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MCQOPTIONS
This section includes 91 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Function which involves independent and dependent variable in form ax²+bx+c is classified as |
| A. | zero-degree function |
| B. | one-degree function |
| C. | quadratic function |
| D. | addition function |
| Answer» D. addition function | |
| 2. |
Functions expressed in form of ratios and form of quotient of polynomials are |
| A. | ratio function |
| B. | quotient function |
| C. | rational functions |
| D. | irrational functions |
| Answer» D. irrational functions | |
| 3. |
In quadratic if a will become zero than quadratic function becomes |
| A. | single function |
| B. | linear function |
| C. | composite function |
| D. | dependent function |
| Answer» C. composite function | |
| 4. |
In quadratic function ax²+bx+c, condition for solving is |
| A. | a cannot be equal to zero |
| B. | c cannot be equal to zero |
| C. | a is equal to zero |
| D. | b is equal to zero |
| Answer» B. c cannot be equal to zero | |
| 5. |
'concave up' parabola point where it bottoms out is considered as |
| A. | left vertex |
| B. | convex vertex |
| C. | concave vertex |
| D. | vertex of parabola |
| Answer» E. | |
| 6. |
Polynomial function general form with degree n,independent variable x and dependant variable is |
| A. | f = x(y) |
| B. | f = (x)(y) |
| C. | x = ƒ(y) |
| D. | y = ƒ(x) |
| Answer» E. | |
| 7. |
Linear function is considered as |
| A. | first-degree polynomial function |
| B. | second-degree polynomial function |
| C. | third-degree polynomial function |
| D. | four-degree polynomial function |
| Answer» B. second-degree polynomial function | |
| 8. |
A parabola graph which opens upward is classified as |
| A. | concave up |
| B. | concave left |
| C. | concave right |
| D. | concave down |
| Answer» B. concave left | |
| 9. |
Linear and quadratic functions are examples of |
| A. | mean function |
| B. | variable function |
| C. | constant function |
| D. | polynomial functions |
| Answer» E. | |
| 10. |
In quadratic function, parabola will concave down if |
| A. | a = -2 |
| B. | b = -4 |
| C. | c = -2 |
| D. | c = -5 |
| Answer» B. b = -4 | |
| 11. |
X coordinate of vertex is |
| A. | 2a⁄b |
| B. | b⁄2a |
| C. | 2a⁄b |
| D. | −b⁄2a |
| Answer» E. | |
| 12. |
Sketch of quadratic function parabola can be drawn easily because of predetermined factors which includes |
| A. | concavity |
| B. | a and y intercept |
| C. | vertex of parabola |
| D. | all of above |
| Answer» E. | |
| 13. |
Behavior of function depends upon behavior of |
| A. | lower degree |
| B. | higher degree |
| C. | double degree |
| D. | zero degree |
| Answer» C. double degree | |
| 14. |
In quadratic function, parabola will concave up if |
| A. | a = 3 |
| B. | b = 3 |
| C. | b = 4 |
| D. | a = 0 |
| Answer» B. b = 3 | |
| 15. |
