8666 + Mcqs in Mathematics Page 54 McqOptions

2651.	The number of integral terms in the expansion of \[{{\left( \sqrt{3}+\sqrt[8]{5} \right)}^{256}}\] is [AIEEE 2003]
A.	32
B.	33
C.	34
D.	35
Answer» C. 34

Discussion

2652.	The digit in the unit place of the number \[(183\,!)+{{3}^{183}}\] is [Karnataka CET 2002]
A.	7
B.	6
C.	3
D.	0
Answer» B. 6

Discussion

2653.	The expression \[{{(2+\sqrt{2})}^{4}}\] has value, lying between [AMU 2001]
A.	134 and 135
B.	135 and 136
C.	136 and 137
D.	None of these
Answer» C. 136 and 137

Discussion

2654.	The number of integral terms in the expansion of \[{{({{5}^{1/2}}+{{7}^{1/6}})}^{642}}\] is [Kurukshetra CEE 1996]
A.	106
B.	108
C.	103
D.	109
Answer» C. 103

Discussion

2655.	If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}}\] are the coefficients of any four consecutive terms in the expansion of \[{{(1+x)}^{n}}\], then \[\frac{{{a}_{1}}}{{{a}_{1}}+{{a}_{2}}}+\frac{{{a}_{3}}}{{{a}_{3}}+{{a}_{4}}}\] = [IIT 1975]
A.	\[\frac{{{a}_{2}}}{{{a}_{2}}+{{a}_{3}}}\]
B.	\[\frac{1}{2}\frac{{{a}_{2}}}{({{a}_{2}}+{{a}_{3}})}\]
C.	\[\frac{2{{a}_{2}}}{{{a}_{2}}+{{a}_{3}}}\]
D.	\[\frac{2{{a}_{3}}}{{{a}_{2}}+{{a}_{3}}}\]
Answer» D. \[\frac{2{{a}_{3}}}{{{a}_{2}}+{{a}_{3}}}\]

Discussion

2656.	Find the value of\[\frac{({{18}^{3}}+{{7}^{3}}+3.18.7.25)}{{{3}^{6}}+6.243.2+15.81.4+20.27.8+15.9.16+6.3.32+64}\] [IIT 1960]
A.	1
B.	5
C.	25
D.	100
Answer» B. 5

Discussion

2657.	The coefficient of two consecutive terms in the expansion of \[{{(1+x)}^{n}}\] will be equal, if
A.	n is any integer
B.	n is an odd integer
C.	n is an even integer
D.	None of these
Answer» C. n is an even integer

Discussion

2658.	If number of terms in the expansion of \[{{(x-2y+3z)}^{n}}\]are 45, then n=
A.	7
B.	8
C.	9
D.	None of these
Answer» C. 9

Discussion

2659.	Number of ways of selection of 8 letters from 24 letters of which 8 are \[a\], 8 are \[b\] and the rest unlike, is given by
A.	\[{{2}^{7}}\]
B.	\[8\ .\ {{2}^{8}}\]
C.	\[10\ .\ {{2}^{7}}\]
D.	None of these
Answer» D. None of these

Discussion

2660.	A set contains \[(2n+1)\] elements. The number of sub-sets of the set which contain at most \[n\] elements is
A.	\[{{2}^{n}}\]
B.	\[{{2}^{n+1}}\]
C.	\[{{2}^{n-1}}\]
D.	\[{{2}^{2n}}\]
Answer» E.

Discussion

2661.	The number of divisors of 9600 including 1 and 9600 are [IIT Screening 1993]
A.	60
B.	58
C.	48
D.	46
Answer» D. 46

Discussion

2662.	In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3
A.	70
B.	35
C.	64
D.	192
Answer» C. 64

Discussion

2663.	If \[^{n}{{P}_{3}}{{+}^{n}}{{C}_{n-2}}=14n\], then \[n=\]
A.	5
B.	6
C.	8
D.	10
Answer» B. 6

Discussion

2664.	If \[^{n}{{P}_{r}}=840,{{\,}^{n}}{{C}_{r}}=35,\] then \[n\] is equal to [EAMCET 1986]
A.	1
B.	3
C.	5
D.	7
Answer» E.

