Mathematics questions
18011 published questions with worked solutions.
- If b_1b_2=2 (c_1+c_2 ), then the least one of the equation x^2+b_1x+c_1=0 and x^2+b_2x+c_2=0 has
- The value of x in the given equation 4^x-3^ x- 12 =3^ x+ 12 -2^ 2x-1 is
- If x^2+ax+1 is a factor of ax^3+bx+c, then
- Let p,q 1,2,3,4 . The number of equations of the form px^2+qx+1=0 having real roots, is
- If x is real, the function (x-a)(x-b) (x-c) will assume all real values, provided
- Statement 1: If equations ax^2+bx+c=0, (a,b,c R) and 2x^2+3x+4=0 have a common root, then a:b:c=2:3:4. Statement 2: Roots of...
- If , are the roots of the equation ax^2+bx+c=0 such that < <0, then the quadratic equation whose roots are | |,| |, is given by
- The solution of the quadratic equation (3|x|-3)^2=|x|+7 which belongs to the domain of definition of the function y= x(x-3) are...
- If the roots of the equation 1 x+p + 1 x+q = 1r are equal in magnitude but opposite in sign, then the product of the roots will be
- If _1, _2 and _1, _2 are the roots of the equation ax^2+bx+c=0 and px^2+qx+r=0 respectively and system of equations _1y+ _2z=0...
- If a>0,b>0,c>0, then both the roots of the equation ax^2+bx+c=0
- If and be the roots of x^2+px+q=0, then ( + ^2 ) ( ^2 + ) ^2 + ^2 is equal to
- Let 2 ^2x+3 x-2>0 and x^2-x-2<0, (x is measured in radians). Then x lies in the intervalNot in JEE Main syllabus
- If the product of the roots of the equation (a+1)x^2+(2a+3)x+(3a+4)=0 is 2, then the sum of roots is
- The solution of set of the equation x^ _x(1-x)^2 =9 is
- If at least one root of 2x^2+3x+5=0 and ax^2+bx+c=0, a,b,c N is common, then the maximum value of a+b+c is
- Let , be the roots of the equation ax^2+2bx+c=0 and , be the roots of the equation px^2+2qx+r=0. If , , , are in GP, then
- Let a,b,c,p,q be real numbers. Suppose , are the roots of the equation x^2+2px+q=0 and , 1 are the roots of the equation...
- Let |z|=2 and w= z+1 z-1 where z,w C (where C is the set of complex numbers). Then product of least and greatest value of modulus...
- If the expression (1+ir)^3 is of the form s(1+i) where real s where r is also real and, then the sum of all possible values of r...