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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.
| 7651. |
For \[a>b>c>0,\] the distance between (1, 1) and the point of intersection of the lines \[ax+by+c=0\] and \[bx+ay+c=0\] is less than \[2\sqrt{2}.\] Then |
| A. | \[a+b-c>0\] |
| B. | \[a-b+c<0\] |
| C. | \[a-b+c>0\] |
| D. | \[a+b-c<0\] |
| Answer» B. \[a-b+c<0\] | |
| 7652. |
A straight line through the origin O meets the parallel lines \[4x+2y=9\] and \[2x+y+6=0\] at points P and Q respectively. Then the points O divides the segment PQ in the ratio |
| A. | 0.0430555555555556 |
| B. | 0.127777777777778 |
| C. | 0.0840277777777778 |
| D. | 0.16875 |
| Answer» C. 0.0840277777777778 | |
| 7653. |
The number of equilateral triangles with \[y=\sqrt{3}(x-1)+2\] and \[y=-\sqrt{3x}\] as two of its sides is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» E. | |
| 7654. |
The length of the perpendicular from the origin to a line is 7 and line makes an angle of \[150{}^\circ \] with the positive direction of y-axis, then the equation of the line is |
| A. | \[\sqrt{3}x+y=7\] |
| B. | \[\sqrt{3}x-y=14\] |
| C. | \[\sqrt{3}x+y+14=0\] |
| D. | \[\sqrt{3}x+y-14=0\] |
| Answer» E. | |
| 7655. |
Vertices of a variable triangle are \[(3,4),\]\[(5cos\theta ,5sin\theta )\] and \[(5sin\theta ,-5cos\theta ),\]where \[\theta \in R.\] Locus of its orthocenter is |
| A. | \[{{(x+y-1)}^{2}}+{{(x-y-7)}^{2}}=100\] |
| B. | \[{{(x+y-7)}^{2}}+{{(x-y-1)}^{2}}=100\] |
| C. | \[{{(x+y-7)}^{2}}+{{(x+y-1)}^{2}}=100\] |
| D. | \[{{(x+y-7)}^{2}}+{{(x-y+1)}^{2}}=100\] |
| Answer» E. | |
| 7656. |
The equation of the straight line which passes through the point \[(-4,3)\] such that the portion of the line between the axes is divided internally by the point in the ration 5 : 3 is |
| A. | \[9x-20y+96=0\] |
| B. | \[9x+20y=24\] |
| C. | \[20x+9y+53=0\] |
| D. | None of these |
| Answer» B. \[9x+20y=24\] | |
| 7657. |
The straight lines \[x+2y-9=0,\,\,\,3x+5y-5=0\] and \[ax+by=1\] are concurrent if the straight line \[35x-22y+1=0\] passes through: |
| A. | (a, b) (b) |
| B. | (b, a) |
| C. | (a, -b) (d) |
| D. | (-a, b) |
| Answer» B. (b, a) | |
| 7658. |
If the line segment joining the points \[A(a,b)\] and \[B(c,d)\] subtends an angle \[\theta \] at the origin, then \[\cos \theta =\] |
| A. | \[\frac{ac+bd}{\sqrt{({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})}}\] |
| B. | \[\frac{ab+cd}{\sqrt{({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})}}\] |
| C. | \[\frac{ad+bc}{\sqrt{({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})}}\] |
| D. | None of these |
| Answer» B. \[\frac{ab+cd}{\sqrt{({{a}^{2}}+{{b}^{2}})({{c}^{2}}+{{d}^{2}})}}\] | |
| 7659. |
If 2p is the length of perpendicular from the origin to the lines \[\frac{x}{a}+\frac{y}{b}=1\], then \[{{a}^{2}},8{{p}^{2}},{{b}^{2}}\] are in |
| A. | A.P |
| B. | GP. |
| C. | H.P. |
| D. | None of these |
| Answer» D. None of these | |
| 7660. |
If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is |
| A. | Square |
| B. | Circle |
| C. | Straight line |
| D. | Two intersecting line |
| Answer» B. Circle | |
| 7661. |