Discussion

2665.	The number of numbers of 4 digits which are not divisible by 5 are
A.	7200
B.	3600
C.	14400
D.	1800
Answer» B. 3600

Discussion

2666.	If \[P(n,r)=1680\] and \[C(n,r)=70\], then \[69n+r!=\] [Kerala (Engg.)2005]
A.	128
B.	576
C.	256
D.	625
E.	1152
Answer» C. 256

Discussion

2667.	\[^{n}{{P}_{r}}{{\div }^{n}}{{C}_{r}}\] = [MP PET 1984]
A.	\[n\,!\]
B.	\[(n-r)!\]
C.	\[\frac{1}{r!}\]
D.	\[r\,!\]
Answer» E.

Discussion

2668.	The number of way to sit 3 men and 2 women in a bus such that total number of sitted men and women on each side is 3 [DCE 2005]
A.	5!
B.	\[^{6}{{C}_{5}}\times 5!\]
C.	\[6!\,{{\times }^{6}}{{P}_{5}}\]
D.	\[5!\,{{+}^{6}}{{C}_{5}}\]
Answer» C. \[6!\,{{\times }^{6}}{{P}_{5}}\]

Discussion

2669.	The sum of all positive divisors of 960 is [Karnataka CET 2000]
A.	3048
B.	3087
C.	3047
D.	2180
Answer» B. 3087

Discussion

2670.	The sum \[\sum\limits_{i=0}^{m}{\left( \begin{matrix} 10 \\ i \\ \end{matrix} \right)}\,\left( \begin{matrix} 20 \\ m-i \\ \end{matrix} \right)\,,\] \[\left( \text{where}\,\left( \begin{matrix} p \\ q \\ \end{matrix} \right)\,=0\,\text{if}\,p
A.	5
B.	15
C.	10
D.	20
Answer» C. 10

Discussion

2671.	If \[^{n}{{P}_{r}}\]= 720.\[^{n}{{C}_{r}},\] then r is equal to [Kerala (Engg.) 2001]
A.	6
B.	5
C.	4
D.	7
Answer» B. 5

Discussion

2672.	If \[^{n}{{P}_{4}}=24.{{\,}^{n}}{{C}_{5}},\] then the value of n is [Karnataka CET 2001]
A.	10
B.	15
C.	9
D.	5
Answer» D. 5

Discussion

2673.	Number of divisors of \[n=38808\] (except 1 and n) is [RPET 2000]
A.	70
B.	68
C.	72
D.	74
Answer» B. 68

Discussion

2674.	An n-digit number is a positive number with exactly \[n\] digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of \[n\] for which this is possible is [IIT 1998]
A.	6
B.	7
C.	8
D.	9
Answer» C. 8

Discussion

2675.	The number of ordered triplets of positive integers which are solutions of the equation \[x+y+z=100\] is
A.	6005
B.	4851
C.	5081
D.	None of these
Answer» C. 5081

Discussion

2676.	If\[^{n}{{P}_{4}}=30{{\,}^{n}}{{C}_{5}}\], then \[n=\] [MP PET 1995]
A.	6
B.	7
C.	8
D.	9
Answer» D. 9

Discussion

2677.	If \[^{n}{{C}_{r}}={{\,}^{n}}{{C}_{r-1}}\] and \[^{n}{{P}_{r}}{{=}^{n}}{{P}_{r+1}}\], then the value of n is
A.	3
B.	4
C.	2
D.	5
Answer» B. 4

Discussion

2678.	The points with position vectors \[60\,\mathbf{i}+3\,\mathbf{j}\], \[40\,\mathbf{i}-8\mathbf{j},\], \[a\,\mathbf{i}-52\,\mathbf{j}\] are collinear, if \[a=\] [RPET 1991; IIT 1983; MP PET 2002]
A.	40
B.	40
C.	20
D.	None of these
Answer» B. 40

Discussion

2679.	If the position vectors of the points A, B, C be \[\mathbf{a},\ \mathbf{b}\], \[3\mathbf{a}-2\mathbf{b}\] respectively, then the points A, B, C are [MP PET 1989]
A.	Collinear
B.	Non-collinear
C.	Form a right angled triangle
D.	None of these
Answer» B. Non-collinear

Discussion

2680.	The vectors \[3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}\] and \[a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}\]are collinear, if [RPET 1986; MP PET 1988]
A.	\[a=3,\,\,b=1\]
B.	\[a=9,\,\,b=1\]
C.	\[a=3,\,\,b=3\]
D.	\[a=9,\,\,b=3\]
Answer» E.

