Question 1: Palette 1/63

JEE Advanced 2026 MSQ

Let a, b, c be positive integers in arithmetic progression such that the equation

$ax^2 + bx + c = 0$

has only integer solutions.

Then which of the following statements is (are) TRUE?

A

c - b is an integer multiple of a

B

Both the roots of the equation $ax^2 + bx + c = 0$ are odd integers

C

If $c = 15$, then $ab = 8$

D

If $b = 8$, then $x = 3$ is a root of the equation $ax^2 + bx + c = 0$

Question 2: Palette 2/63

JEE Advanced 2025 MCQ

Let $\mathbb{R}$ denote the set of all real numbers. Let $a_i, b_i \in \mathbb{R}$ for $i \in \{1, 2, 3\}$.

Define the functions $f: \mathbb{R} \to \mathbb{R}$, $g: \mathbb{R} \to \mathbb{R}$, and $h: \mathbb{R} \to \mathbb{R}$ by

$f(x) = a_1 + 10x + a_2 x^2 + a_3 x^3 + x^4$

$g(x) = b_1 + 3x + b_2 x^2 + b_3 x^3 + x^4$

$h(x) = f(x + 1) - g(x + 2)$

If $f(x) \neq g(x)$ for every $x \in \mathbb{R}$, then the coefficient of $x^3$ in $h(x)$ is

A

8

B

2

C

-4

D

-6

Question 3: Palette 3/63

JEE Advanced 2020 MCQ

Suppose a, b denote the distinct real roots of the quadratic polynomial x² + 20x $-$ 2020 and suppose c, d denote the distinct complex roots of the quadratic polynomial x² $-$ 20x + 2020. Then the value of

ac(a $-$ c) + ad(a $-$ d) + bc(b $-$ c) + bd(b $-$ d) is

A

0

B

8000

C

8080

D

16000

Question 4: Palette 4/63

JEE Advanced 2019 MSQ

Let $\alpha $ and $\beta $ be the roots of${x^2} - x - 1 = 0$, with $\alpha $ > $\beta $. For all positive integers n, define

${a_n} = {{{\alpha ^n} - {\beta ^n}} \over {\alpha - \beta }},\,n \ge 1$

${b_1} = 1\,and\,{b_n} = {a_{n - 1}} + {a_{n + 1}},\,n \ge 2$

Then which of the following options is/are correct?

A

$\sum\limits_{n = 1}^\infty {{{{b_n}} \over {{{10}^n}}}} = {8 \over {89}}$

B

b_n = $\alpha $ⁿ + $\beta $ⁿ for all n $ \ge $ 1

C

a₁ + a₂ + a₃ + ... + a_n = a_n+2 $ - $ 1 for all n $ \ge $ 1

D

$\sum\limits_{n = 1}^\infty {{{{a_n}} \over {{{10}^n}}}} = {10 \over {89}}$

Question 5: Palette 5/63

JEE Advanced 2017 MCQ

a₁₂ = ?

A

a₁₁ + 2a₁₀

B

2a₁₁ + a₁₀

C

a₁₁ $-$ a₁₀

D

a₁₁ + a₁₀

Question 6: Palette 6/63

JEE Advanced 2017 MCQ

If a₄ = 28, then p + 2q =

A

14

B

7

C

21

D

12

Question 7: Palette 7/63

JEE Advanced 2016 MCQ

Let $ - {\pi \over 6} < \theta < - {\pi \over {12}}.$ Suppose ${\alpha _1}$ and ${\beta_1}$ are the roots of the equation ${x^2} - 2x\sec \theta + 1 = 0$ and ${\alpha _2}$ and ${\beta _2}$ are the roots of the equation ${x^2} + 2x\,\tan \theta - 1 = 0.$ $If\,{\alpha _1} > {\beta _1}$ and ${\alpha _2} > {\beta _2},$ then ${\alpha _1} + {\beta _2}$ equals

A

$2\left( {\sec \theta - \tan \theta } \right)$

B

$2\,\sec \,\theta $

C

$ - 2\tan \theta $

D

$0$

Question 8: Palette 8/63

JEE Advanced 2015 MSQ

Let $S$ be the set of all non-zero real numbers $\alpha $ such that the quadratic equation $\alpha {x^2} - x + \alpha = 0$ has two distinct real roots ${x_1}$ and ${x_2}$ satisfying the inequality $\left| {{x_1} - {x_2}} \right| < 1.$ Which of the following intervals is (are) $a$ subset(s) os $S$?