What is the radius of the circle passing through the point \[(2,4)\] and having centre at the intersection of the lines \[x-y=4\] and \[2x+3y+7=0?\] |
| A. | 3 units |
| B. | 5 units |
| C. | \[3\sqrt{3}\] Units |
| D. | \[5\sqrt{2}\] units |
| Answer» E. | |
| 7662. |
The area of the triangle formed by the line \[x\sin \alpha +y\cos \alpha =\sin 2\alpha \]and the coordinates axes is |
| A. | \[\sin 2\alpha \] |
| B. | \[\cos 2\alpha \] |
| C. | \[2\sin 2\alpha \] |
| D. | \[2\cos 2\alpha \] |
| Answer» B. \[\cos 2\alpha \] | |
| 7663. |
The triangle formed by the lines \[x+y-4=0,\,\] \[3x+y=4,\] \[x+3y=4\] is [RPET 2002; IIT 1983; MNR 1992; UPSEAT 2001] |
| A. | Isosceles |
| B. | Equilateral |
| C. | Right?angled |
| D. | None of these |
| Answer» B. Equilateral | |
| 7664. |
Area of the parallelogram formed by the lines \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}=0\],\[{{a}_{1}}x+{{b}_{1}}y+{{d}_{1}}=0\]and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}=0\], \[{{a}_{2}}x+{{b}_{2}}y+{{d}_{2}}=0\]is |
| A. | \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{[(a_{1}^{2}+b_{1}^{2})(a_{2}^{2}+b_{2}^{2})]}^{1/2}}}\] |
| B. | \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{a}_{2}}-{{b}_{1}}{{b}_{2}}}\] |
| C. | \[\frac{({{d}_{1}}+{{c}_{1}})({{d}_{2}}+{{c}_{2}})}{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}}\] |
| D. | \[\frac{({{d}_{1}}-{{c}_{1}})({{d}_{2}}-{{c}_{2}})}{{{a}_{1}}{{b}_{2}}-{{a}_{2}}{{b}_{1}}}\] |
| Answer» E. | |
| 7665. |
If a variable line drawn through the point of intersection of straight lines \[\frac{x}{\alpha }+\frac{y}{\beta }=1\]and \[\frac{x}{\beta }+\frac{y}{\alpha }=1\] meets the coordinate axes in A and B, then the locus of the mid point of \[AB\] is |
| A. | \[\alpha \beta (x+y)=xy(\alpha +\beta )\] |
| B. | \[\alpha \beta (x+y)=2xy(\alpha +\beta )\] |
| C. | \[(\alpha +\beta )(x+y)=2\alpha \beta xy\] |
| D. | None of these |
| Answer» C. \[(\alpha +\beta )(x+y)=2\alpha \beta xy\] | |
| 7666. |
The point A (2, 1) is translated parallel to the line x-y=3 by a distance of 4 units, if the new position A' is in the third quadrant, then the coordinates of A' are |
| A. | \[(2+2\sqrt{2,}\,1+2\sqrt{2})\] |
| B. | \[(-2+\sqrt{2,}\,-1-2\sqrt{2})\] |
| C. | \[(2-2\sqrt{2,}\,1-2\sqrt{2})\] |
| D. | None of these |
| Answer» C. \[(2-2\sqrt{2,}\,1-2\sqrt{2})\] | |
| 7667. |
A straight line through the point A.(3, 4) is such that its intercept between the axes is bisected at A. its equation is |
| A. | \[x+y=7\] |
| B. | \[3x-4y+7=0\] |
| C. | \[4x+3y=24\] |
| D. | \[3x+4y=25\] |
| Answer» D. \[3x+4y=25\] | |
| 7668. |
The equations of the sides of a triangle are\[x+y-5=0,\text{ }x-y+1=0,\text{ }and\text{ }y-1=0,\] then the coordinates of the circumcenter are |
| A. | (2, 1) |
| B. | (1, 2) |
| C. | (2, -2) |
| D. | (1, -2) |
| Answer» B. (1, 2) | |
| 7669. |
The pedal points of a perpendicular drawn from origin on the line \[3x+4y-5=0\], is [RPET 1990] |
| A. | \[\left( \frac{3}{5},2 \right)\] |
| B. | \[\left( \frac{3}{5},\frac{4}{5} \right)\] |
| C. | \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] |
| D. | \[\left( \frac{30}{17},\frac{19}{17} \right)\] |