Discussion

2681.	If \[A,\,B,\,C\] are the vertices of a triangle whose position vectors are a, b, c and G is the centroid of the \[\Delta ABC,\] then \[\overrightarrow{GA}+\overrightarrow{GB}\,+\overrightarrow{GC}\] is [Karnataka CET 2000]
A.	0
B.	\[\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}\]
C.	\[\frac{\mathbf{a}+\mathbf{b}+\mathbf{c}}{3}\]
D.	\[\frac{\mathbf{a}+\mathbf{b}-\mathbf{c}}{3}\]
Answer» B. \[\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}\]

Discussion

2682.	If the points \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\,\mathbf{b}\] be collinear, then k =
A.	0
B.	2
C.	2
D.	Any real number
Answer» E.

Discussion

2683.	If the position vectors of the points A, B, C be \[\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}\] and \[a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}\] respectively, then the points A, B, C are collinear if
A.	\[a=b=c=1\]
B.	\[a=1,\,\,b\] and \[c\] are arbitrary scalars
C.	\[a=b=c=0\]
D.	\[c=0,\,\,a=1\] and b is arbitrary scalars
Answer» E.

Discussion

2684.	If \[D,\,E,\,F\] are respectively the mid points of \[AB,\,AC\]and \[BC\] in \[\Delta ABC\], then \[\overrightarrow{BE}\]\[+\overrightarrow{AF}=\] [EAMCET 2003]
A.	\[\overrightarrow{DC}\]
B.	\[\frac{1}{2}\overrightarrow{BF}\]
C.	\[2\overrightarrow{BF}\]
D.	\[\frac{3}{2}\overrightarrow{BF}\]
Answer» B. \[\frac{1}{2}\overrightarrow{BF}\]

Discussion

2685.	If position vectors of a point A is a + 2b and a divides AB in the ratio \[2:3\], then the position vector of B is [MP PET 2002]
A.	2a ? b
B.	b ? 2a
C.	a ? 3b
D.	b
Answer» D. b

Discussion

2686.	If O is origin and C is the mid-point of \[A(2,\,\,-1)\] and \[B(-4,\,3)\]. Then value of \[\overrightarrow{OC}\] is [RPET 2001]
A.	i + j
B.	i ? j
C.	i + j
D.	i ? j
Answer» D. i ? j

Discussion

2687.	If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is [RPET 1996]
A.	\[\frac{\mathbf{a}+2\mathbf{b}}{3}\]
B.	\[\frac{2\mathbf{a}+\mathbf{b}}{3}\]
C.	\[\frac{\mathbf{a}+2}{3}\]
D.	\[\frac{\mathbf{a}+\mathbf{b}}{2}\]
Answer» B. \[\frac{2\mathbf{a}+\mathbf{b}}{3}\]

Discussion

2688.	If position vector of points A, B, C are respectively i, j, k and \[AB=CX,\] then position vector of point X is [MP PET 1994]
A.	\[-\,\mathbf{i}+\mathbf{j}+\mathbf{k}\]
B.	\[\mathbf{i}-\mathbf{j}+\mathbf{k}\]
C.	\[\mathbf{i}+\mathbf{j}-\mathbf{k}\]
D.	\[\mathbf{i}+\mathbf{j}+\mathbf{k}\]
Answer» B. \[\mathbf{i}-\mathbf{j}+\mathbf{k}\]

Discussion

2689.	The sum of the three vectors determined by the medians of a triangle directed from the vertices is [MP PET 1997]
A.	0
B.	1
C.	1
D.	\[\frac{1}{3}\]
Answer» B. 1

Discussion

2690.	If \[\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC},\] then A, B, C form [IIT 1983]
A.	Equilateral triangle
B.	Right angled triangle
C.	Isosceles triangle
D.	Line
Answer» D. Line

Discussion

2691.	In a triangle ABC, if \[2\overrightarrow{AC}=3\overrightarrow{CB},\] then \[2\overrightarrow{OA}+3\overrightarrow{OB}\] equals [IIT 1988; Pb. CET 2003]
A.	\[5\overrightarrow{OC}\]
B.	\[\frac{1}{3}\,(2\mathbf{i}-2\mathbf{j}+\mathbf{k})\]
C.	\[\,\overrightarrow{OC}\]
D.	None of these
Answer» B. \[\frac{1}{3}\,(2\mathbf{i}-2\mathbf{j}+\mathbf{k})\]

Discussion

2692.	If \[\mathbf{p}=7\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[\mathbf{q}=3\mathbf{i}+\mathbf{j}+5\mathbf{k},\] then the magnitude of \[\mathbf{p}-2\mathbf{q}\] is [MP PET 1987]
A.	\[\sqrt{29}\]
B.	4
C.	\[\sqrt{62}-2\sqrt{35}\]
D.	\[\sqrt{66}\]
Answer» E.