Function behaves as x assuming larger positive values and negative values is classified as |
| A. | larger direction |
| B. | smaller direction |
| C. | ultimate direction |
| D. | ultimate variables |
| Answer» D. ultimate variables | |
| 16. |
Quadratic function is considered as |
| A. | first-degree polynomial function |
| B. | second-degree polynomial function |
| C. | third-degree polynomial function |
| D. | four-degree polynomial function |
| Answer» C. third-degree polynomial function | |
| 17. |
X-intercept of parabola shows value of x when value of |
| A. | a = 2 |
| B. | b = 2 |
| C. | c = 2 |
| D. | y = 0 |
| Answer» E. | |
| 18. |
Concave up parabola point where it peaks out is considered as |
| A. | left vertex |
| B. | convex vertex |
| C. | concave vertex |
| D. | vertex of parabola |
| Answer» E. | |
| 19. |
Quadratic function parabola graph is concave up if |
| A. | a > 0 |
| B. | b > 0 |
| C. | c > 0 |
| D. | a < 0 |
| Answer» B. b > 0 | |
| 20. |
Cubic function is considered as |
| A. | first-degree polynomial function |
| B. | second-degree polynomial function |
| C. | third-degree polynomial function |
| D. | four-degree polynomial function |
| Answer» D. four-degree polynomial function | |
| 21. |
Point in parabola where it passes through y-axis is classified as |
| A. | x-intercept of parabola |
| B. | y-intercept of parabola |
| C. | a-intercept of parabola |
| D. | c-intercept of parabola |
| Answer» C. a-intercept of parabola | |
| 22. |
Graph of quadratic function is classified as |
| A. | parabolas |
| B. | annual graph |
| C. | quarter graph |
| D. | composite graph |
| Answer» B. annual graph | |
| 23. |
Axis of symmetry in form of vertical line separates parabola into |
| A. | one equal halves |
| B. | two equal halves |
| C. | three equal halves |
| D. | four equal halves |
| Answer» D. four equal halves | |
| 24. |
A parabola graph which opens downward is classified as |
| A. | concave down |
| B. | concave right |
| C. | concave left |
| D. | concave up |
| Answer» B. concave right | |
| 25. |
Quadratic function parabola graph is concave down if |
| A. | a = 0 |
| B. | c < 0 |
| C. | b < 0 |
| D. | a < 0 |
| Answer» E. | |
| 26. |
The region of the complex plane for which \[\left| \frac{z-a}{z+\overline{a}} \right|=1\,\] \[\,[R(a)\ne 0]\] is |
| A. | \[x-\]axis |
| B. | \[y-\]axis |
| C. | The straight line \[x=a\] |
| D. | None of these |
| Answer» C. The straight line \[x=a\] | |
| 27. |
If \[{{\left( \frac{1+i\sqrt{3}}{1-i\sqrt{3}} \right)}^{n}}\] is an integer, then n is[UPSEAT 2002] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 28. |
\[{{\left( \frac{\sqrt{3}+i}{2} \right)}^{6}}+{{\left( \frac{i-\sqrt{3}}{2} \right)}^{6}}\]is equal to [RPET 1997] |
| A. | \[-2\] |
| B. | 0 |
| C. | 2 |
| D. | 1 |
| Answer» B. 0 | |
| 29. |
If\[z=\frac{\sqrt{3}+i}{2}\], then the value of\[{{z}^{69}}\] is [RPET 2002] |
| A. | \[-i\] |
| B. | \[i\] |
| C. | 1 |