| Answer» C. \[\left( -\frac{3}{5},-\frac{4}{5} \right)\] | |
| 7670. |
The length of the perpendicular from the point \[(b,a)\]to the line \[\frac{x}{a}-\frac{y}{b}=1\], is |
| A. | \[\left| \frac{{{a}^{2}}-ab+{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| B. | \[\left| \frac{{{b}^{2}}-ab-{{a}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| C. | \[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] |
| D. | None of these |
| Answer» C. \[\left| \frac{{{a}^{2}}+ab-{{b}^{2}}}{\sqrt{{{a}^{2}}+{{b}^{2}}}} \right|\] | |
| 7671. |
The sides \[AB,BC,CD\] and \[DA\]of a quadrilateral are \[x+2y=3,\,x=1,\] \[x-3y=4,\,\] \[\,5x+y+12=0\] respectively. The angle between diagonals \[AC\]and \[BD\]is [Roorkee 1993] |
| A. | \[{{45}^{o}}\] |
| B. | \[{{60}^{o}}\] |
| C. | \[{{90}^{o}}\] |
| D. | \[{{30}^{o}}\] |
| Answer» D. \[{{30}^{o}}\] | |
| 7672. |
In what direction a line be drawn through the point (1, 2) so that its points of intersection with the line \[x+y=4\] is at a distance \[\frac{\sqrt{6}}{3}\] from the given point [IIT 1966; MNR 1987] |
| A. | \[{{30}^{o}}\] |
| B. | \[{{45}^{o}}\] |
| C. | \[{{60}^{o}}\] |
| D. | \[{{75}^{o}}\] |
| Answer» E. | |
| 7673. |
The mean of 13 observations is 14. If the mean of the first 7 observations is 12. And that of the least 7 observations is 16, what is the value of the 7th observations? |
| A. | 12 |
| B. | 13 |
| C. | 14 |
| D. | 15 |
| Answer» D. 15 | |
| 7674. |
The arithmetic mean of numbers a, b, c, d, e, is M. What is the value of \[(a-M)+(b-M)+(c-M)+(d-M)+(e-M)?\] |
| A. | M |
| B. | \[a+b+c+d+e\] |
| C. | 0 |
| D. | 5 M |
| Answer» D. 5 M | |
| 7675. |
An incomplete frequency distribution is given below Variate Frequency 10-20 20-30 30-40 40-50 50-60 60-70 70-80 12 30 ? 65 45 25 18 Total 229 Median value is 46, the missing frequency is |
| A. | 33.5 |
| B. | 35 |
| C. | 34 |
| D. | 26 |
| Answer» D. 26 | |
| 7676. |
If the mean of few observations is 40 and standard deviation is 8, then what is the coefficient of variation? |
| A. | 0.01 |
| B. | 0.1 |
| C. | 0.2 |
| D. | 0.3 |
| Answer» D. 0.3 | |
| 7677. |
In a binomial distribution, the mean is 4 and the variance is. What is the mode? |
| A. | 6 |
| B. | 5 |
| C. | 4 |
| D. | 3 |
| Answer» D. 3 | |
| 7678. |
Consider the frequency distribution of the given numbers. Value 1 2 3 4 Frequency 5 4 6 f If the mean is known to be 3, then the value of f is |
| A. | 3 |
| B. | 7 |
| C. | 10 |
| D. | 14 |
| Answer» E. | |
| 7679. |
In a series of \[2n\]observations, half of them equals \['a'\] and remaining equals '__a'. If S.D. is 2, then \[\left| a \right|\] equals |
| A. | \[\frac{1}{n}\] |
| B. | \[\sqrt{2}\] |
| C. | \[2\] |
| D. | \[\frac{\sqrt{2}}{n}\] |
| Answer» D. \[\frac{\sqrt{2}}{n}\] | |
| 7680. |
Let r be the range and \[{{S}^{2}}=\frac{1}{n-1}\sum\limits_{i=1}^{n}{{{({{x}_{i}}-\bar{x})}^{2}}}\] be the S.D. of a set of observations \[{{x}_{1}},{{x}_{2}},...{{x}_{n}},\] then |
| A. | \[S\le r\sqrt{\frac{n}{n-1}}\] |
| B. | \[S=r\sqrt{\frac{n}{n-1}}\] |
| C. | \[S\ge r\sqrt{\frac{n}{n-1}}\] |
| D. | None of these |
| Answer» B. \[S=r\sqrt{\frac{n}{n-1}}\] | |
