Mathematics is a key part of our everyday lives. It’s the basis for many fields, like science, engineering, economics, and technology. Understanding math is important not just for school but for solving real-life problems too. Whether you’re a student studying for exams, a professional needing a refresher, or someone who enjoys math challenges, working on different math problems can improve your thinking skills.
This collection includes the top 100 Maths questions, chosen to cover various topics and levels of difficulty. You’ll find questions on basic arithmetic, algebra, calculus, statistics, and more. Each question comes with a detailed solution to help you understand and learn different math techniques.
Practicing these questions will not only make you more confident but also help you appreciate the importance and beauty of math. So, jump in, challenge yourself, and enjoy exploring the world of numbers and equations.
List of Top 100 Maths Questions
Here are top 100 Maths questions with answers:
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| Top 100 Maths Questions with Answers |
| If sin A = sin 2 B and 2 cos 2 A = 3 cos 2 B then |
If ω ≠ 1 is a cube root of unity, then 1 1 + i + ω 2 ω 2 1 − i − 1 ω 2 − 1 − i − i + ω − 1 − 1 equal |
| If a , b , c are three real numbers such that a + b + c = 0 (at least one a , b , c is not equal to zero) and a z 1 + b z 2 + c z 3 = 0 , then z 1 , z 2 , z 3 : |
The radius of the circle in which the sphere x 2 + y 2 + z 2 + 2 z − 2 y − 4 z − 19 = 0 is cut by the plane x+2y+22+7=0 is |
| Three dice are rolled simultaneously. The probability that the numbers on them are different is |
If tan θ = − 4 3 and θ does not lie in the IV quadrant then 5 sin θ + 10 cos θ + 9 sec θ + 16 cos e c θ + 4 cot θ = |
| If α , β and γ are roots of 4 x 3 + 8 x 2 − x − 2 = 0 , then the value of 4 ( α + 1 ) ( β + 1 ) ( γ + 1 ) α β γ is |
The value of Arg [ i ln ( a − i b a + i b ) ] ; where a and b are real numbers |
| The number of rectangles that can be found on a chess board is |
For 0 ≤ r < 2 n , 2 n + r C n 2 n − r C n cannot exceed |
| A chord of length 16 units is at a distance of 6 units from the centre of a circle then its radius is |
Solution of the differential equation 1 + y + x 2 y d x + x + x 3 d y = 0 is |
| The value of ∫ sin α 1 + cos α d α is |
A flagstaff stands at the center of a rectangular field whose diagonal is 1200m, and subtends angles 15 0 and 45 0 at the mid points of the sides of the field. The height of the flagstaff is |
| The rectangle formed by the pair of lines 2 h x y + 2 g x + 2 f y + c = 0 with the coordinate axes has the area equal to |
The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is: |
| The expression 1 4 x + 1 1 + 4 x + 1 2 7 − 1 − 4 x + 1 2 7 is a polynomial in x of degree. |
n whole numbers are randomly chosen and multiplied. Now, match the following lists: List I List II a. The probability that the last digit is 1, 3, 7, or 9 is p. 8 n − 4 n 10 n b. The probability that the last digit is 2, 4, 6, 8 is q. 5 n − 4 n 10 n c. The probability that the last digit is 5 is r. 4 n 10 n d. The probability that the last digit is zero is s. 10 n − 8 n − 5 n + 4 n 10 n |
| For two data sets, each of size 5, the variance is given to be 4 and 5 and the corresponding means are given to be 2 and 4 respectively. The variance of the combined dataset is |
The value of 3 log 4 5 − 5 log 4 3 is |
| The line x − 2 3 = y + 1 2 = z − 1 − 1 intersects the curve x y = c 2 , z = 0 if c= |
L i m x π 2 cot x − cos x ( π 2 − x ) 3 = |
| The equation of line segment AB is y = x. If A & B lie on same side of line mirror 2 x – y = 1 , then the equation of image of AB with respect to line mirror 2 x – y = 1 is |
Let m be the smallest positive integer such that the coefficient of X 2 in the expansion of ( 1 + x ) 2 + ( 1 + x ) 3 + … + ( 1 + x ) 49 + ( 1 + mx ) 50 is ( 3 n + 1 ) 51 C 3 for some positive integer n. Then the value of n is |
