`a^2 < 1/2`
`a^2 > 1/2`
`a^2 <= 1/2`
`a^2 >= 1/2`
sometimes complex
always irrational
always complex
always real
exactly one real root
at least one real root
at least two real roots
at most two real roots
One
Two
Four
No real root
are imaginary
are distinct and real
are equal and real
Cannot be determined
one real root
two real roots
two imaginary roots
four real roots
`p = 25//12`
`p < 25//12`
`p >25//12`
`p <= 25//12`
`4`
`3`
`2`
`1`
`| r/p -7 | ge 4 sqrt (3)`
`|p/r -7 | < 4 sqrt (3)`
all `p` and `r`
no `p` and `r`
both roots are greater than `-b/(2a)`
both roots are less than `- b/(2a)`
one of the roots exceeds `-b/(2a)`
None of the above
`alpha +beta`
`alpha - beta`
`(sqrt(alpha) + sqrt (beta))^2`
`(alpha - beta)^2`
k = 0 only
k = - 3 only
k = 0 or k = 3
k = 0 or k = - 3
` - 1/3`
`- 1/2`
`0`
`1`
real roots
non-real roots
purely imaginary roots
none of these
not necessarily real, if the coefficients are real
always imaginary
always real
real, if the coefficients are real
always complex
always real
always purely imaginary
None of the above
real
imaginary
positive
negative
`- 3 < b < 3`
`- 2 < b < 2`
`b > 2`
`b < - 2`
4 or 8
5 or 10
6 or 12
3 or 6
`2b = a + c`
`b^2 = ac`
`b + c = 2a`
`b = ac`
`a > 0 , b > 0 ,c > 0`
`a > 0, b < 0, c > 0`
`a < 0, b > 0, c < 0`
`a < 0 ,c > 0`
complex
pure imaginary
irrational
rational
`2`
`5`
`2 + 5i`
`2 - 5i`
`0`
`1`
`2`
`3`
non-real
equal
irrational
rational
`theta` is an acute angle
`theta` is right angle
`theta` is an obtuse angle
No value of `theta` is possible
`(c - 1)/b`
`(1 - c)/b`
`b/(c - 1)`
`b/(1 - c)`
AP
GP
HP
None of the above
`p` and `q`
`1/p` and `1/q`
`-p` and `-q`
`p + q` and `p- q`
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
3, 8
-3, -8
3, -8
-3, 8
`a/(bc)`
`b/(ac)`
`(-b)/(ac)`
`(-a)/(bc)`
`1/2`
`1`
`2`
`4`
`b(c- 1)`
`c(b- 1)`
`c(b- 1)^(-1)`
`b(c - 1)^(-1)`
`b`
`-b`
`c`
`-c`
`4096`
`2048`
`1024`
`512`
` - 9/8`
`9/8`
`- 8/9`
`8/9`
Only 1
Only 2
Both 1 and 2
Neither 1 nor 2
`2`
`3`
`5`
`8`
`(alpha^4 - beta^4 )` is real
`2(alpha^5 + beta^5 ) = (alpha beta )^5`
`(alpha^6 - beta^6) = 0`
`(alpha^8 + beta^8) = (alpha beta)^8`
`-1`
`0`
`1`
`2`
`-2`
`0`
`30`
`34`
`(b/B)^2`
`(a/A)^2`
`(a^2b^2)/(A^2B^2)`
`(ab)/(AB)`
`a^2 + b^2 = 2ac`
`b^2 - c^2 = 2ab`
`b^2 - a^2 = 2ac`
`b^2 + c^2 = 2ab`
`6`
`3 sqrt(2)`
`4 sqrt(2)`
`12`
`2n^2`
`2n^4`
`2`
`n^2`
`2`
`3`
`4`
`9`
` - 2/3`
`2/3`
`4`
`8`
`p^2 - 4q`
`(p^2 - 4q)/2`
`(p^2 - 4q)/q^2`
`(p^2 - 2q)/q^2`
`1`
`2`
`-2`
`3`
`p^2 + q^2 -2pr = 0`
`p^2 - q^2 + 2pr = 0`
`(p + r)^2 = 2(p^2 + r^2 )`
`(p- r)^2 = q^2 + r^2`
`((B^2 - 4AC))/A^2`
`((B^2 - 4AC))/A^2`
`((2AC - B^2))/A^2`
`B^2 - 2C`
`12`
`15`
`16`
`18`
`aq = 2(b + p)`
`aq = b + p`
`ap = 2(b + q)`
`ap= b + q`
`2 - sqrt(3)`
`2 + sqrt(3)`
`7 - 4sqrt(3)`
`4`
`2a^2 = 9bc`
`2b^2 = 9ac`
`2c^2 = 9ab`
None of these
`1`
`b`
`-b`
`0`
` - b/a`
`b/c`
`c/b`
` - c/b`
`q + r`
`p + q`
`q + r`
`p + q`
`47//49`
`49//47`
`-47 //49`
`- 49//47`
`2`
`5//12`
`12//25`
`25//12`
` - ( b (c - a))/(a(b - c))`
` ( b (c - a))/(a(b - c))`
` ( c (a - b))/(a(b - c))`
` - ( c (a - b))/(a(b - c))`
`170`
`180`
`190`
`290`
`b^2 = a(a + 4c)`
`a^2 = b(b + 4c)`
`a^2 = c(a + 4c)`
`b^2 = a(b + 4c)`
`-1`
`1`
`2`
`-2`
`1 - r`
`q- r`
`1 + r`
`q + r`
`a^(2) + b^(2) = c^(2)`
`a^(2) + b^(2) = a +b`
`ab + b^(2) = 2ac`
`ab - b^(2) = 2ac`
` 1/2 (b/a - q/p)`
` 1/2 (- b/a + q/p)`
` 1/2 (b/p + q/a)`
` 1/2 (- b/p + q/a)`
`ab`
`bc`
`ca`
`abc`
`n^(2) - 4m- 1 = 0`
`n^(2) + 4m- 1 = 0`
`m^(2) + 4n + 1 = 0`
`m^(2) - 4n - 1 = 0`
`- \frac{3}{4}`
`- \frac{3}{7}`
`\frac{3}{7}`
`\frac{4}{7}`
`2`
`2 + sqrt2`
`2 sqrt2`
`2 - sqrt2`
`9x^2+ 3x + 2 = 0`
`9x^2 - 3x + 2 = 0`
`9x^2+ 3x - 2 = 0`
`9x^2 - 3x + 2 = 0`
`alpha^(-1) , beta^(-1)`
`alpha^2 , beta^2`
`alpha beta^(-1) , alpha^(-1) beta`
`alpha^(-2) , beta^(-2)`
`p^2 m = l^2q`
`m^2p = l^2q`
`m^2p = q^2l`
`m^2p^2 = l^2q`
`(0,2)`
`(2,3)`
`(3,4)`
`(-2, 0)`
`- 2 < k < 2 `
`-5 < k < 3`
`-3 < k < 5`
`-1 < k < 3`
Only `b <= -4`
Only `b >= 4`
`-4 < b < 4`
`b <= - 4, b >= 4`
`- 2 < k < 2 `
`-5 < k < 3`
`-3 < k < 5`
`-1 < k < 3`
(This question may have multiple correct answers)
`-2 < m < 0`
`m > 3`
`-1 < m < 3`
`1 < m < 4`
`a^2k + abk + ac < 0`
`a^2k^2 + ab + ac < 0`
`a^2k^2 + abk + ac < 0`
`ak^2 + abk + ac < 0`
`a⊂ (−∞,9/4)`
None of these.
`a ⊂ ( – ∞ , 2 )`
`(−2,9/4)`
Both the roots are real
One root is real and the other is complex
Both the roots are complex
Cannot say
` |P| < 4`
` |P| <= 4`
` |P| > 4`
` |P| >= 4`
Signs of a and c should be like
Signs of b and c should be like
Signs of a and b should be like
None of the above
Both the roots are real
One root is real and the other is complex
Both the roots are complex
Cannot say
`b^2 - 4ac > 0`
`b < 0`
`a > 0`
`c < 0`
`x^ 2 - 10 x + 9 = 0`
`x^ 2 + 10 x + 9 = 0`
`x^ 2 - 10 x + 16 = 0`
`x^ 2 - 8 x - 9 = 0`
`x^2 - 6ax + 9a^2 - b = 0`
`3ax^2 + x - sqrt(b) = 0`
`x^2 + 3ax + sqrt(b) = 0`
` sqrt(b)x^2 + x - 3a = 0`
`x^2 - (b^2 - 2ac) x + c = 0`
`a^2x^2 - (b^2 - 2ac)x + c = 0`
`ax^2 - (b^2 - 2ac)x + c^2 = 0`
`a^2x^2 - (b^2 - 2ac)x + c^2 = 0`
`2x^2 - x + 3= 0 `
`x^2 - 3x + 2 = 0`
`x^2 + 3x + 2 = 0`
`x^2 - 3x - 2 = 0`
`x^2 - x - 1 = 0`
`x^2 - x + 1 = 0`
`x^2 + x - 1 = 0`
`x^2 + x + 1 = 0`
`x^2 + 2 mx + m^2 - mn + n^2 = 0`
`x^2 + 2 mx + (m - n)^2 = 0`
`x^2 - 2 mx + m^2 - n^2 = 0`
`x^2 + 2 mx + m^2 - n^2 = 0`
6, - 4, 1
4, 6, - 1
3,- 2, 1
6, 4, 1
`x^2 - 2px - (p^2 - q) = 0`
`x^2 - 2px + (p^2 - q) = 0`
`x^2 + 2px - (p^2 - q) = 0`
`x^2 + 2px + (p^2 - q) = 0`
`- 3/4`
`3/4`
` - 4/3`
` -4/5`
`5` units
`10` units
`15` units
`20` units
`-7//2,2`
`-3//2,4`
`-5//3,3`
`3//2,4`
10
8
6
4
1, 0
0, 1
-2, 0
-2, 1
` (c-a)/(b - c)`
` (a - b)/(b - c)`
` ( b - c)/(a - b)`
`(c -a)/(a - b)`
`1` unit
`2` units
`3` units
`4` units
`4`
`3`
`2`
`1`
`(a, c)`
`(b, c)`
`(a, b)`
`(a + b, a + c)`
`- 15`
`9`
`15`
`24`
`1 ± i`
`2 ± i `
`1 ± sqrt(2)`
`2 ± i sqrt(2)`
`10`
`15`
`20`
`30`
`alpha^7` and `beta^(13)`
`alpha^(13)` and `beta^7`
`alpha^(20)` and `beta^(20)`
None of these
` a/2`
`a/3`
`a/4`
`0`
`5`
`sqrt5`
`1`
`(5)^(1//4)`
`-1 <= x <= 4`
`2 <= x <= 4`
`-1 < x <= 1`
`-1 <= x <= 1` or `2 < x <= 4`
`x in (-1, 4)`
`x in [-1, 4]`
`x in (-oo, -1) cup (4, oo)`
`x in (-oo , 1) cup [4, oo)`