Math Chapter Wise

EnglishUPPSC Ashram Paddhati 2021

Q41.ABCD is a parallelogram with AC and BD as its diagonals, then AC – BD is equal to

A4 AB B3 AB C2 AB D0

Show answer

EnglishUPPSC Ashram Paddhati 2021

Q42.The angle between the vectors a×b and b×a is

A0° B45° C90° D180°

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q43.The angle between a diagonal of a cube and its coterminous edge is:

A1 1 cos 3 − B1 2 cos 3 − C−1/tan 2 DNone of these

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q44.If a,b,c are three unit vectors such that a +b +c = 0, then a.b + b.c + c.a is equal to:

A0 B1 C-3/2 D-1

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q45.A two dimensional vector a has its components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in anti-clockwise direction. If, with respect to new system, a has components p + 1 and 1 then

Ap = 0/ p = 0 Bp = 1 or p = 1 3 − Cp = –1 or p = 1 3 Dp = 1 or p = 1

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q46.If the vectors ˆ ˆ ˆ αi+j+k, ˆ ˆ ˆ i +βj+k and ˆ ˆ ˆ i +j+γk are coplanar, then the value of 1 1 1 1 α 1 β 1 γ + + − − − is:

A0 B–1 C1 D2

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q47.If, for any vector a, it is given that () () () 2 2 2 2 ˆ ˆ ˆ a i a j a k α a, × + × + × = then the value of α is:

A1 B2 C–2 D0

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q48.If a,b and c are any three vectors, then the value of a –b, b –c,c –a is:

Aa, b, c B2 a, b, c Ca, b, c DNone of these

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q49.Let vectors α (4y)a (2 y 1)b = + + + + x x and β (y 2 2)a (2 3y 1)b = − + + − − x x, where a and b are non-zero and non-collinear. If 3α 2β =, then

Ax = 1, y = 2 Bx = 2, y = 1 Cx = –1, y = 2 Dx= 2, y = –1

Show answer

EnglishUP TGT 1999 UKPSC Lecturer (Mains) 2020

Q50.If a and b are two unit vectors inclined at an angle of 600 to each other then-

Aa b 3 + = Ba b 1/+ < Ca b 1/− > Da b 1/− <

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q51.If a b c 0 + + = and a 3, b 5, c 7 =, then the angle between a and b is:

A1 2 cos 15 − B1 11 cos 14 − C1 47 cos 40 − D1 1 cos 2 −

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q52.The number of distinct real values of λ,for which the vectors – and 2 ˆ ˆ ˆ i + j – λ k are coplanar is:

A0 B1 C2 D3

Show answer

EnglishUKPSC Lecturer (Mains) 2020

Q53.If ˆ ˆ ˆ ˆ ˆ ˆ a = i + 4j + 2k, b = 3i – 2j + 7k and ˆ ˆ ˆ c = 2i – j+ 4k, then a vector d which is perpendicular to both a and b and satisfies c. d =15, is:

Aˆ ˆ ˆ 32i j 14k − − Bˆ ˆ ˆ 32i j 14k + + C5 ˆ ˆ ˆ (32i j 14k) 3 − − D1 ˆ ˆ ˆ (32i j 14k) 9 + +

Show answer

EnglishHaryana PGT 2019

Q54.a = 2i + j – k and b = j+ k. Vector c is such that a.c = 4 and a×c = b, then c is:

Aˆ ˆ ˆ i j k + − Bˆ ˆ ˆ 3i j k + + Cˆ ˆ ˆ i 3j k + + Dˆ ˆ ˆ 2i j k − −

Show answer

EnglishHaryana PGT 2019

Q55.The value of 'a' for which the points A,B,C with position vectors ˆ ˆ ˆ 2i j k − +, ˆ ˆ ˆ i 3j 5k − −, ˆ ˆ ˆ ai – 3j k + and respectively are the vertices of right- angled triangle with ∠ ∠ ∠C = 2 π, are:

A–2 and –1 B–2 and 1 C2 and –1 D2 and 1

Show answer

EnglishHaryana PGT 2019

Q56.a i j, = + b j k = + and c xa yb = +. If ˆ i 2j k, 3i 2j k − + + − and c are coplanar, then x y =

A–2 B–3 C2/3 D–1

Show answer

EnglishUK SSSC LT 2020

Q57.The vector in the direction of the vector ˆ ˆ ˆ i 2j 2k − + − + that has magnitude 9 is:

Aˆ ˆ ˆ i 2j 2k − + Bˆ ˆ ˆ i 2j 2k 3 − + C() ˆ ˆ ˆ 3 i 2j 2k − + D() ˆ ˆ ˆ 9 i 2j 2k − +

Show answer

EnglishHaryana PGT 2020

Q58.a2 b2 – () 2 a×b =

A() 2 a.b B() () a b. a b + − C() 2 a b − D() 2 a b +

Show answer

EnglishHaryana PGT 2018

Q59.Let ˆ ˆ ˆ ˆ a = i + j and b = 2i - k, then the point of intersection of the lines r×a = b×a and r×b = a×b is:

A(1, –1, –1) B(–1, 1, 1) C(3, –1, –1) D(3, 1, –1)

Show answer

EnglishUKPSC GIC 2018

Q60.If the position vector a of a point (12, n) is such that a = 13, then the value of n is

A±25 B±12 C±7 D±5

Show answer