Mathematics questions
18011 published questions with worked solutions.
- Let S be the set of all α ∈ R such that the equation, cos 2x + α sin x = 2α − 7 has a solution. Then S is equal to:Not in JEE Main syllabus
- Let z ∈ C with Im(z) = 10 and it satisfies 2z - n 2z + n = 2i - 1 for some natural number n. Then:
- Let f(x) = 5 − |x − 2| and g(x) = |x + 1|, x ∈ R. If f(x) attains maximum value at α and g(x) attains minimum value at β, then _...
- The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be 45º from a point A on the...Not in JEE syllabus
- A value of (0, 3 ), for which vmatrix 1 + ^2 & ^2 & 4 6 ^2 & 1 + ^2 & 4 6 ^2 & ^2 & 1 + 4 6 vmatrix = 0, is:Not in JEE Main syllabus
- If a_1, a_2, a_3, are in A.P. such that a_1 + a_7 + a_ 16 = 40, then the sum of the first 15 terms of this A.P. is:
- The term independent of x in the expansion of ( 1 60 - x^8 81 ) (2x^2 - 3 x^2 )^6 is equal to:
- The value of for which 4 _ -1 ^ 2 e^ - |x| dx=5, is:
- Let f(x) be a polynomial of degree 5 such that x= 1 are its critical points. If _ x 0 (2+ f(x) x^3 )=4, then which one of the...
- Let a , b and c be three unit vectors such that a + b + c = 0 . If = a b + b c + c a and d = a b + b c + c a , then the ordered...
- Let y = y(x) be a function of x satisfying y 1-x^2 =k-x 1-y^2 where k is a constant and y ( 1 2 )=- 1 4 . Then dy dx at x= 1 2 ,...
- The coefficient of x^7 in the expression (1+x)^ 10 +x(1+x)^9+x^2(1+x)^8+ +x^ 10 is:
- Let and be the roots of the equation x^2-x-1=0. If p_k=( )^k+( )^k, k 1, then which one of the following statements is not true?
- If the sum of the first 40 terms of the series, 3 + 4 + 8 + 9 + 13 + 14 + 18 + 19 +…… is (102)m, then m is equal to:
- The area (in sq. units) of the region (x, y) R^2 4x^2 y 8x+12 is:
- Let a_1, a_2, a_3, be a G.P. such that a_1<0, a_1+a_2=4 and a_3+a_4=16. If _ i=1 ^ 9 a_i=4 , then is equal to:
- If _1 and _2 be respectively the smallest and the largest values of in (0, 2 )- which satisfy the equation, 2 ^2 - 5 +4=0, then _...Not in JEE Main syllabus
- If 3x+4y=12 2 is a tangent to the ellipse x^2 a^2 + y^2 9 =1 for some a R, then the distance between the foci of the ellipse is:
- Let A=[a_ ij ] and B=[b_ ij ] be two 3 3 real matrices such that b_ ij =(3)^ (i+j-2) a_ ji , where i, j = 1, 2, 3. If the...
- The locus of the mid-points of the perpendiculars drawn from points on the line, x = 2y to the line x = y is: