A) =0 done clear
B) > 0 done clear
C) <0 done clear
D) \[\ge 0\] done clear
View Solution play_arrowquestion_answer2) lf\[x=\sqrt{2+\sqrt{2+\sqrt{2+.........}}}\], then __________.
A) \[x=1\] done clear
B) \[0<x<1\] done clear
C) x is infinite done clear
D) \[x=2\] done clear
View Solution play_arrowA) 8 done clear
B) \[-8\] done clear
C) 16 done clear
D) \[-16\] done clear
View Solution play_arrowA) \[\frac{b(c-a)}{a(b-c)}\] done clear
B) \[\frac{a(b-c)}{c(a-b)}\] done clear
C) \[\frac{a(b-c)}{b(c-a)}\] done clear
D) \[\frac{c(a-b)}{a(b-c)}\] done clear
View Solution play_arrowA) \[2b=a+c\] done clear
B) \[2a=b+c\] done clear
C) \[2c=a+b\] done clear
D) \[\frac{1}{b}=\frac{1}{a}+\frac{1}{c}\] done clear
View Solution play_arrowA) \[3,-2\] done clear
B) \[-3,2\] done clear
C) \[-6,-1\] done clear
D) \[6,-1\] done clear
View Solution play_arrowquestion_answer7) If \[\sqrt{x-1}-\sqrt{x+1}+1=0,\] then 4x is equal to_____.
A) \[4\sqrt{-1}\] done clear
B) \[0\] done clear
C) 5 done clear
D) \[1\frac{1}{4}\] done clear
View Solution play_arrowA) \[-3\sqrt{2}\] done clear
B) \[8\sqrt{2}\] done clear
C) \[12\sqrt{2}\] done clear
D) \[-2\sqrt{2}\] done clear
View Solution play_arrowA) \[a<0\] done clear
B) \[-1<a<0\] done clear
C) \[-1<a<1\] done clear
D) None of these done clear
View Solution play_arrowquestion_answer10) Roots of the quadratic equation \[{{x}^{2}}+x-(a+1)\,(a+2)=0\] are _____.
A) \[-(a+1),\,(a+2)\] done clear
B) \[(a+1),\,-(a+2)\] done clear
C) \[(a+1),(a+2)\] done clear
D) \[-(a+1),-(a+2)\] done clear
View Solution play_arrowA) \[9{{x}^{2}}+28x+25=0\] done clear
B) \[9{{x}^{2}}+30x+25=0\] done clear
C) \[9{{x}^{2}}+28x-25=0\] done clear
D) \[16{{x}^{2}}+22x-30=0\] done clear
View Solution play_arrowA) \[2b=a+c\] done clear
B) \[{{b}^{2}}=ac\] done clear
C) \[b=\frac{2ac}{a+c}\] done clear
D) \[b=ac\] done clear
View Solution play_arrowA) \[{{x}^{2}}-12x+30=0\] done clear
B) \[{{x}^{2}}-12x+32=0\] done clear
C) \[2{{x}^{2}}-6x+7=0\] done clear
D) \[2{{x}^{2}}-24x+43=0\] done clear
View Solution play_arrowquestion_answer14) The roots of the equation \[{{x}^{2/3}}+{{x}^{1/3}}-2=0\]are _____.
A) \[1,-8\] done clear
B) \[1,-2\] done clear
C) \[\frac{2}{3},\frac{1}{3}\] done clear
D) \[-2,-8\] done clear
View Solution play_arrowA) \[\frac{1}{2}\] done clear
B) \[-\frac{1}{2}\] done clear
C) 0 done clear
D) 1 done clear
View Solution play_arrowA) 1690 done clear
B) 999 done clear
C) 538 done clear
D) Can't be determined done clear
View Solution play_arrowA) 3 km/hr done clear
B) 4 km/hr done clear
C) - 6 km/hr or 4 km/hr done clear
D) 5 km/hr done clear
View Solution play_arrow(i) One of them made a mistake in the constant term and got the roots as 5 I and 9. |
(ii) Another one committed an error in the coefficient of x and he got the roots as 12 and 4. |
A) \[{{x}^{2}}+4x+14=0\] done clear
B) \[2{{x}^{2}}+7x-24=0\] done clear
C) \[{{x}^{2}}\text{-}14x+48=0\] done clear
D) \[3{{x}^{2}}-17x+52=0\] done clear
View Solution play_arrowA) 50 done clear
B) 60 done clear
C) 45 done clear
D) 55 done clear
View Solution play_arrowA) 5 km/hr done clear
B) 2 km/hr done clear
C) 3 km/hr done clear
D) 4 km/hr done clear
View Solution play_arrowquestion_answer21) Which of the following equations has two distinct real roots?
A) \[2{{x}^{2}}-3\sqrt{2}x+\frac{9}{4}=0\] done clear
B) \[{{x}^{2}}+x-5=0\] done clear
C) \[{{x}^{2}}+3x+2\sqrt{2}=0\] done clear
D) \[5{{x}^{2}}-3x+1=0\] done clear
View Solution play_arrowquestion_answer22) Read the statements carefully. .
Statement I: The quadratic equation \[a{{x}^{2}}+bx+c=0\] has two distinct real roots, if\[{{b}^{2}}-4ac>0\]. |
Statement II: The quadratic equation \[2({{a}^{2}}+{{b}^{2}}){{x}^{2}}+2(a+b)x+1=0\]has no real roots, when \[a\ne b\]. |
A) Both Statement - I and Statement - II are true. done clear
B) Statement - I is true but Statement - II is false. done clear
C) Statement - I is false but Statement - II is true. done clear
D) Both Statement - I and Statement - II are false. done clear
View Solution play_arrowA) Real done clear
B) Equal done clear
C) No real done clear
D) Can't be determined done clear
View Solution play_arrowquestion_answer24) Read the statement carefully and state 'T' for true and 'F' for false.
(i) The value of \[2+\frac{1}{2+\frac{1}{2+......\infty }}\] is \[\sqrt{2}\]. |
(ii) A line segment AB of length 2 m is divided at C into two parts such that\[A{{C}^{2}}=AB-CB\] The length of the part CB is\[3+\sqrt{5}\]. |
(iii) Every quadratic equation can have at most two real roots. |
(iv) A real number a is said to be root of the quadratic equation \[a{{x}^{2}}+bx+c=0,\] if\[a{{\alpha }^{2}}+b\alpha +c=0\]. |
A) i-F ii-T iii-T iv-T done clear
B) i-F ii-T iii-T iv-F done clear
C) i-T ii-F iii-F iv-T done clear
D) i-F ii-F iii-T iv-T done clear
View Solution play_arrowA) \[\frac{3}{7}\] done clear
B) \[\frac{7}{3}\] done clear
C) \[\frac{4}{3}\] done clear
D) \[\frac{3}{4}\] done clear
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