| 7681. |
The mean of 20 observations is 15. On checking, it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is |
| A. | 15 |
| B. | 15.15 |
| C. | 15.35 |
| D. | 16 |
| Answer» C. 15.35 | |
| 7682. |
The scores of 15 students in an examination were recorded as 10, 5, 8, 16, 18, 20, 8, 10, 16, 20, 18, 11, 16, 14 and 12. After calculating the mean, median and mode, an error is found. One of the values is wrongly written as 16 instead of 18. Which of the following measures of central tendency will change? |
| A. | Mean and median |
| B. | Median and mode |
| C. | Mode only |
| D. | Mean and mode |
| Answer» E. | |
| 7683. |
The mean weight per student in a group of seven students is 55 kg. if the individual weights of six students are 52, 58, 55, 53, 56 and 54, then the weight of the seventh student is |
| A. | 55 kg |
| B. | 60 kg |
| C. | 57 kg |
| D. | 50 kg |
| Answer» D. 50 kg | |
| 7684. |
The mean of n times is \[\overline{x}\]. If the first terms is increased by 1, second by 2 and so on, then new mean is |
| A. | \[\bar{x}+n\] |
| B. | \[\bar{x}+\frac{n}{2}\] |
| C. | \[\bar{x}+\frac{n+1}{2}\] |
| D. | None of these |
| Answer» D. None of these | |
| 7685. |
An aeroplane flies around a squares, the sides of which measure 100 miles each. The aeroplane covers at speed of 100 m/h the first side, at 200 m/h the second side. At 300 m/h the third side and 400 m/h the fourth side. The average speed of the aeroplane around the square is |
| A. | 900 m/h |
| B. | 195 m/h |
| C. | 192 m/h |
| D. | 200 m/h |
| Answer» D. 200 m/h | |
| 7686. |
The 'less than' ogive curve and the 'more than' ogive curve intersect at |
| A. | Median |
| B. | Mode |
| C. | Arithmetic |
| D. | None of these |
| Answer» B. Mode | |
| 7687. |
Mean of 100 items is 49. It was discovered that three items which should have been 60, 70, 80 were wrongly read as 40, 20, 50 respectively. The correct mean is |
| A. | 48 |
| B. | \[82\frac{1}{2}\] |
| C. | \[50\] |
| D. | \[80\] |
| Answer» D. \[80\] | |
| 7688. |
The mean of a set of observation is \[\bar{x}.\]if each observation is divided by \[\alpha ,a\ne 0\] and then is increased by 10, then the mean of the new set is |
| A. | \[\frac{{\bar{x}}}{a}\] |
| B. | \[\frac{\bar{x}+10}{a}\] |
| C. | \[\frac{\bar{x}+10a}{a}\] |
| D. | \[a\bar{x}+10\] |
| Answer» D. \[a\bar{x}+10\] | |
| 7689. |
Let \[{{x}_{1}},{{x}_{2}},...{{x}_{n}}\] be n observations such that \[\sum{x_{i}^{2}=400}\] and \[\sum{{{x}_{i}}=80.}\] Then the possible value of n among the following is |
| A. | 15 |
| B. | 18 |
| C. | 9 |
| D. | 12 |
| Answer» C. 9 | |
| 7690. |
The mean and S.D. of the marks of 200 candidates were found to be 40 and 15 respectively. Later, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S.D. respectively are |
| A. | \[14.98,39.95\] |
| B. | \[39.95,14.98\] |
| C. | \[39.95,224.5\] |
| D. | None of these |
| Answer» C. \[39.95,224.5\] | |
| 7691. |
The mean and S.D of the marks of 200 candidates were found to be 40 and 15 respectively. Latter, it was discovered that a score of 40 was wrongly read as 50. The correct mean and S. D respectively are |