Discussion

2693.	ABCDE is a pentagon. Forces \[\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}\] act at a point. Which force should be added to this system to make the resultant \[{{\cos }^{-1}}\frac{4}{5}\] [MNR 1984]
A.	\[\overrightarrow{AC}\]
B.	\[\overrightarrow{AD}\]
C.	\[\overrightarrow{BC}\]
D.	\[\overrightarrow{BD}\]
Answer» D. \[\overrightarrow{BD}\]

Discussion

2694.	If in a triangle \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{b}\] and D, E are the mid-points of AB and AC respectively, then \[\overrightarrow{DE}\] is equal to [RPET 1986]
A.	\[\frac{\mathbf{a}}{4}-\frac{\mathbf{b}}{4}\]
B.	\[\frac{\mathbf{a}}{2}-\frac{\mathbf{b}}{2}\]
C.	\[\frac{\mathbf{b}}{4}-\frac{\mathbf{a}}{4}\]
D.	\[\frac{\mathbf{b}}{2}-\frac{\mathbf{a}}{2}\]
Answer» E.

Discussion

2695.	In the triangle ABC, \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{c},\,\,\overrightarrow{BC}=\mathbf{b}\], then [RPET 1984]
A.	\[\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\]
B.	\[\mathbf{a}+\mathbf{b}-\mathbf{c}=\mathbf{0}\]
C.	\[\mathbf{a}-\mathbf{b}+\mathbf{c}=\mathbf{0}\]
D.	\[-\,\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}\]
Answer» C. \[\mathbf{a}-\mathbf{b}+\mathbf{c}=\mathbf{0}\]

Discussion

2696.	If C is the middle point of AB and P is any point outside AB, then [MNR 1991; UPSEAT 2000; AIEEE 2005]
A.	\[\overrightarrow{PA}+\overrightarrow{PB}=\overrightarrow{PC}\]
B.	\[\overrightarrow{PA}+\overrightarrow{PB}=2\,\overrightarrow{PC}\]
C.	\[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\]
D.	\[\overrightarrow{PA}+\overrightarrow{PB}+2\,\overrightarrow{PC}=0\]
Answer» C. \[\overrightarrow{PA}+\overrightarrow{PB}+\overrightarrow{PC}=0\]

Discussion

2697.	If the position vectors of the points A and B are \[c=(2\,-2,\,4)\] and \[3\mathbf{i}-\mathbf{j}-3\mathbf{k},\] then what will be the position vector of the mid-point of AB [MP PET 1992]
A.	\[\mathbf{i}+2\mathbf{j}-\mathbf{k}\]
B.	\[2\mathbf{i}+\mathbf{j}-2\mathbf{k}\]
C.	\[2\mathbf{i}+\mathbf{j}-\mathbf{k}\]
D.	\[\mathbf{i}+\mathbf{j}-2\mathbf{k}\]
Answer» C. \[2\mathbf{i}+\mathbf{j}-\mathbf{k}\]

Discussion

2698.	If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by \[\overrightarrow{AE}\] will be
A.	\[2\,\mathbf{b}-\mathbf{a}\]
B.	\[\mathbf{b}-\mathbf{a}\]
C.	\[2\,\mathbf{a}-\mathbf{b}\]
D.	\[\mathbf{a}+\mathbf{b}\]
Answer» B. \[\mathbf{b}-\mathbf{a}\]

Discussion

2699.	A and B are two points. The position vector of A is \[6\mathbf{b}-2\mathbf{a}.\] A point P divides the line AB in the ratio 1 : 2. If \[\mathbf{a}-\mathbf{b}\] is the position vector of P, then the position vector of B is given by [MP PET 1993]
A.	\[7\mathbf{a}-15\mathbf{b}\]
B.	\[7\mathbf{a}+15\mathbf{b}\]
C.	\[2\pi /3\]
D.	\[15\mathbf{a}+7\mathbf{b}\]
Answer» B. \[7\mathbf{a}+15\mathbf{b}\]

Discussion

2700.	The position vector of a point C with respect to B is \[\mathbf{i}+\mathbf{j}\] and that of B with respect to A is \[\mathbf{i}-\mathbf{j}.\] The position vector of C with respect to A is [MP PET 1989]
A.	2 i
B.	2 j
C.	2 j
D.	2 i
Answer» B. 2 j