| If a circle passes through ( 1 , 2 ) and cuts the circle x 2
+ y 2 = 4 orthogonally then the equation of the locus of its centre, is |
If m, n are any two odd positive integer with n<m, then the largest positive integers which divides all the numbers of the type m 2 − n 2 is |
| If the term free from x is the expansion of x − k x 2 10 is 405 , then the value of k . |
The sum of the digits of the number of positive integral solutions satisfying the equation x 1 + x 2 + x 3 y 1 + y 2 = 77 |
| Seven persons sit in a row at random. The probability that three persons A, B, C sit together in a particular order is |
The number of 9 digit numbers which have all distinct digits, is |
| The system of linear equations x + y + z = 2 , 2 x + y − z = 3 , 3 x + 2 y + k z = 4 has a unique solution if |
If 1 2 ≤ x ≤ 1 then cos − 1 x 2 + 1 2 3 − 3 x 2 + cos − 1 x = |
| The equation of straight line passing through ( − a , 0 ) and making the triangle with axes of area T is |
The number of ways in which 30 marks can be alloted to 8 questions if each question carries at least 2 marks, is |
| The equation of the smallest circle passing through the points of intersection of the line x + y − 1 = 0 and the circle x 2 + y 2 = 9 |
The largest term common to the sequences 1, 11, 21, 31…….. to 100 terms and 31, 36, 41, 46……. to 100 terms is |
| If the difference between the roots of the equation x 2 + a x + 1 = 0 less then 5 , then the set of possible value of a is |
The exponent of 3 in 100! is |
| If the absolute value of the difference of the roots of the equation x 2 + a x + 1 = 0 exceeds 3 a , then |
The direction ratios of two lines are given by a + b + c = 0 and a b + b c − 2 c a = 0 . Then the angle between the lines is |
| The A.M of all the solutions of 4 cos 3 x − 4 cos 2 x − cos ( π + x ) + 1 = 0 i n ( 0 , 315 ) i s |
The interior angles of a convex polygon forms on A.P with common difference of 4 ∘ . If the largest interior angle is 172 ∘ then the number of sides is |
| If f ( x ) = { 6 x − 3 x − 2 x + 1 2 sin 2 ( x 2 ) , if x ≠ 0 K , if x = 0 is continuous at x = 0 , then K = |
If a , b , c are real, then both the roots of the equation ( x − b ) ( x − c ) + ( x − c ) ( x − a ) + ( x − a ) ( x − b ) = 0 (1) are always |
| The internal angles of a convex polygon are in A.P. The smallest angle is 120 0 and the common difference is 5 0 ,then number of sides of the polygon is |
Let a and b be two real numbers such that a > 1 , b > 1. I f A = a 0 0 b then lim n ∞ A − n is |
| If A is a square matrix of order 2 x 2 such that |A| = 27, then sum of the infinite series | A | + 1 2 A + 1 4 A + 1 8 A + … is equal to . |
One vertex of an equilateral triangle is (2,3) and the equation of one side is x-y+5=0. Then the equations to other sides are |
| x x n − 1 − na n − 1 + a n ( n − 1 ) is divisible by ( x − a ) 2 for |
L e t A d e n o t e t h e e v e n t t h a t a 6 – d i g i t i n t e g e r f o r m e d b y 0 , 1 , 2 , 3 , 4 , 5 , 6 w i t h o u t r e p e t i t i o n s , b e d i v i s i b l e b y 3 . T h e n p r o b a b i l i t y o f e v e n t A i s e q u a l t o : |
| In an examination, a student has to answer 4 questions out of 5 questions; questions 1 and 2 are however compulsory. Find the number of ways in which the student can make the choice. |
| I n = ∫ tan n x d x then I n + I n + 2 is equal to |
Let R be a reflexive relation on a finite set A having elements, and let there be m ordered pairs in R. Then |
| p = b × c [ a b c ] , q = c × a [ a b c ] and r = a × b [ a b c ] where a , b and c are thee non-coplanar vectors, then the value of the expression ( a + b + c ) ⋅ ( p + q + r ) is |
A curve is given by the equations x = sec 2 θ , y = cotθ . If the tangent at P where θ = π 4 meets the curve again at Q, then [PQ] is, where [ . ] represents the greatest integer function |
| The number of positive integers < 1,00,000 which contain exactly one 2, one 5 and one 7 in its decimal representation is |