| A. | 14.98, 39.95 |
| B. | 39.95, 14.98 |
| C. | 39.95, 224.5 |
| D. | None of these |
| Answer» C. 39.95, 224.5 | |
| 7692. |
The average of n numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] is M. If \[{{x}_{n}}\] is replaced by \[x',\] then new average is |
| A. | \[M-{{x}_{n}}+x'\] |
| B. | \[\frac{nM-{{x}_{n}}+x'}{n}\] |
| C. | \[\frac{(n-1)M+x'}{n}\] |
| D. | \[\frac{M-{{x}_{n}}+x'}{n}\] |
| Answer» C. \[\frac{(n-1)M+x'}{n}\] | |
| 7693. |
Mean of the numbers \[1,2,3,...,n\] with respective weights \[{{1}^{2}}+1,\,\,{{2}^{2}}+2,\,\,{{3}^{3}}+3,\,\,...{{n}^{2}}+n\] is |
| A. | \[\frac{3n(n+1)}{2(2n+1)}\] |
| B. | \[\frac{2n+1}{3}\] |
| C. | \[\frac{3n+1}{4}\] |
| D. | \[\frac{3n+1}{2}\] |
| Answer» D. \[\frac{3n+1}{2}\] | |
| 7694. |
For 10 observations on price (x) and supply (y), the following data was obtained: \[\sum{x=130,\sum{y=220,}}\] \[\sum{{{x}^{2}}=2288,\sum{{{y}^{2}}=5506}}\] and \[\sum{xy=3467}\] What is line of regression of y on x? |
| A. | \[y=0.91x+8.74\] |
| B. | \[y=1.02x+8.74\] |
| C. | \[y=1.02x-7.02\] |
| D. | \[y=0.91x-7.02\] |
| Answer» C. \[y=1.02x-7.02\] | |
| 7695. |
In an experiment with 15 observations on X, the following results were available \[\Sigma {{x}^{2}}=2830,\] \[\Sigma x=170.\] On observation that was 20 was found to be wrong and was replaced by the correct value 30. Then the corrected variance is |
| A. | 78 |
| B. | \[188.66\] |
| C. | \[177.33\] |
| D. | \[8.33\] |
| Answer» B. \[188.66\] | |
| 7696. |
If the arithmetic mean of the numbers \[{{x}_{1}},{{x}_{2}},{{x}_{3}},...{{x}_{n}}\] is \[\bar{x}\]. Then the arithmetic mean of numbers \[a{{x}_{1}}+b,a{{x}_{2}}+b,a{{x}_{3}}+b,...a{{x}_{n}}+b,\] Where a, b are two constants would be |
| A. | \[\bar{x}\] |
| B. | \[na\bar{x}+nb\] |
| C. | \[a\bar{x}\] |
| D. | \[a\bar{x}+b\] |
| Answer» E. | |
| 7697. |
In a study of two groups, the following results were obtained:Group GroupABSample Size2025Sample mean2223Sample standard Deviation1012Which of the following statements is correct? |
| A. | Group A is less variable then Group B because Group A's standard deviation is smaller. |
| B. | Group A is less variable then Group B because Group A's sample size is smaller. |
| C. | Group A is less variable then group B because Group A's sample mean is smaller. |
| D. | Group A is less variable then group B because Group A's coefficient of variation is smaller. |
| Answer» E. | |
| 7698. |
A school has four sections of chemistry in class XII having 40, 35, 45 and 42 students. The mean marks obtained in Chemistry test are 50, 60, 55 and 45 respectively for the four sections, the overall average of marks per students is |
| A. | 53 |
| B. | 45 |
| C. | 55.3 |
| D. | 52.25 |
| Answer» E. | |
| 7699. |
The variance of the following distribution is \[{{x}_{i}}\] 2 3 11 \[f({{x}_{i}})\] \[\frac{1}{3}\] \[\frac{1}{2}\] \[\frac{1}{6}\] |
| A. | 10 |
| B. | 16 |
| C. | 8 |
| D. | 7.5 |
| Answer» B. 16 | |
| 7700. |
Section-wise expenditure of a State Govt. is shown in the given figure. The expenditure incurred on transport is |
| A. | 0.25 |
| B. | 0.3 |
| C. | 0.32 |
| D. | 0.35 |
| Answer» C. 0.32 | |