A

$\left( { - {1 \over 2} - {1 \over {\sqrt 5 }}} \right)$

B

$\left( { - {1 \over {\sqrt 5 }},0} \right)$

C

$\left( {0,{1 \over {\sqrt 5 }}} \right)$

D

$\left( {{1 \over {\sqrt 5 }},{1 \over 2}} \right)$

Question 9: Palette 9/63

JEE Advanced 2014 MCQ

The quadratic equation $p(x)$ $ = 0$ with real coefficients has purely imaginary roots. Then the equation $p(p(x))=0$ has

A

one purely imaginary root

B

all real roots

C

two real and two purely imaginary roots

D

neither real nor purely imaginary roots

Question 10: Palette 10/63

JEE Advanced 2013 MSQ

If ${3^x}\, = \,{4^{x - 1}},$ then $x\, = $

A

${{2{{\log }_3}\,2} \over {2{{\log }_3}\,2 - 1}}$

B

${2 \over {2 - {{\log }_2}\,3}}$

C

${1 \over {1 - {{\log }_4}\,3}}$

D

${{2{{\log }_2}\,3} \over {2{{\log }_2}\,3 - 1}}$

Question 11: Palette 11/63

JEE Advanced 2012 MCQ

Let $\alpha$(a) and $\beta$(a) be the roots of the equation $(\root 3 \of {1 + a} - 1){x^2} + (\sqrt {1 + a} - 1)x + (\root 6 \of {1 + a} - 1) = 0$ where $a > - 1$. Then $\mathop {\lim }\limits_{a \to {0^ + }} \alpha (a)$ and $\mathop {\lim }\limits_{a \to {0^ + }} \beta (a)$ are

A

$ - {5 \over 2}$

B

$ - {1 \over 2}$

C

$ - {7 \over 2}$

D

$ - {9 \over 2}$

Question 12: Palette 12/63

JEE Advanced 2011 MCQ

Let $\left( {{x_0},{y_0}} \right)$ be the solution of the following equations
$\matrix{ {{{\left( {2x} \right)}^{\ell n2}}\, = {{\left( {3y} \right)}^{\ell n3}}} \cr {{3^{\ell nx}}\, = {2^{\ell ny}}} \cr } $
Then ${x_0}$ is

A

${1 \over 6}$

B

${1 \over 3}$

C

${1 \over 2}$

D

$6$

Question 13: Palette 13/63

JEE Advanced 2011 MCQ

Let $\alpha $ and $\beta $ be the roots of ${x^2} - 6x - 2 = 0,$ with $\alpha > \beta .$ If ${a_n} = {\alpha ^n} - {\beta ^n}$ for $\,n \ge 1$ then the value of ${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$ is

A

1

B

2

C

3

D

4

Question 14: Palette 14/63

JEE Advanced 2011 MCQ

A value of $b$ for which the equations $$\matrix{ {{x^2} + bx - 1 = 0} \cr {{x^2} + x + b = 0} \cr } $$

have one root in common is

A

$ - \sqrt 2 $

B

$ - i\sqrt 3$

C

$i\sqrt 5 $

D

$\sqrt 2 $

Question 15: Palette 15/63

JEE Advanced 2010 MCQ

Let $p$ and $q$ be real numbers such that $p \ne 0,\,{p^3} \ne q$ and ${p^3} \ne - q.$ If ${p^3} \ne - q.$ and $\,\beta $ are nonzero complex numbers satisfying $\alpha \, + \beta = - p\,$ and ${\alpha ^3} + {\beta ^3} = q,$ then a quadratic equation having ${\alpha \over \beta }$ and ${\beta \over \alpha }$ as its roots is

A

$\left( {{p^3} + q} \right){x^2} - \left( {{p^3} + 2q} \right)x + \left( {{p^3} + q} \right) = 0$

B

$\left( {{p^3} + q} \right){x^2} - \left( {{p^3} - 2q} \right)x + \left( {{p^3} + q} \right) = 0$

C

$\left( {{p^3} - q} \right){x^2} - \left( {5{p^3} - 2q} \right)x + \left( {{p^3} - q} \right) = 0$

