Question 1 :
If one of the roots of the equation {tex} x ^ { 2 } + p x + q {/tex} is {tex} \sqrt { 3 } + 2 , {/tex} then the value of 'p' and 'q' is
Question 2 :
The quadratic equation {tex} x ^ { 2 } - 2 k x + 16 = 0 {/tex} will have equal roots when the value of 'k' is
Question 3 :
If roots of equation {tex} x ^ { 2 } + x + r = 0 {/tex} are {tex} ^ { \prime } \alpha ^ { \prime } {/tex} and {tex} ^ { \prime } \beta ^ { \prime } {/tex} and {tex} \alpha ^ { 3 } + \beta ^ { 3 } = - 6 . {/tex} Find the value {tex} r {/tex}
Question 4 :
The equation {tex} x + 5 y = 33 ; \frac { x + y } { x - y } = \frac { 13 } { 3 } {/tex} has the solution {tex} ( x , y ) {/tex} as :
Question 5 :
If {tex} \alpha {/tex} and {tex} \beta {/tex} be the roots of the quadratic equation {tex} 2 x ^ { 2 } - 4 x = 1 {/tex}, the value of {tex} \frac { \alpha ^ { 2 } } { \beta } + \frac { \beta ^ { 2 } } { \alpha } {/tex} _______
Question 6 :
If the roots of the equation {tex} 4 x ^ { 2 } - 12 x + k = 0 {/tex} are equal, then the value of {tex} k {/tex} is :
Question 7 :
The lines {tex} 3 x - 4 y + 5 = 0,7 x - 8 y + 5 = 0,4 x + 5 y - 45 = 0 {/tex} are
Question 8 :
A person on a tour has {tex}9,600{/tex} for his expenses. If his tour is extended by 16 days, he has to cut down his daily expenses by {tex} 20 , {/tex} his original duration of tour had been
Question 9 :
If {tex} b ^ { 2 } - 4 a c {/tex} is a perfect square but not equal to zero than the roots are:
Question 10 :
The value of {tex} 2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \frac { 1 } { 2 + \ldots \ldots \ldots \ldots \infty } } } {/tex} is:
Question 11 :
If area and perimeter of a rectangle is {tex} 6000 \mathrm { cm } ^ { 2 } {/tex} and {tex} 340 \mathrm { cm } {/tex} respectively, then the length of rectangle is :
Question 12 :
Positive value of 'k' for which the roots of equation {tex} 12 x ^ { 2 } + k x + 5 = 0 {/tex} are in ratio {tex} 3: 2 , {/tex} is
Question 13 :
The number of students in each section of a school is {tex} 36 . {/tex} After admiting 12 new students, four new sections were started. If total number of students in each section now is {tex} 30 , {/tex} then the number of sections initially were
Question 14 :
If one root of the {tex} x ^ { 2 } - 3 x + k = 0 {/tex} is {tex} 2 , {/tex} then value of {tex} k {/tex} will be
Question 15 :
The quadratic equation {tex} x ^ { 2 } - 2 k x + 16 = 0 {/tex} will have equal roots when the value of 'k' is
Question 16 :
The roots of the cubic equation {tex} x ^ { 3 } - 7 x + 6 = 0 {/tex} are :
Question 17 :
Roots of the equation {tex} 3 x ^ { 2 } - 14 x + k = 0 {/tex} will be reciprocal of each other if :
Question 18 :
One root of the equation {tex} : x ^ { 2 } - 2 ( 5 + m ) x + 3 ( 7 + m ) = 0 {/tex} is reciprocal of the other. Find the value of {tex} M {/tex}.
Question 19 :
If {tex} ( 2 \pm \sqrt { 3 } ) {/tex} is a root of a quadratic equation {tex} x ^ { 2 } + p x + q = 0 {/tex} then find the value of {tex} p {/tex} and {tex} q {/tex}
Question 20 :
A straight line of {tex} x = 15 {/tex} is :
Question 21 :
The present age of man is 8 years more than thrice the sum of the ages of his two grandsons who are twins. After 8 years, his age will be 10 years more than twice the sum of the ages of his grandsons. The age of a man when his grandsons were born was
Question 22 :
If {tex} \alpha {/tex} and {tex} \beta {/tex} are the roots of the equation {tex} x ^ { 2 } + 7 x + 12 = 0 {/tex}, then the equation whose roots {tex} ( \alpha + \beta ) ^ { 2 } {/tex} and {tex} ( \alpha - \beta ) ^ { 2 } {/tex} will be:
Question 23 :
The value of 'K' for which the system of equations {tex} k x + 2 y = 5 {/tex} and {tex} 3 x + y = 1 {/tex} has no solution is
Question 24 :
If {tex} | x - 2 | + | x - 3 | = 7 {/tex} then, {tex}' x ' {/tex}will be equal to
Question 25 :
If the ratio of the roots of the Equation {tex} 4 x ^ { 2 } - 6 x + p = 0 {/tex} is {tex}1:2{/tex} then the value of {tex} p {/tex} is
Question 26 :
The minimum value of the function {tex} x ^ { 2 } - 6 x + 10 {/tex} is _______
Question 27 :
If one root of the Equation {tex} \mathrm { px } ^ { 2 } + \mathrm { qx } + \mathrm { r } = 0 {/tex} is {tex} \mathrm { r } {/tex} then other root of the Equation will be
Question 28 :
If {tex} k x - 4 = ( k - 1 ) x , {/tex} then which of the following is true?
Question 29 :
Roots of equation {tex} 2 x ^ { 2 } + 3 x + 7 = 0 {/tex} are {tex} \alpha {/tex} and {tex} \beta . {/tex} The value of {tex} \alpha \beta ^ { - 1 } + \beta \alpha ^ { - 1 } {/tex} is
Question 30 :
If {tex} \alpha + \beta = - 2 {/tex} and {tex} \alpha \beta = - 3 , {/tex} then {tex} \alpha , \beta {/tex} are the roots of the equation, which is
