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MCQOPTIONS
This section includes 8666 Mcqs, each offering curated multiple-choice questions to sharpen your Joint Entrance Exam - Main (JEE Main) knowledge and support exam preparation. Choose a topic below to get started.
| 6701. |
If \[f(x)=\left\{ \begin{align} & x-1,\,\,\,x0 \\ \end{align} \right.\], then [Roorkee 1988] |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)=1\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)=1\] |
| C. | \[f(x)\]is discontinuous at\[x=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 6702. |
If \[f(x)=\left\{ \begin{align} & \frac{1}{x}\sin {{x}^{2}},\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,x=0 \\ \end{align} \right.\], then |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)\ne 0\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)\ne 0\] |
| C. | f(x) is continuous at\[x=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 6703. |
If \[f(x)=\left\{ \begin{align} & {{2}^{1/x}},\text{for}\,x\ne 0 \\ & \,\,\,\,\,\,\,3,\text{for}\,x=\text{0} \\ \end{align} \right.\], then |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)=0\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)=\infty \] |
| C. | \[f(x)\]is continuous at\[x=0\] |
| D. | None of these |
| Answer» E. | |
| 6704. |
If \[f(x)=\left\{ \begin{align} & {{(1+2x)}^{1/x}},\,\text{for }x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{e}^{2}},\,\text{for }x=0\,\,\, \\ \end{align} \right.\], then |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)=e\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)={{e}^{2}}\] |
| C. | \[f(x)\]is discontinuous at \[x=0\] |
| D. | None of these |
| Answer» C. \[f(x)\]is discontinuous at \[x=0\] | |
| 6705. |
If \[f(x)=\left\{ \begin{align} & \frac{x}{{{e}^{1/x}}+1},\,\,\text{when}\,\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\text{when }x=0 \\ \end{align} \right.\], then |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)=1\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)=1\] |
| C. | \[f(x)\]is continuous at\[x=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 6706. |
The value of k so that the function \[f(x)=\left\{ \begin{align} & k(2x-{{x}^{2}}),\ \ \ \text{when}\,x |
| A. | 1 |
| B. | 2 |
| C. | 4 |
| D. | None of these |
| Answer» E. | |
| 6707. |
If \[f(x)=\left\{ \begin{align} & {{x}^{2}}\sin \frac{1}{x},\ \ \ \text{when }x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,0,\,\,\,\,\text{when}\,x=0 \\ \end{align} \right.\], then |
| A. | \[f(0+0)=1\] |
| B. | \[f(0-0)=1\] |
| C. | f is continuous at\[x=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 6708. |
If \[f(x)=\left\{ \begin{matrix} {{e}^{x}}+ax, & x |
| A. | \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)\ne 2\] |
| B. | \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)=0\] |
| C. | \[f(x)\]is continuous at\[x=0\] |
| D. | None of these |
| Answer» D. None of these | |
| 6709. |
