MathsMaths QuestionsTop 100 Maths Questions for CBSE Class 5 to 12

Top 100 Maths Questions for CBSE Class 5 to 12

Following are the important 100 Maths Questions for Class 5 to 12 that students should prepare for exams like JEE Main and Advanced –

If sin ⁡ A = sin 2 ⁡ B and 2 cos 2 ⁡ A = 3 cos 2 ⁡ B then

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    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.

    The letters of the word “ARTICLE” are taken four at a time and arranged in all possible ways. The number of arrangements containing ‘R’ and not containing ‘E’ is

    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

    Evaluate ∫ x − sin ⁡ x 1 − cos ⁡ x d x

    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 bag contains a white and b black balls. Two players A and B alternately draw a ball from the bag, replacing the ball each time after the draw till one of them draws a white ball and wins the game. A begins the game. If the probability of A winning the game is three times that of B, the ratio a:b is

    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    a n d    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

    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 ).

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