| The points of intersection of curves whose parametric equations are x = t 2 + 1 , y = 2 t and x = 2 S , y = 2 S is |
Two numbers are selected at random from a set of first 120 natural numbers, then the probability that product of selected number is divisible by 3 is |
| The mean value of the function f ( x ) = 2 e x + 1 on the interval [0, 2] is |
If A and B are two matrices such that AB = B and BA = A, then A 2 + B 2 = |
| If the equation cot 4 x − 2 cosec 2 x + a 2 = 0 has at least one solution, then the sum of all possible integral values of a is equal to |
Point of intersection of pair of lines a ( x − α ) 2 + 2 h ( x − α ) ( y − β ) + b ( y − β ) 2 = 0 is |
| If f ( x ) = a − 1 0 ax a − 1 ax 2 ax a , then f ( 2 x ) − f ( x ) is divisible by |
If both p and q are true, then |
| Sum of the series ∑ r = 1 n r ( r + 1 ) ! is |
The equation formed by decreasing each root of a x 2 + b x + c = 0 by 1 is 2 x 2 + 8 x + 2 = 0 , then: |
| If A is non-singular and A 2 – 5 A + 7 I = 0 then I = |
IF I = 2 π ∫ − π / 4 π / 4 d x 1 + e sin x 2 − cos 2 x then the value of 27 I 2 is |
| If f ( x ) = a x 2 + b x + c and f ( − 1 ) ≥ − 4 , f ( 1 ) ≤ 0 and f ( 3 ) ≥ 5 , then the least value of a is |
If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation x + y = 1 , then the orihocenire of the triangle is |
| tan 2 θ + sec θ = 5 ⇒ sec θ = |
In how many ways can 20 oranges be given to four children if each child should get at least one orange? |
| The negation of the following statement P: Neha lives in Ludhiana or she lives in Gurudaspur. |
The length of foot of perpendicular drawn from the point P ( – 3 , – 4 , 5 ) on y – a x i s |
| log ( x – 7) is |
∫ e − 1 e 2 | ln x x | d x = |
| The sine of the angle between the straight line x − 2 3 = y − 3 4 = z − 4 5 and the plane 2 x − 2 y + z = 5 is |
If cos A = 3 / 4 , then the value of 16 cos 2 ( A / 2 ) − 32 sin ( A / 2 ) sin ( 5 A / 2 ) is |
| The value of parameter, for which the function f ( x ) = 1 + α x , ≠ 0 is the inverse of itself is |
A circle touches the line 4 x + 3 y = 12 at D and positive x , y axes. Let DE be diameter of circle and OE intersect the line at F , then [ 4 DF ] is equal to ( [ . ] is GIF) (Provided OE < OD and O being origin ). |
| Let P be a point on the circle x 2 + y 2 = 9 , Q a point on the line 7 x + y + 3 = 0 , and the perpendicular bisector of P Q be the line x − y + 1 = 0 . Then, the coordinates of P are |
If cot θ + tan θ = x and sec θ − cos θ = y , then |
| I f x i > 0 , 1 ≤ i ≤ n , and x 1 + x 2 + x 3 … + x n = π , then the greatest value of sin x 1 + sin x 2 + sin x 3 + … + sin x n = |
If α and β are the roots of the equation x 2 − x + 1 = 0 , then α 2009 + β 2009 = |
| If Z be a complex number satisfying z 4 + z 3 + 2 z 2 + z + 1 = 0 then | z | is equal to |
Let A = a i j and B = b i j be two 3 X 3 real matrices such that b i j = 3 i + j − 2 a j i , where i , j = 1 , 2 , 3. If the determinant of B is 81 then the determinant of A is |
| Let f ( x ) = [ a ] 2 − 5 [ a ] + 4 x 3 − 6 { a } 2 − 5 { a } + 1 x − ( tan x ) × sgn x be an even function for all x ∈ R . Then the sum of all possible values of a is (where [ ] and { ⋅ } denote greatest integer function and fractional part function, respectively) |
An ordered pair (a,b) for which the system of linear equations 1 + a x + b y + z = 2 , a x + 1 + b y + z = 3 , a x + b y + 2 z = 2 has a unique solution is |
| Evaluate lim n ∞ { 1 2 tan x 2 + 1 2 2 tan x 2 2 + …. + 1 2 n tan x 2 n } |
Lim x ∞ a 1 / x + b y x + c y x 3 x = where a ~ b,c are real and non-zero) |
| Let p and q be two statements, then ~ p q ∧ ( ~ q ) is equivalent to |
Let Δ = 0 b − a c − a a − b 0 c − b a − c b − c 0 , then ∆ equals |
| The general solution of the differential equation y ( 1 − xy ) dx = x ( 1 + xy ) dy is |
If θ ∈ π 2 , 3 π 2 , then sin – 1 ( sin θ ) equals |
| The condition for the roots of the equation, ( c 2 – ab ) x 2 – 2 ( a 2 – bc ) x + ( b 2 – ac ) = 0 to be equals |
C o s e e − 1 C o s x is defined if |
