Mathematics questions
18011 published questions with worked solutions.
- Let a_1,a_2, ,a_n be in A.P. If a_5=2a_7 and a_ 11 =18, then 12 ( 1 a_ 10 + a_ 11 + 1 a_ 11 + a_ 12 + + 1 a_ 17 + a_ 18 ) is...
- The sum of the common terms of the following three arithmetic progressions 3,7,11,15, ,399; 2,5,8,11, ,359 and 2,7,12,17, ,197,...
- The 8^ th common term of the series S_1=3+7+11+15+19+ and S_2=1+6+11+16+21+ is
- The sum 1^2-2 3^2+3 5^2-4 7^2+5 9^2- +15 29^2 is
- If the mean and variance of the following data: 6, 10, 7, 13, a, 12, b, 12 are 9 and 37 4 respectively, then (a-b)^2 is equal to :
- The value of _ n 1 n _ j=1 ^n (2j-1)+8n (2j-1)+4n is equal to :
- Let a = i + j +2 k and b =- i +2 j +3 k . Then the vector product ( a + b ) (( a ( a - b )) b ) is equal to :
- The value of the definite integral _ /4 ^ /4 dx (1+e^ x x )( ^4x+ ^4x) is equal to :
- Let C be the set of all complex numbers Let S_1= z ||z-3-2i|²=8 , S_2= z |Re(z) 5 and S_3= z ||z- z| 8 . Then the number of...
- If the area of the bounded region R = (x,y) : max 0, _ex 2^x, 1 2 x 2 is, ( _e2)^ -1 + ( _e2)+ , then the value of ( + -2 )^2 is...
- A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected...
- If the coefficients of x^7 in (x^2+ 1 bx )^ 11 and x^ -7 in (x- 1 bx^2 )^ 11 , b 0, are equal, then the value of b is equal to :
- If + = 1 2 , then 16( (2 )+ (4 )+ (6 )) is equal to :
- Let A = bmatrix 1&2 -1&4 bmatrix . If A^ -1 = I+ A, , R, I is a 2 × 2 identity matrix, then 4( - ) is equal to :
- Let y = y(x) be solution of the differential equation _e ( dy dx ) = 3x + 4y, with y(0) = 0. If y (- 2 3 _e2 )= _e2, then the...
- Let the plane passing through the point (–1, 0, –2) and perpendicular to each of the planes 2x + y – z = 2 and x – y – z = 3 be...
- The tangents are drawn from the point P(–1, 1) to the circle x^2+y^2-2x-6y+6=0. If these tangents touch the circle at points A...
- Let f:R R be a function such that f(2) = 4 and f'(2) = 1. Then, the value of _ x 2 x^2f(2)-4f(x) x-2 is equal to :
- Let , be two roots of the equation x^2+(20)^ 1/4 x+(5)^ 1/2 =0. Then ^8+ ^8 is equal to
- The probability that a randomly selected 2-digit number belongs to the set n N : (2^n-2) is a multiple of 3 is equal to