The points at which the function \[f(x)=\frac{x+1}{{{x}^{2}}+x-12}\] is discontinuous, are |
| A. | ?3, 4 |
| B. | 3, ?4 |
| C. | ?1,?3, 4 |
| D. | ?1, 3, 4 |
| Answer» C. ?1,?3, 4 | |
| 6710. |
If \[f(x)=\left\{ \begin{align} & \frac{{{x}^{2}}-4x+3}{{{x}^{2}}-1},\ \text{for}\ x\ne 1 \\ & \ \ \ \ \ \ \ \ \ \ \ \ \ \ 2,\ \text{for }x=1 \\ \end{align} \right.\], then [IIT 1972] |
| A. | \[\underset{x\to 1+}{\mathop{\lim }}\,f(x)=2\] |
| B. | \[\underset{x\to 1-}{\mathop{\lim }}\,f(x)=3\] |
| C. | \[f(x)\]is discontinuous at \[x=1\] |
| D. | None of these |
| Answer» D. None of these | |
| 6711. |
If\[f(x)=|x-2|\], then [Roorkee 1984] |
| A. | \[\underset{x\to 2+}{\mathop{\lim }}\,f(x)\ne 0\] |
| B. | \[\underset{x\to 2-}{\mathop{\lim }}\,f(x)\ne 0\] |
| C. | \[\underset{x\to 2+}{\mathop{\lim }}\,f(x)\ne \underset{x\to 2-}{\mathop{\lim }}\,f(x)\] |
| D. | \[f(x)\]is continuous at \[x=2\] |
| Answer» E. | |
| 6712. |
8th term of the series \[2\sqrt{2}+\sqrt{2}+0+.....\] will be |
| A. | \[-5\sqrt{2}\] |
| B. | \[5\sqrt{2}\] |
| C. | \[10\sqrt{2}\] |
| D. | \[-10\sqrt{2}\] |
| Answer» B. \[5\sqrt{2}\] | |
| 6713. |
The radius of a sphere is measured to be 20 cm with a possible error of 0.02 of a cm. The consequent error in the surface of the sphere is |
| A. | \[10.5\] sq cm |
| B. | 5.025 sq cm |
| C. | 10.05 sq cm |
| D. | None of these |
| Answer» D. None of these | |
| 6714. |
In a Boolean Algebra B, for all x, y in B,\[(x\vee y{)}'=\] |
| A. | \[{x}'\vee {y}'\] |
| B. | \[{x}'\wedge {y}'\] |
| C. | 1 |
| D. | None of these |
| Answer» C. 1 | |
| 6715. |
In a bag there are three tickets numbered 1, 2, 3. A ticket is drawn at random and put back and this is done four times. The probability that the sum of the numbers is even, is |
| A. | \[\frac{41}{81}\] |
| B. | \[\frac{39}{81}\] |
| C. | \[\frac{40}{81}\] |
| D. | None of these |
| Answer» B. \[\frac{39}{81}\] | |
| 6716. |
In a Boolean Algebra B, for all x in B, \[{0}'\] is equal to |
| A. | 0 |
| B. | 1 |
| C. | \[x.0\] |
| D. | None of these |
| Answer» C. \[x.0\] | |
| 6717. |
A spherical balloon is being inflated at the rate of 35 cc/min. The rate of increase of the surface area of the balloon when its diameter is 14 cm is [Karnataka CET 2005] |
| A. | 7 sq. cm/min |
| B. | 10 sq. cm/min |
| C. | 17.5 sq. cm/min |
| D. | 28 sq. cm/min |
| Answer» C. 17.5 sq. cm/min | |
| 6718. |
If the line \[2x+3ay-1=0\] and \[3x+4y+1=0\] are mutually perpendicular, then the value of a will be [MNR 1975] |
| A. | \[\frac{1}{2}\] |
| B. | 2 |
| C. | \[-\frac{1}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 6719. |
If \[A\] be a arithmetic mean between two numbers and \[S\] be the sum of \[n\] arithmetic means between the same numbers, then |
| A. | \[S=n\,A\] |
| B. | \[A=n\,S\] |
| C. | \[A=S\] |
| D. | None of these |
| Answer» B. \[A=n\,S\] | |
| 6720. |
If x is real, then the maximum and minimum values of expression \[\frac{{{x}^{2}}+14x+9}{{{x}^{2}}+2x+3}\] will be [Dhanbad Engg. 1968] |