D

$\left( {{p^3} - q} \right){x^2} - \left( {5{p^3} + 2q} \right)x + \left( {{p^3} - q} \right) = 0$

Question 16: Palette 16/63

JEE Advanced 2008 MCQ

Let $a,\,b,c$, $p,q$ be real numbers. Suppose $\alpha ,\,\beta $ are the roots of the equation ${x^2} + 2px + q = 0$ and $\alpha ,{1 \over \beta }$ are the roots of the equation $a{x^2} + 2bx + c = 0,$ where ${\beta ^2} \in \left\{ { - 1,\,0,\,1} \right\}$

STATEMENT - 1 : $\left( {{p^2} - q} \right)\left( {{b^2} - ac} \right) \ge 0$

and STATEMENT - 2 : $b \ne pa$ or $c \ne qa$

A

STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is a correct explanation for
STATEMENT - 1

B

STATEMENT - 1 is True, STATEMENT - 2 is True;
STATEMENT - 2 is NOT a correct explanation for
STATEMENT - 1

C

STATEMENT - 1 is True, STATEMENT - 2 is False

D

STATEMENT - 1 is False, STATEMENT - 2 is True

Question 17: Palette 17/63

JEE Advanced 2007 MCQ

Let $\alpha ,\,\beta $ be the roots of the equation ${x^2} - px + r = 0$ and ${\alpha \over 2},\,2\beta $ be the roots of the equation ${x^2} - qx + r = 0$. Then the value of $r$

A

${2 \over 9}\left( {p - q} \right)\left( {2q - p} \right)$

B

${2 \over 9}\left( {q - p} \right)\left( {2p - q} \right)$

C

${2 \over 9}\left( {q - 2p} \right)\left( {2q - p} \right)$

D

${2 \over 9}\left( {2p - q} \right)\left( {2q - p} \right)$

Question 18: Palette 18/63

JEE Advanced 2007 MCQ

Let $\alpha,\beta$ be the roots of the equation $x^2-px+r=0$ and $\frac{\alpha}{2},2\beta$ be the roots of the equation $x^2-qx+r=0$. Then the value of r is

A

$\frac{2}{9}(p-q)(2q-p)$

B

$\frac{2}{9}(q-p)(2p-q)$

C

$\frac{2}{9}(q-2p)(2q-p)$

D

$\frac{2}{9}(2p-q)(2q-p)$

Question 19: Palette 19/63

JEE Advanced 2006 MCQ

Let $a, b, c$ be the sides of a triangle. No two of them are equal and $\lambda \in R$. If the roots of the equation $x^{2}+2(a+b+c) x+3 \lambda(a b+b c+c a)=0$ are real, then,

A

$\lambda<\frac{4}{3}$

B

$\lambda>\frac{5}{3}$

C

$\lambda \in\left(\frac{1}{3}, \frac{5}{3}\right)$

D

$\lambda \in\left(\frac{4}{3}, \frac{5}{3}\right)$

Question 20: Palette 20/63

JEE Advanced 2004 MCQ

For all $'x',{x^2} + 2ax + 10 - 3a > 0,$ then the interval in which '$a$' lies is

A

$a < - 5$

B

$ - 5 < a < 2$

C

$a > 5$

D

$2 < a < 5$

Question 21: Palette 21/63

JEE Advanced 2004 MCQ

If one root is square of the other root of the equation ${x^2} + px + q = 0$, then the realation between $p$ and $q$ is

A

${p^3} - q\left( {3p - 1} \right) + {q^2} = 0$

B

${p^3} - q\left( {3p + 1} \right) + {q^2} = 0$

C

${p^3} + q\left( {3p - 1} \right) + {q^2} = 0$

D

${p^3} + q\left( {3p + 1} \right) + {q^2} = 0$

Question 22: Palette 22/63

JEE Advanced 2003 MCQ

If $\,\alpha \in \left( {0,{\pi \over 2}} \right)\,\,then\,\,\sqrt {{x^2} + x} + {{{{\tan }^2}\alpha } \over {\sqrt {{x^2} + x} }}$ is always greater than or equal to

A

$2\,\tan \alpha \,$

B

1

C

2

D

${\sec ^2}\,\alpha $

Question 23: Palette 23/63

JEE Advanced 2002 MCQ

The set of all real numbers x for which ${x^2} - \left| {x + 2} \right| + x > 0$, is

A

$( - \infty ,\, - 2) \cup (2,\infty )$

B

$( - \infty ,\, - \sqrt 2 ) \cup (\sqrt 2 ,\infty )$

C

$( - \infty ,\, - 1) \cup (1,\infty )$

D

$(\sqrt 2 ,\infty )$

Question 24: Palette 24/63

JEE Advanced 2002 MCQ

If ${a_1},{a_2}.......,{a_n}$ are positive real numbers whose product is a fixed number c, then the minimum value of ${a_1} + {a_2} + ..... + {a_{n - 1}} + 2{a_n}$ is

A

$n{(2c)^{1/n}}$

B

$(n + 1){c^{1/n}}$

C

$2n{c^{1/n}}$

D

$(n + 1)\,{(2c)^{1/n}}$

Question 25: Palette 25/63

JEE Advanced 2000 MCQ

For the equation $3{x^2} + px + 3 = 0$. p > 0, if one of the root is square of the other, then p is equal to

A

1/3

B

1

C

3

D

2/3

Question 26: Palette 26/63

JEE Advanced 2000 MCQ

If a, b, c, d are positive real numbers such that a + b + c + d = 2, then M = (a + b) (c + d) satisfies the relation

A

$0 \le M \le 1$

B

$1 \le M \le 2$

C

$2 \le M \le 3$

D

$3 \le M \le 4$

Question 27: Palette 27/63

JEE Advanced 2000 MCQ

If $\alpha \,\text{and}\,\beta $ $(\alpha \, < \,\beta )$ are the roots of the equation ${x^2} + bx + c = 0\,$, where $c < 0 < b$, then

A

$0 < \alpha \, < \,\beta \,$

B

$\alpha \, < \,0 < \beta \,<\left| \alpha \right|$

C

$\alpha \, < \beta \, < 0\,$

D

$\alpha \, < \,0 < \left| \alpha \right| < \beta $

Question 28: Palette 28/63

JEE Advanced 2000 MCQ

If b > a, then the equation (x - a) (x - b) - 1 = 0 has

A

both roots in (a, b)

B

both roots in (- $\infty $, a)

C

both roots in (b, + $\infty $)

D

one root in (- $\infty $, a) and the other in (b, + $\infty $)

Question 29: Palette 29/63

JEE Advanced 1999 MCQ

If the roots of the equation ${x^2} - 2ax + {a^2} + a - 3 = 0$ are real and less than 3, then

A

$a < 2$

B

$2 \le a \le 3$

C

$3 < a \le 4$

D

$a > 4$

Question 30: Palette 30/63

JEE Advanced 1998 MCQ

Number of divisor of the form 4$n$$ + 2\left( {n \ge 0} \right)$ of the integer 240 is

A

4

B

8

C

10

D

3

Question 31: Palette 31/63

JEE Advanced 1994 MCQ

Let $p,q \in \left\{ {1,2,3,4} \right\}\,$. The number of equations of the form $p{x^2} + qx + 1 = 0$ having real roots is

A

15

B

9

C

7

D

8

Question 32: Palette 32/63

JEE Advanced 1994 MCQ

The number of points of intersection of two curves y = 2 sin x and y $ = 5{x^2} + 2x + 3$ is

A

0

B

1

C

2

D

$\infty $

Question 33: Palette 33/63

JEE Advanced 1994 MCQ

If p, q, r are + ve and are on A.P., the roots of quadratic equation $p{x^2} + qx + r = 0$ are all real for

A

$\left| {{r \over p} - 7} \right| \ge 4\sqrt 3 $

B

$\left| {{p \over r} - 7} \right| \ge 4\sqrt 3 $

C

all p and r

D

no p and r

Question 34: Palette 34/63

JEE Advanced 1992 MCQ

Let $\alpha \,,\,\beta $ be the roots of the equation (x - a) (x - b) = c, $c \ne 0$. Then the roots of the equation $(x - \alpha \,)\,(x - \beta ) + c = 0$ are

A

a, c

B

b, c

C

a, b

D

a + c, b + c

Question 35: Palette 35/63

JEE Advanced 1991 MCQ

The product of $n$ positive numbers is unity. Then their sum is

A

a positive integer

B

divisible by $n$

C

equal to $n + {1 \over n}$

D

never less than $n$

Question 36: Palette 36/63

JEE Advanced 1990 MCQ

The number of solutions of the equation sin${(e)^x} = {5^x} + {5^{ - x}}$ is

A

0

B

1

C

2

D

Infinitely many

Question 37: Palette 37/63

JEE Advanced 1989 MSQ

The equation ${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $ has

A

at least one real solution

B

exactly three solutions

C

exactly one irrational solution

D

complex roots.

Question 38: Palette 38/63

JEE Advanced 1989 MCQ

If $\alpha $ and $\beta $ are the roots of ${x^2}$+ px + q = 0 and ${\alpha ^4},{\beta ^4}$ are the roots of $\,{x^2} - rx + s = 0$, then the equation ${x^2} - 4qx + 2{q^2} - r = 0$ has always

A

two real roots

B

two positive roots

C

two negative roots

D

one positive and one negative root.

Question 39: Palette 39/63

JEE Advanced 1989 MCQ

Let a, b, c be real numbers, $a \ne 0$. If $\alpha \,$ is a root of ${a^2}{x^2} + bx + c = 0$. $\beta \,$ is the root of ${a^2}{x^2} - bx - c = 0$ and $0 < \alpha \, < \,\beta $, then the equation ${a^2}{x^2} + 2bx + 2c = 0$ has a root $\gamma $ that always satisfies

A

$\gamma = {{\alpha + \beta } \over 2}$

B

$\gamma = \alpha + {\beta \over 2}$

C

$\gamma = \alpha $

D

$\alpha < \gamma < \beta $

Question 40: Palette 40/63

JEE Advanced 1989 MCQ

If x and y are positive real numbers and m, n are any positive integers, then ${{{x^n}\,{y^m}} \over {(1 + {x^{2n}})\,(1 + {y^{2m}})}} > {1 \over 4}$

A

TRUE

B

FALSE

Question 41: Palette 41/63

JEE Advanced 1987 MCQ

If $a,\,b,\,c,\,d$ and p are distinct real numbers such that $$\left( {{a^2} + {b^2} + {c^2}} \right){p^2} - 2\left( {ab + bc + cd} \right)p + \left( {{b^2} + {c^2} + {d^2}} \right) \le 0$$
then $a,\,b,\,c,\,d$

A

are in A. P.

B

are in G P.

C

are in H. P.

D

satisfy $ab = cd$

Question 42: Palette 42/63

JEE Advanced 1986 MCQ

If $a,\,b$ and $c$ are distinct positive numbers, then the expression
$\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc$ is

A

positive

B

negative

C

non-positive

D

non-negative

Question 43: Palette 43/63

JEE Advanced 1986 MSQ

If $S$ is the set of all real $x$ such that ${{2x - 1} \over {2{x^3} + 3{x^2} + x}}$ is positive, then $S$ contains

A

$\left( { - \infty ,\, - {\textstyle{3 \over 2}}} \right)$

B

$\left( { - {3 \over 2},\, - {1 \over 4}} \right)$

C

$\left( { - {1 \over 4},\,{1 \over 2}} \right)$

D

$\left( {{1 \over 2},\,3} \right)\,\,\,\,$

Question 44: Palette 44/63

JEE Advanced 1985 MCQ

If ${\log _{0.3}}\,(x\, - \,1) < {\log _{0.09}}(x - 1)$, then x lies in the interval-

A

$(2,\infty )$

B

(1, 2)

C

(- 2, - 1)

D

none of these

Question 45: Palette 45/63

JEE Advanced 1985 MCQ

If $P(x) = a{x^2} + bx + c\,\,and\,\,Q(x) = - a{x^2} + dx + c$, where $ac \ne \,0$, then P(x) Q(x) = 0 has at least two real roots.

A

TRUE

B

FALSE

Question 46: Palette 46/63

JEE Advanced 1985 MCQ

If ${n_1}$, ${n_2}$,.......${n_p}$ are p positive integers, whose sum is an even number, then the number of odd integers among them is odd.

A

TRUE

B

FALSE

Question 47: Palette 47/63

JEE Advanced 1984 MCQ

The equation $x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$ has

A

no root

B

one root

C

two equal root

D

infinitely many roots

Question 48: Palette 48/63

JEE Advanced 1984 MCQ

If $\,{a^2} + {b^2} + {c^2} = 1$, then ab + bc + ca lies in the interval

A

$[{1 \over 2},2]\,\,$

B

$[ - 1,2]$

C

$\,[ - {1 \over 2},1]\,$

D

$\,[ - 1,{1 \over 2}]\,\,$

Question 49: Palette 49/63

JEE Advanced 1984 MSQ

For real $x$, the function $\,{{\left( {x - a} \right)\left( {x - b} \right)} \over {x - c}}$ will assume all real values provided

A

$a > b > c$

B

$a < b < c$

C

$a > c > b$

D

$a < c < b$

Question 50: Palette 50/63

JEE Advanced 1984 MCQ

If a < b < c < d, then the roots of the equation (x - a) (x - c) + 2 ( x - b) (x - d) = 0 are real and distinct.

A

TRUE

B

FALSE

Question 51: Palette 51/63

JEE Advanced 1983 MCQ

The equation $2{x^2} + 3x + 1 = 0$ has an irrational root.

A

TRUE

B

FALSE

Question 52: Palette 52/63

JEE Advanced 1982 MCQ

The number of real solutions of the equation ${\left| x \right|^2} - 3\left| x \right| + 2 = 0$ is

A

4

B

1

C

3

D

2

Question 53: Palette 53/63

JEE Advanced 1982 MCQ

Two towns A and B are 60 km apart. A school is to be built to serve 150 students in town A and 50 students in town B. If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at

A

town B

B

45 km from town A

C

town A

D

45 km from town B

Question 54: Palette 54/63

JEE Advanced 1982 MCQ

If p, q, r are any real numbers, then

A

max (p, q) < max (p, q, r )

B

min (p, q) = ${1 \over 2}\left( {p + q - \left| {p - q} \right|} \right)$

C

max (p, q) < min (p, q, r)

D

none of these

Question 55: Palette 55/63

JEE Advanced 1982 MCQ

The largest interval for which ${x^{12}} - {x^9} + {x^4} - x + 1 > 0$ is

A

$ - 4 < x \le 0$

B

$\,0 < x < 1$

C

$ - 100 < x < 100$

D

$ - \infty < x < \infty $

Question 56: Palette 56/63

JEE Advanced 1981 MCQ

For every integer n > 1, the inequality ${(n!)^{1/n}} < {{n + 1} \over 2}$ holds.

A

TRUE

B

FALSE

Question 57: Palette 57/63

JEE Advanced 1980 MCQ

Both the roots of the equation (x - b) (x - c) + (x - a) (x - c) + (x - a) (x - b) = 0 are always

A

positive

B

real

C

negative

D

none of these.

Question 58: Palette 58/63

JEE Advanced 1980 MCQ

The least value of the expression $2\,\,{\log _{10}}\,x\, - \,{\log _x}(0.01)$ for x > 1, is

A

10

B

2

C

- 0.01

D

none of these.

Question 59: Palette 59/63

JEE Advanced 1980 MCQ

If $\,({x^2} + px + 1)\,$ is a factor of $(a{x^3} + bx + c)$, then

A

${a^2} + {c^2} = - ab\,$

B

${a^2} - {c^2} = - ab$

C

${a^2} - {c^2} = ab$

D

none of these

Question 60: Palette 60/63

JEE Advanced 1979 MCQ

Let a > 0, b > 0 and c > 0. Then the roots of the equation $a{x^2} + bx + c = 0$

A

are real and negative

B

have negative real parts

C

both (a) and (b)

D

none of these

Question 61: Palette 61/63

JEE Advanced 1979 MCQ

The equation x + 2y + 2z = 1 and 2x + 4y + 4z = 9 have

A

only one solution

B

only two solution

C

Infinite number of solutions

D

None of these.

Question 62: Palette 62/63

JEE Advanced 1979 MCQ

If x, y and z are real and different and $\,u = {x^2} + 4{y^2} + 9{z^2} - 6yz - 3zx - 2xy$, then u is always.

A

non negative

B

zero

C

non positive

D

none of these

Question 63: Palette 63/63

JEE Advanced 1979 MCQ

If $\ell $, m, n are real, $\ell \ne m$, then the roots by the equation :
$(\ell - m)\,{x^2} - 5\,(\ell + m)\,x - 2\,(\ell - m) = 0$ are

A

Real and equal

B

Complex

C

Real and unequal

D

None of these.