6}\)
3. \(\frac{2}{3} [  ] \frac{2}{4}\)
4. \(\frac{6}{6} [  ] \frac{3}{3}\)
5. \(\frac{5}{6} [  ] \frac{5}{5}\)
   Make five more such problems yourself and solve them with your friends.

The number of girl students in each class of a co-educational middle school is depicted by the pictograph : 

Observe this pictograph and answer the following questions :

1. Which class has the minimum number of girl students?
2.  Is the number of girls in Class VI less than the number of girls in Class V?
3. How many girls are there in Class VII?

Following pictograph shows the number of tractors in five villages.

Observe the pictograph and answer the following questions.

1. Which village has the minimum number of tractors?
2. Which village has the maximum number of tractors?
3. How many more tractors village C has as compared to village B.
4. What is the total number of tractors in all the five villages?

Catherine threw a dice 40 times and noted the number appearing each time as shown below :

Make a table and enter the data using tally marks. Find the number that appeared.

1. The minimum number of times
2. The maximum number of times
3. Find those numbers that appear an equal number of times.

In a Mathematics test, the following marks were obtained by 40 students. Arrange these marks in a table using tally marks.

(a) Find how many students obtained marks equal to or more than 7.
(b) How many students obtained marks below 4?

Make five more such pairs and put appropriate signs.