| A. | 4, - 5 |
| B. | 5, - 4 |
| C. | - 4, 5 |
| D. | - 4, - 5 |
| Answer» B. 5, - 4 | |
| 6721. |
The \[{{n}^{th}}\] term of an A.P. is \[3n-1\].Choose from the following the sum of its first five terms [MP PET 1983] |
| A. | 14 |
| B. | 35 |
| C. | 80 |
| D. | 40 |
| Answer» E. | |
| 6722. |
The sum of the numbers between 100 and 1000 which is divisible by 9 will be [MP PET 1982] |
| A. | 55350 |
| B. | 57228 |
| C. | 97015 |
| D. | 62140 |
| Answer» B. 57228 | |
| 6723. |
\[2+4+7+11+16+......\]to \[n\] terms = [Roorkee 1977] |
| A. | \[\frac{1}{6}({{n}^{2}}+3n+8)\] |
| B. | \[\frac{n}{6}({{n}^{2}}+3n+8)\] |
| C. | \[\frac{1}{6}({{n}^{2}}-3n+8)\] |
| D. | \[\frac{n}{6}({{n}^{2}}-3n+8)\] |
| Answer» C. \[\frac{1}{6}({{n}^{2}}-3n+8)\] | |
| 6724. |
. If \[{{\log }_{3}}2,\ {{\log }_{3}}({{2}^{x}}-5)\] and \[{{\log }_{3}}\left( {{2}^{x}}-\frac{7}{2} \right)\] are in A.P., then \[x\] is equal to [IIT 1990] |
| A. | \[1,\ \frac{1}{2}\] |
| B. | \[1,\ \frac{1}{3}\] |
| C. | \[1,\ \frac{3}{2}\] |
| D. | None of these |
| Answer» E. | |
| 6725. |
\[{{99}^{th}}\] term of the series \[2+7+14+23+34+.....\] is [Pb. CET 2003] |
| A. | 9998 |
| B. | 9999 |
| C. | 10000 |
| D. | 100000 |
| Answer» B. 9999 | |
| 6726. |
Two cards are drawn one by one from a pack of cards. The probability of getting first card an ace and second a colored one is (before drawing second card first card is not placed again in the pack) [UPSEAT 1999; 2003] |
| A. | \[\frac{1}{26}\] |
| B. | \[\frac{5}{52}\] |
| C. | \[\frac{5}{221}\] |
| D. | \[\frac{4}{13}\] |
| Answer» D. \[\frac{4}{13}\] | |
| 6727. |
The points \[(at_{1}^{2},2a{{t}_{1}}),(at_{2}^{2},2a{{t}_{2}})\]and \[(a,0)\]will be collinear, if |
| A. | \[{{t}_{1}}{{t}_{2}}=1\] |
| B. | \[{{t}_{1}}{{t}_{2}}=-1\] |
| C. | \[{{t}_{1}}+{{t}_{2}}=1\] |
| D. | \[{{t}_{1}}+{{t}_{2}}=-1\] |
| Answer» C. \[{{t}_{1}}+{{t}_{2}}=1\] | |
| 6728. |
If the ordinate \[x=a\] divides the area bounded by the curve \[y=\left( 1+\frac{8}{{{x}^{2}}} \right)\,,\] \[x-\]axis and the ordinates \[x=2,\] \[x=4\] into two equal parts, then \[a=\] [IIT 1983] |
| A. | 8 |
| B. | \[2\sqrt{2}\] |
| C. | 2 |
| D. | \[\sqrt{2}\] |
| Answer» C. 2 | |
| 6729. |
The vector equation of the plane passing through the origin and the line of intersection of the plane \[\mathbf{r}.\mathbf{a}=\lambda \] and \[\mathbf{r}.\mathbf{b}=\mu \] is |
| A. | \[\mathbf{r}.(\lambda \mathbf{a}-\mu \mathbf{b})=0\] |
| B. | \[\mathbf{r}.\,(\lambda \mathbf{b}-\mu \mathbf{a})=0\] |
| C. | \[\mathbf{r}.(\lambda \mathbf{a}+\mu \mathbf{b})=0\] |
| D. | \[\mathbf{r}.(\lambda \mathbf{b}+\mu \mathbf{a})=0\] |
| Answer» C. \[\mathbf{r}.(\lambda \mathbf{a}+\mu \mathbf{b})=0\] | |
| 6730. |
If \[{{z}_{1}}\] and \[{{z}_{2}}\] are two non-zero complex numbers such that \[|{{z}_{1}}+{{z}_{2}}|=|{{z}_{1}}|+|{{z}_{2}}|,\]then arg \[({{z}_{1}})-\]arg \[({{z}_{2}})\] is equal to [IIT 1979, 1987; EAMCET 1986; RPET 1997; MP PET 2001; AIEEE 2005] |
| A. | \[-\pi \] |