| The slope of the normal to the curve x = a ( cos θ + θ sin θ ) y = a ( sin θ − θ cos θ ) at any point θ is |
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Benefits of Solving Top 100 Maths Questions
Solving the top 100 math questions can be very beneficial for students. Here are some key advantages:
- Better Problem-Solving Skills: Practicing many math problems helps students become better at solving them, which is important for handling difficult questions.
- Deeper Understanding: Working on different types of math problems helps students understand math concepts more deeply and apply them in various situations.
- More Confidence: Regular practice boosts students’ confidence in their math abilities, which is important for doing well in exams.
- Exam Preparation: Solving past exam questions and important math problems helps students get used to the format and types of questions they will face, making them better prepared.
- Time Management: Practicing math questions helps students use their time more efficiently during exams, preventing them from wasting time on problems they already know.
- Creative Thinking: Working on different math problems encourages students to think creatively and develop flexible approaches to solving problems.
- Real-World Applications: Many math problems relate to real-life situations, helping students see how math is useful in everyday life and making learning more interesting.
- Efficient Test Strategies: Practicing math problems helps students develop good test-taking strategies, such as breaking problems into smaller parts and double-checking their answers.
- Personalized Learning: Online platforms like BYJU’S offer personalized learning and virtual tutors, giving students tailored support as they solve math problems.
- Monetary Rewards: Some platforms, like Photomath, offer money for solving math problems, giving students an extra incentive to practice and improve.
By solving the top 100 math questions, students can build a strong math foundation, improve their problem-solving skills, and better understand math concepts.
FAQs on Top 100 Maths Questions
Why is it called maths?
The term maths is commonly used in British English to refer to the subject of mathematics. It is derived from the Greek word mathēmatiká (μαθηματικά), meaning all things mathematical. The term mathematics is used in American English, and both terms are used to describe the study of numbers, shapes, and space using reason and a special system of symbols and notation.
What is the full form of maths?
The full form of maths is mathematics. It is a subject that deals with numbers, shapes, logic, quantity, and arrangements, and it teaches students to solve problems based on numerical calculations and find solutions.
Who created math?
The origin of mathematics is difficult to pinpoint, as it has evolved over thousands of years through contributions from many cultures and mathematicians. However, some notable mathematicians who have significantly contributed to the development of mathematics include Euclid, Archimedes, and Isaac Newton.
Who found zero?
The origin of the concept of zero is also difficult to pinpoint, but it is believed to have been developed in ancient India around the 7th century. The Indian mathematician Aryabhata is credited with being the first to use zero as a placeholder in a decimal system.
What are some good questions for math?
There are many important and challenging math questions that can help students improve their problem-solving skills. Here are a few examples: In how many different ways can the letters of the word BLOATING be arranged? (Answer: 40320) 64 men can complete a piece of work in 40 days. In how many days can 32 men complete the same piece of work? (Answer: 80 days) What is the area of a circle whose circumference is 1447 meters? (Use π = 3.14) (Answer: 166698.73 m^2). These questions cover various math topics and can be used to assess students' understanding of different concepts.