| D. | \[-1\] |
| Answer» B. \[i\] | |
| 30. |
If\[x=a,y=b\omega ,z=c{{\omega }^{2}}\], where \[\omega \] is a complex cube root of unity, then \[\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=\] [AMU 1983] |
| A. | 3 |
| B. | 1 |
| C. | 0 |
| D. | None of these |
| Answer» D. None of these | |
| 31. |
If \[\alpha \]and \[\beta \] are imaginary cube roots of unity, then \[{{\alpha }^{4}}+{{\beta }^{4}}\] + \[\frac{1}{\alpha \beta }=\] [IIT 1977] |
| A. | 3 |
| B. | 0 |
| C. | 1 |
| D. | 2 |
| Answer» C. 1 | |
| 32. |
\[\frac{{{(\cos \theta +i\sin \theta )}^{4}}}{{{(\sin \theta +i\cos \theta )}^{5}}}\] is equal to [MNR 1985; UPSEAT 2000] |
| A. | \[\cos \theta -i\sin \theta \] |
| B. | \[\cos 9\theta -i\sin 9\theta \] |
| C. | \[\sin \theta -i\cos \theta \] |
| D. | \[\sin 9\theta -i\cos 9\theta \] |
| Answer» E. | |
| 33. |
If \[\frac{1}{x}+x=2\cos \theta ,\] then \[{{x}^{n}}+\frac{1}{{{x}^{n}}}\] is equal to [UPSEAT 2001] |
| A. | \[2\cos n\theta \] |
| B. | \[2\sin n\theta \] |
| C. | \[\cos n\,\theta \] |
| D. | \[\sin \,n\theta \] |
| Answer» B. \[2\sin n\theta \] | |
| 34. |
The value of expression \[\left( \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right)\] \[\,\left( \cos \frac{\pi }{{{2}^{2}}}+i\sin \frac{\pi }{{{2}^{2}}} \right)\]........to \[\infty \] is [Kurukshetra CEE 1998] |
| A. | \[-1\] |
| B. | \[1\] |
| C. | 0 |
| D. | 2 |
| Answer» B. \[1\] | |
| 35. |
If \[a=\cos \alpha +i\,\sin \alpha ,\,\,b=\cos \beta +i\,\sin \beta ,\]\[c=\cos \gamma +i\,\sin \gamma \,\,\text{and}\,\,\frac{b}{c}+\frac{c}{a}+\frac{a}{b}=1,\] then \[\cos (\beta -\gamma )+\cos (\gamma -\alpha )+\cos (\alpha -\beta )\] is equal to [RPET 2001] |
| A. | 3/2 |
| B. | - 3/2 |
| C. | 0 |
| D. | 1 |
| Answer» E. | |
| 36. |
If \[\sqrt{3}+i=(a+ib)(c+id)\], then \[{{\tan }^{-1}}\left( \frac{b}{a} \right)+\] \[{{\tan }^{-1}}\left( \frac{d}{c} \right)\] has the value |
| A. | \[\frac{\pi }{3}+2n\pi ,n\in I\] |
| B. | \[n\pi +\frac{\pi }{6},n\in I\] |
| C. | \[n\pi -\frac{\pi }{3},n\in I\] |
| D. | \[2n\pi -\frac{\pi }{3},n\in I\] |
| Answer» C. \[n\pi -\frac{\pi }{3},n\in I\] | |
| 37. |
If \[a,b,c\] are in G.P., then the equations \[a{{x}^{2}}+2bx+c=0\] and \[d{{x}^{2}}+2ex+f=0\] have a common root if \[\frac{d}{a},\frac{e}{b},\frac{f}{c}\] are in [IIT 1985; Pb. CET 2000; DCE 2000] |
| A. | A.P. |
| B. | G.P. |
| C. | H.P. |
| D. | None of these |
| Answer» B. G.P. | |
| 38. |
If the roots of equation \[\frac{{{x}^{2}}-bx}{ax-c}=\frac{m-1}{m+1}\]are equal but opposite in sign, then the value of \[m\] will be [RPET 1988, 2001; MP PET 1996, 2002; Pb. CET 2000] |
| A. | \[\frac{a-b}{a+b}\] |
| B. | \[\frac{b-a}{a+b}\] |
| C. | \[\frac{a+b}{a-b}\] |
| D. | \[\frac{b+a}{b-a}\] |
| Answer» B. \[\frac{b-a}{a+b}\] | |
| 39. |
The amplitude of\[\frac{1+\sqrt{3}i}{\sqrt{3}+1}\] is [Karnataka CET 1992; Pb CET 2001] |
| A. | \[\frac{\pi }{3}\] |
| B. | \[-\frac{\pi }{3}\] |