| B. | \[-\frac{\pi }{2}\] |
| C. | \[\frac{\pi }{2}\] |
| D. | 0 |
| Answer» E. | |
| 6731. |
Two cards are drawn successively with replacement from a well shuffled deck of 52 cards then the mean of the number of aces is [J & K 2005] |
| A. | 1/13 |
| B. | 3/13 |
| C. | 2/13 |
| D. | None of these |
| Answer» D. None of these | |
| 6732. |
The ratio of sum of \[m\] and \[n\] terms of an A.P. is \[{{m}^{2}}:{{n}^{2}}\], then the ratio of \[{{m}^{th}}\]and \[{{n}^{th}}\] term will be [Roorkee 1963; MP PET 1995; Pb. CET 2001] |
| A. | \[\frac{m-1}{n-1}\] |
| B. | \[\frac{n-1}{m-1}\] |
| C. | \[\frac{2m-1}{2n-1}\] |
| D. | \[\frac{2n-1}{2m-1}\] |
| Answer» D. \[\frac{2n-1}{2m-1}\] | |
| 6733. |
The conjugate of \[\frac{{{(2+i)}^{2}}}{3+i},\] in the form of a + ib, is [Karnataka CET 2001; Pb. CET 2001] |
| A. | \[\frac{13}{2}+i\,\left( \frac{15}{2} \right)\] |
| B. | \[\frac{13}{10}+i\left( \frac{-15}{2} \right)\] |
| C. | \[\frac{13}{10}+i\,\left( \frac{-9}{10} \right)\] |
| D. | \[\frac{13}{10}+i\,\left( \frac{9}{10} \right)\] |
| Answer» D. \[\frac{13}{10}+i\,\left( \frac{9}{10} \right)\] | |
| 6734. |
The area bounded by the circle \[{{x}^{2}}+{{y}^{2}}=4,\] line \[x=\sqrt{3}y\] and \[x-\]axis lying in the first quadrant, is [RPET 1997; Kurukshetra CEE 1998] |
| A. | \[\frac{\pi }{2}\] |
| B. | \[\frac{\pi }{4}\] |
| C. | \[\frac{\pi }{3}\] |
| D. | \[\pi \] |
| Answer» D. \[\pi \] | |
| 6735. |
In a Boolean Algebra B, for all x in B, \[x\vee x=\] |
| A. | 0 |
| B. | 1 |
| C. | x |
| D. | None of these |
| Answer» D. None of these | |
| 6736. |
Area of the ellipse \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1\] is [Karnataka CET 1993] |
| A. | \[\pi \,ab\]sq. unit |
| B. | \[\frac{1}{2}\pi \,ab\]sq. unit |
| C. | \[\frac{1}{4}\pi \,ab\]sq. unit |
| D. | None of these |
| Answer» B. \[\frac{1}{2}\pi \,ab\]sq. unit | |
| 6737. |
A particle moves in a straight line so that its velocity at any point is given by \[{{v}^{2}}=a+bx\], where \[a,b\ne 0\]are constants. The acceleration is [MP PET 1989] |
| A. | Zero |
| B. | Uniform |
| C. | Non-uniform |
| D. | Indeterminate |
| Answer» C. Non-uniform | |
| 6738. |
If \[{{n}^{th}}\] terms of two A.P.'s are \[3n+8\] and \[7n+15\], then the ratio of their \[{{12}^{th}}\] terms will be [MP PET 1986] |
| A. | 44443 |
| B. | 42552 |
| C. | 44380 |
| D. | 42217 |
| Answer» B. 42552 | |
| 6739. |
A stone moving vertically upwards has its equation of motion \[s=490t-4.9{{t}^{2}}\]. The maximum height reached by the stone is |
| A. | 12250 |
| B. | 1225 |
| C. | 36750 |
| D. | None of these |
| Answer» B. 1225 | |
| 6740. |
\[{{(r+1)}^{th}}\] term in the expansion of \[{{(1-x)}^{-4}}\]will be |
| A. | \[\frac{{{x}^{r}}}{r!}\] |
| B. | \[\frac{(r+1)(r+2)(r+3)}{6}{{x}^{r}}\] |
| C. | \[\frac{(r+2)(r+3)}{2}{{x}^{r}}\] |
| D. | None of these |
| Answer» C. \[\frac{(r+2)(r+3)}{2}{{x}^{r}}\] | |
| 6741. |
The angle between the lines \[xy=0\]is equal to [Pb. CET 2003] |
| A. | \[{{45}^{o}}\] |