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

The number of integral terms in the expansion of \[{{\left( \sqrt{3}+\sqrt[8]{5} \right)}^{256}}\] is [AIEEE 2003]

The digit in the unit place of the number \[(183\,!)+{{3}^{183}}\] is [Karnataka CET 2002]

The expression \[{{(2+\sqrt{2})}^{4}}\] has value, lying between [AMU 2001]

The number of integral terms in the expansion of \[{{({{5}^{1/2}}+{{7}^{1/6}})}^{642}}\] is [Kurukshetra CEE 1996]

If \[{{a}_{1}},{{a}_{2}},{{a}_{3}},{{a}_{4}}\] are the coefficients of any four consecutive terms in the expansion of \[{{(1+x)}^{n}}\], then \[\frac{{{a}_{1}}}{{{a}_{1}}+{{a}_{2}}}+\frac{{{a}_{3}}}{{{a}_{3}}+{{a}_{4}}}\] = [IIT 1975]

Find the value of\[\frac{({{18}^{3}}+{{7}^{3}}+3.18.7.25)}{{{3}^{6}}+6.243.2+15.81.4+20.27.8+15.9.16+6.3.32+64}\] [IIT 1960]

The coefficient of two consecutive terms in the expansion of \[{{(1+x)}^{n}}\] will be equal, if

If number of terms in the expansion of \[{{(x-2y+3z)}^{n}}\]are 45, then n=

Number of ways of selection of 8 letters from 24 letters of which 8 are \[a\], 8 are \[b\] and the rest unlike, is given by

A set contains \[(2n+1)\] elements. The number of sub-sets of the set which contain at most \[n\] elements is

The number of divisors of 9600 including 1 and 9600 are [IIT Screening 1993]

In how many ways can Rs. 16 be divided into 4 person when none of them get less than Rs. 3

If \[^{n}{{P}_{3}}{{+}^{n}}{{C}_{n-2}}=14n\], then \[n=\]

If \[^{n}{{P}_{r}}=840,{{\,}^{n}}{{C}_{r}}=35,\] then \[n\] is equal to [EAMCET 1986]

The number of numbers of 4 digits which are not divisible by 5 are

If \[P(n,r)=1680\] and \[C(n,r)=70\], then \[69n+r!=\] [Kerala (Engg.)2005]

\[^{n}{{P}_{r}}{{\div }^{n}}{{C}_{r}}\] = [MP PET 1984]

The number of way to sit 3 men and 2 women in a bus such that total number of sitted men and women on each side is 3 [DCE 2005]

The sum of all positive divisors of 960 is [Karnataka CET 2000]

The sum \[\sum\limits_{i=0}^{m}{\left( \begin{matrix} 10 \\ i \\ \end{matrix} \right)}\,\left( \begin{matrix} 20 \\ m-i \\ \end{matrix} \right)\,,\] \[\left( \text{where}\,\left( \begin{matrix} p \\ q \\ \end{matrix} \right)\,=0\,\text{if}\,p

If \[^{n}{{P}_{r}}\]= 720.\[^{n}{{C}_{r}},\] then r is equal to [Kerala (Engg.) 2001]

If \[^{n}{{P}_{4}}=24.{{\,}^{n}}{{C}_{5}},\] then the value of n is [Karnataka CET 2001]

Number of divisors of \[n=38808\] (except 1 and n) is [RPET 2000]

An n-digit number is a positive number with exactly \[n\] digits. Nine hundred distinct n-digit numbers are to be formed using only the three digits 2, 5 and 7. The smallest value of \[n\] for which this is possible is [IIT 1998]

The number of ordered triplets of positive integers which are solutions of the equation \[x+y+z=100\] is

If\[^{n}{{P}_{4}}=30{{\,}^{n}}{{C}_{5}}\], then \[n=\] [MP PET 1995]

If \[^{n}{{C}_{r}}={{\,}^{n}}{{C}_{r-1}}\] and \[^{n}{{P}_{r}}{{=}^{n}}{{P}_{r+1}}\], then the value of n is

The points with position vectors \[60\,\mathbf{i}+3\,\mathbf{j}\], \[40\,\mathbf{i}-8\mathbf{j},\], \[a\,\mathbf{i}-52\,\mathbf{j}\] are collinear, if \[a=\] [RPET 1991; IIT 1983; MP PET 2002]

If the position vectors of the points A, B, C be \[\mathbf{a},\ \mathbf{b}\], \[3\mathbf{a}-2\mathbf{b}\] respectively, then the points A, B, C are [MP PET 1989]

The vectors \[3\,\mathbf{i}+\mathbf{j}-5\,\mathbf{k}\] and \[a\,\mathbf{i}+b\,\mathbf{j}-15\,\mathbf{k}\]are collinear, if [RPET 1986; MP PET 1988]

If \[A,\,B,\,C\] are the vertices of a triangle whose position vectors are a, b, c and G is the centroid of the \[\Delta ABC,\] then \[\overrightarrow{GA}+\overrightarrow{GB}\,+\overrightarrow{GC}\] is [Karnataka CET 2000]

If the points \[\mathbf{a}+\mathbf{b},\,\,\mathbf{a}-\mathbf{b}\] and \[\mathbf{a}+k\,\mathbf{b}\] be collinear, then k =

If the position vectors of the points A, B, C be \[\mathbf{i}+\mathbf{j},\,\,\,\mathbf{i}-\mathbf{j}\] and \[a\,\,\mathbf{i}+b\,\mathbf{j}+c\,\mathbf{k}\] respectively, then the points A, B, C are collinear if

If \[D,\,E,\,F\] are respectively the mid points of \[AB,\,AC\]and \[BC\] in \[\Delta ABC\], then \[\overrightarrow{BE}\]\[+\overrightarrow{AF}=\] [EAMCET 2003]

If position vectors of a point A is a + 2b and a divides AB in the ratio \[2:3\], then the position vector of B is [MP PET 2002]

If O is origin and C is the mid-point of \[A(2,\,\,-1)\] and \[B(-4,\,3)\]. Then value of \[\overrightarrow{OC}\] is [RPET 2001]

If a and b are P.V. of two points A and B and C divides AB in ratio 2 : 1, then P.V. of C is [RPET 1996]

If position vector of points A, B, C are respectively i, j, k and \[AB=CX,\] then position vector of point X is [MP PET 1994]

The sum of the three vectors determined by the medians of a triangle directed from the vertices is [MP PET 1997]

If \[\overrightarrow{AO}+\overrightarrow{OB}=\overrightarrow{BO}+\overrightarrow{OC},\] then A, B, C form [IIT 1983]

In a triangle ABC, if \[2\overrightarrow{AC}=3\overrightarrow{CB},\] then \[2\overrightarrow{OA}+3\overrightarrow{OB}\] equals [IIT 1988; Pb. CET 2003]

If \[\mathbf{p}=7\mathbf{i}-2\mathbf{j}+3\mathbf{k}\] and \[\mathbf{q}=3\mathbf{i}+\mathbf{j}+5\mathbf{k},\] then the magnitude of \[\mathbf{p}-2\mathbf{q}\] is [MP PET 1987]

ABCDE is a pentagon. Forces \[\overrightarrow{AB},\,\overrightarrow{AE},\,\overrightarrow{DC},\,\overrightarrow{ED}\] act at a point. Which force should be added to this system to make the resultant \[{{\cos }^{-1}}\frac{4}{5}\] [MNR 1984]

If in a triangle \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{b}\] and D, E are the mid-points of AB and AC respectively, then \[\overrightarrow{DE}\] is equal to [RPET 1986]

In the triangle ABC, \[\overrightarrow{AB}=\mathbf{a},\,\,\overrightarrow{AC}=\mathbf{c},\,\,\overrightarrow{BC}=\mathbf{b}\], then [RPET 1984]

If C is the middle point of AB and P is any point outside AB, then [MNR 1991; UPSEAT 2000; AIEEE 2005]

If the position vectors of the points A and B are \[c=(2\,-2,\,4)\] and \[3\mathbf{i}-\mathbf{j}-3\mathbf{k},\] then what will be the position vector of the mid-point of AB [MP PET 1992]

If the vectors represented by the sides AB and BC of the regular hexagon ABCDEF be a and b, then the vector represented by \[\overrightarrow{AE}\] will be

A and B are two points. The position vector of A is \[6\mathbf{b}-2\mathbf{a}.\] A point P divides the line AB in the ratio 1 : 2. If \[\mathbf{a}-\mathbf{b}\] is the position vector of P, then the position vector of B is given by [MP PET 1993]

The position vector of a point C with respect to B is \[\mathbf{i}+\mathbf{j}\] and that of B with respect to A is \[\mathbf{i}-\mathbf{j}.\] The position vector of C with respect to A is [MP PET 1989]