Practice questions
88551 published questions with worked solutions.
- 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:
- Let the tangents drawn from the origin to the circle, x^2+y^2-8x-4y+16=0 touch it at the points A and B. The (AB)^2 is equal to:
- The value of c in the Lagrange's mean value theorem for the function f(x)=x^3-4x^2+8x+11, when x [0,1] is:
- Let A, B, C and D be four non-empty sets. The contrapositive statement of "If A B and B D, then A C" is:Not in JEE syllabus
- If 3+i 4-i , [0,2 ], is a real number, then an argument of +i is:
- In a workshop, there are five machines and the probability of any one of them to be out of service on a day is 1 4 . If the...
- Let X= n N: 1 n 50 . If A= n X: n is a multiple of 2 and B= n X: n is a multiple of 7 , then the number of elements in the...
- If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then x.y is equal to_________.
- If the function f defined on (- 1 3 , 1 3 ) by f(x)= cases 1 x _e ( 1+3x 1-2x ), & when x 0 k, & when x=0 cases is continuous,...
- If the system of linear equations, x+y+z=6 x+2y+3z=10 3x+2y+ z= has more than two solutions, then - ^2 is equal to_________.
- If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through ( , 7, 1) is ( 5 3 , 7 3 , 17 3 ), then...
- For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) A_1 =...