| B. | \[60{}^\circ \] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{180}^{o}}\] |
| Answer» D. \[{{180}^{o}}\] | |
| 6742. |
One dice is thrown three times and the sum of the thrown numbers is 15. The probability for which number 4 appears in first throw [MP PET 2004] |
| A. | \[\frac{1}{18}\] |
| B. | \[\frac{1}{36}\] |
| C. | \[\frac{1}{9}\] |
| D. | \[\frac{1}{3}\] |
| Answer» B. \[\frac{1}{36}\] | |
| 6743. |
The centre of the conic represented by the equation \[2{{x}^{2}}-72xy+23{{y}^{2}}-4x-28y-48=0\] is |
| A. | \[\left( \frac{11}{15},\ \frac{2}{25} \right)\] |
| B. | \[\left( \frac{2}{25},\ \frac{11}{25} \right)\] |
| C. | \[\left( \frac{11}{15},\ -\frac{2}{25} \right)\] |
| D. | \[\left( -\frac{11}{25},\ -\frac{2}{25} \right)\] |
| Answer» B. \[\left( \frac{2}{25},\ \frac{11}{25} \right)\] | |
| 6744. |
A line through (0,0) cuts the circle \[{{x}^{2}}+{{y}^{2}}-2ax=0\] at A and B, then locus of the centre of the circle drawn on AB as a diameter is [RPET 2002] |
| A. | \[{{x}^{2}}+{{y}^{2}}-2ay=0\] |
| B. | \[{{x}^{2}}+{{y}^{2}}+ay=0\] |
| C. | \[{{x}^{2}}+{{y}^{2}}+ax=0\] |
| D. | \[{{x}^{2}}+{{y}^{2}}-ax=0\] |
| Answer» E. | |
| 6745. |
If the equation \[{{x}^{2}}+px+q=0\] and \[{{x}^{2}}+qx+p=0\], have a common root, then \[p+q+1=\] [Orissa JEE 2002] |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» B. 1 | |
| 6746. |
For two events A and B, if \[P(A)=P\left( \frac{A}{B} \right)=\frac{1}{4}\] and \[P\,\left( \frac{B}{A} \right)=\frac{1}{2},\] then |
| A. | A and B are independent |
| B. | \[P\,\left( \frac{{{A}'}}{B} \right)=\frac{3}{4}\] |
| C. | \[P\,\left( \frac{{{B}'}}{{{A}'}} \right)=\frac{1}{2}\] |
| D. | All of the above |
| Answer» E. | |
| 6747. |
Middle point of the chord of the circle \[{{x}^{2}}+{{y}^{2}}=25\] intercepted on the line \[x-2y=2\]is |
| A. | \[\left( \frac{3}{5},\frac{4}{5} \right)\] |
| B. | \[(-2,-2)\] |
| C. | \[\left( \frac{2}{5},-\frac{4}{5} \right)\] |
| D. | \[\left( \frac{8}{3},\frac{1}{3} \right)\] |
| Answer» D. \[\left( \frac{8}{3},\frac{1}{3} \right)\] | |
| 6748. |
The sum of \[n\] arithmetic means between \[a\] and \[b\], is [RPET 1986] |
| A. | \[\frac{n(a+b)}{2}\] |
| B. | \[n(a+b)\] |
| C. | \[\frac{(n+1)(a+b)}{2}\] |
| D. | \[(n+1)(a+b)\] |
| Answer» B. \[n(a+b)\] | |
| 6749. |
If a curve \[y=a\sqrt{x}+bx\] passes through the point (1, 2) and the area bounded by the curve, line \[x=4\] and x-axis is 8 sq. unit, then [MP PET 2002] |
| A. | \[a=3,\,b=-1\] |
| B. | \[a=3,\,b=1\] |
| C. | \[a=-3,\,b=1\] |
| D. | \[a=-3,\,b=-1\] |
| Answer» B. \[a=3,\,b=1\] | |
| 6750. |
A real value of x will satisfy the equation \[\left( \frac{3-4ix}{3+4ix} \right)=\] \[\alpha -i\beta \,(\alpha ,\beta \,\text{real),}\] if [Orissa JEE 2003] |
| A. | \[{{\alpha }^{2}}-{{\beta }^{2}}=-1\] |
| B. | \[{{\alpha }^{2}}-{{\beta }^{2}}=1\] |
| C. | \[{{\alpha }^{2}}+{{\beta }^{2}}=1\] |
| D. | \[{{\alpha }^{2}}-{{\beta }^{2}}=2\] |
| Answer» D. \[{{\alpha }^{2}}-{{\beta }^{2}}=2\] | |