Modulus Equations and Inequalities

JEE Main Mathematics · Basic Maths · 19 questions, latest first

• The number of the real solutions of the equation: x|x+3|+|x-1|-2=0 is202624 January, Shift 1 · Q5
• The number of distinct real solutions of the equation x|x+4|+3|x+2|+10=0 is202622 January, Shift 1 · Q3
• The sum of all the roots of the equation (x-1)^2-5|x-1|+6=0, is:202621 January, Shift 1 · Q3
• The sum of the squares of the roots of |x-2|^2+|x-2|-2=0 and the squares of the roots of x^2-2|x-3|-5=0, is20258 April, Shift 2 · Q2
• The number of real roots of the equation x|x-2|+3|x-3|+1=0 is:20257 April, Shift 2 · Q3
• The sum, of the squares of all the roots of the equation x^2+|2 x-3|-4=0, is202528 January, Shift 1 · Q4
• Let A={x ∈(0, π)-{(π)/2}: log_(2 / π)| sin x|+ log_(2 / π)| cos x|=2} and B={x ≥ 0: √x(√x-4)-3|√x-2|+6=0}. Then n(A ∪ B) is equal…202524 January, Shift 2 · Q2
• The number of real solution(s) of the equation x^2+3 x+2= min {|x-3|,|x+2|} is:202524 January, Shift 2 · Q3
• The number of distinct real roots of the equation |x+1||x+3|-4|x+2|+5=0, is ____20248 April, Shift 2 · Q21
• The number of real solutions of the equation x|x+5|+2|x+7|-2=0 is ____.20245 April, Shift 2 · Q30
• If S={a ∈ R:|2 a-1|=3[a]+2{a}}, where [t] denotes the greatest integer less than or equal to t and {t} represents the fractional…20245 April, Shift 1 · Q21
• The number of distinct real roots of the equation |x||x+2|-5|x+1|-1=0 is ____.20245 April, Shift 1 · Q22
• The number of real solutions of the equation x(x^2+3|x|+5|x-1|+6|x-2|)=0 is ____.202430 January, Shift 2 · Q22
• The number of real roots of the equation x|x|-5|x+2|+6=0, is202315 April, Shift 1 · Q2
• The set of all a ∈ R for which the equation x|x-1|+|x+2|+a=0 has exactly one real root, is202313 April, Shift 1 · Q2
• The number of elements in the set {n ∈ Z:|n^2-10 n+19|<6} is ____.202310 April, Shift 1 · Q22
• Let m and n be the numbers of real roots of the quadratic equations x^2-12 x+[x]+31=0 and x^2-5|x+2|-4=0 respectively, where [x]…20238 April, Shift 2 · Q22
• The sum of all the roots of the equation |x^2-8 x+15|-2 x+7=0 is:20236 April, Shift 1 · Q2
• Let λ ∈ R and let the equation E be |x|^2-2|x|+|λ-3|=0. Then the largest element in the set S= {x+λ: x is an integer solution of…202324 January, Shift 1 · Q86