Question 1 :
The set of all real values of x satisfying the inequality <br>|x² + x - 6| < 6 is :<br>

Question 2 :
If p,q&isin;{1, 2, 3, 4, 5} then number of equations of form p²x² + q²x + 1 = 0 having real roots is <br>

Question 3 :
If the roots of the equation x³ - 12x² + 39x -28 = 0 are in A.P. then their common difference is<br>

Question 4 :
The number of real roots of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7463fd4b0dee62042068ca' height='44' width='108' >= 0 is-<br>

Question 5 :
The value of x satisfying the equation <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7463ecaed3b362852447e6' height='35' width='91' ><br>=<img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7463ec4b0dee62042068a4' height='35' width='91' > is :<br>

Question 6 :
The values of x for which <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7463d0aed3b362852447b0' height='47' width='68' >< 0 is :<br>

Question 7 :
Let a, b, c be three real numbers such that 2a + 3b + 6c = 0. Then the quadratic equation ax² + bx + c = 0 has -<br>

Question 8 :
The solution set of equation sin⁴x = 1 + cos⁶x is<br>

Question 9 :
If a, b, c &isin; R and 1 is a root of equation ax² + bx + c = 0, then equation 4ax² + 3bx + 2c = 0, c &ne; 0 has<br>

Question 10 :
If {tex} r {/tex} be the ratio of the roots of the equation {tex} a x ^ { 2 } + b x + c = 0 {/tex} and {tex} r ^ { 2 } + r + 1 = 0 , {/tex} then {tex} a , b , c {/tex} are in

Question 11 :
If the difference between the roots of the equation {tex} x ^ { 2 } + a x + 1 = 0 {/tex} is less than {tex} \sqrt { 5 } , {/tex} then the set of possible values of {tex} a {/tex} is

Question 12 :
If {tex} f ( x ) = \left( x - a _ { 1 } \right) ^ { 2 } + \left( x - a _ { 2 } \right) ^ { 2 } + \dots + \left( x - a _ { n } \right) ^ { 2 } , {/tex} find {tex} x {/tex} where {tex} f ( x ) {/tex} is minimum.

Question 13 :
If 2x^1/3 + 2x^-1/3 = 5, then x is equal to -<br>

Question 14 :
If 1 lies between the roots of the equation {tex} a x ^ { 2 } + b x - \sin \theta = 0, {/tex} {tex} a > 0 , {/tex} then {tex} a + b {/tex} is always less than

Question 15 :
If {tex} f ( x ) = \left( \frac { 3 } { 5 } \right) ^ { x } + \left( \frac { 4 } { 5 } \right) ^ { x } - 1 , {/tex} where {tex} x \in R , {/tex} then the equation {tex} f ( x ) {/tex} {tex} = 0 {/tex} has

Question 16 :
The set of possible values of &lambda; for which <br>x² - (&lambda;² - 5&lambda; + 5) x + (2&lambda;² - 3&lambda; - 4) = 0 has roots, whose sum and product are both less than 1, is -<br>

Question 17 :
If {tex} c > 0 {/tex} and {tex} 4 a + c < 2 b , {/tex} then {tex} a x ^ { 2 } - b x + c = 0 {/tex} has a root in the interval

Question 18 :
The value of a for which the equation {tex} \left( a ^ { 2 } + 4 a + 3 \right) x ^ { 2 } {/tex} {tex} + \left( a ^ { 2 } - a - 2 \right) x + ( a + 1 ) a = 0 {/tex} has more than two roots is

Question 19 :
If x be real, then the minimum value of <img style='object-fit:contain' src='https://storage.googleapis.com/teachmint/question_assets/JEE%20Main/5e7463134b0dee62042066f4' height='19' width='68' > is<br>

Question 20 :
If 6^x + 6^x+1 = 2^x+ 2^x+1 + 2^x+2the number of solutions of x is-<br>

Question 22 :
If &alpha;, &beta; are the roots of equation x² + px + q = 0 and &gamma;, &delta; are roots of equation x² + rx + s = 0 then the value of (&alpha; - &gamma;)² + (&beta; - &gamma;)² +(&alpha; - &delta;)²+ (&beta; - &delta;)²is -<br>

Question 23 :
If x² - 3x + 2 is a factor of x⁴ - px² + q, then p,q are -<br>

Question 24 :
If b > a, then the equation (x - a) (x - b) = 1 has -<br>

Question 25 :
(x-a) (x-b) + c = 0 (c &ne; 0), then the roots of the equation <br>(x - c - &alpha;) (x - c - &beta;) = c are -<br>