| C. | \[\frac{\pi }{6}\] |
| D. | \[-\frac{\pi }{6}\] |
| Answer» B. \[-\frac{\pi }{3}\] | |
| 40. |
If \[|z|\,=1\] and \[\omega =\frac{z-1}{z+1}\] (where \[z\ne -1)\], then \[\operatorname{Re}(\omega )\] is [IIT Screening 2003] |
| A. | \[0\] |
| B. | \[-\frac{1}{|z+1{{|}^{2}}}\] |
| C. | \[\left| \frac{z}{z+1} \right|\,.\frac{1}{|z+1{{|}^{2}}}\] |
| D. | \[\frac{\sqrt{2}}{|z+1{{|}^{2}}}\] |
| Answer» B. \[-\frac{1}{|z+1{{|}^{2}}}\] | |
| 41. |
\[\left| (1+i)\frac{(2+i)}{(3+i)} \right|=\] [MP PET 1995, 99] |
| A. | \[-\frac{1}{2}\] |
| B. | \[\frac{1}{2}\] |
| C. | 1 |
| D. | \[-1\] |
| Answer» D. \[-1\] | |
| 42. |
If \[\frac{2{{z}_{1}}}{3{{z}_{2}}}\] is a purely imaginary number, then \[\left| \frac{{{z}_{1}}-{{z}_{2}}}{{{z}_{1}}+{{z}_{2}}} \right|\] = [MP PET 1993] |
| A. | 3/2 |
| B. | 1 |
| C. | 2/3 |
| D. | 4/9 |
| Answer» B. 1 | |
| 43. |
If \[\frac{z-i}{z+i}(z\ne -i)\] is a purely imaginary number, then \[z.\bar{z}\] is equal to |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» C. 2 | |
| 44. |
If \[x\] is real, the function \[\frac{(x-a)(x-b)}{(x-c)}\] will assume all real values, provided [IIT 1984; Karnataka CET 2002] |
| A. | \[a>b>c\] |
| B. | \[a<b<c\] |
| C. | \[a>c<b\] |
| D. | \[a<c<b\] |
| Answer» E. | |
| 45. |
. Which of the following equations can represent a triangle [Orissa JEE 2005] |
| A. | \[|z-1|\,=\,|z-2|\] |
| B. | \[|z-1|=|z-2|=|z-i|\] |
| C. | \[|z-1|-|z-2|=2a\] |
| D. | \[|z-1{{|}^{2}}+|z-2{{|}^{2}}=4\] |
| Answer» C. \[|z-1|-|z-2|=2a\] | |
| 46. |
If the amplitude of \[z-2-3i\] is \[\pi /4\], then the locus of \[z=x+iy\] is [EAMCET 2003] |
| A. | \[x+y-1=0\] |
| B. | \[x-y-1=0\] |
| C. | \[x+y+1=0\] |
| D. | \[x-y+1=0\] |
| Answer» E. | |
| 47. |
Let the complex numbers \[{{z}_{1}},{{z}_{2}}\] and \[{{z}_{3}}\] be the vertices of an equilateral triangle. Let \[{{z}_{0}}\]be the circumcentre of the triangle, then \[z_{1}^{2}+z_{2}^{2}+z_{3}^{2}=\] [IIT 1981] |
| A. | \[z_{0}^{2}\] |
| B. | \[-z_{0}^{2}\] |
| C. | \[3z_{0}^{2}\] |
| D. | \[-3z_{0}^{2}\] |
| Answer» D. \[-3z_{0}^{2}\] | |
| 48. |
For all complex numbers \[{{z}_{1}},{{z}_{2}}\]satisfying \[|{{z}_{1}}|\,=12\,\] \[\,\text{and }\,|{{z}_{2}}-3-4i|\,=5,\] the minimum value of \[|{{z}_{1}}-{{z}_{2}}|\] is [IIT Screening 2002] |
| A. | 0 |
| B. | 2 |
| C. | 7 |
| D. | 17 |
| Answer» C. 7 | |
| 49. |
A rectangle is constructed in the complex plane with its sides parallel to the axes and its centre is situated at the origin. If one of the vertices of the rectangle is \[a+ib\sqrt{3}\], then the area of the rectangle is |
| A. | \[ab\sqrt{3}\] |
| B. | \[2ab\sqrt{3}\] |
| C. | \[3ab\sqrt{3}\] |
| D. | \[4ab\sqrt{3}\] |
| Answer» E. | |
| 50. |
Which one is correct from the following [RPET 2001] |
| A. | \[\sin (ix)=i\,\sinh \,x\] |
| B. | \[\cos (ix)=i\,\cosh \,x\] |
| C. | \[\sin (ix)=-i\,\sinh \,x\] |
| D. | \[\tan (ix)=-i\,\tanh \,x\] |
| Answer» B. \[\cos (ix)=i\,\cosh \,x\] | |