Math Chapter Wise

EnglishTGT 2010

Q241.If a be any vector, then 2 2 2 ˆ ˆ ˆ a i a j a k × + × + × = × + × + × = × + × + × = × + × + × =

A0 Ba Ca2 D2a2

Show answer

EnglishTGT 2010

Q242.If ˆ ˆ ˆ ˆ ˆ ˆ a i 2j 2k,b 2i 3j k = + − = + − = + − = + − = + − = + − = + − = + − then a b × × is

A25 B27 C28 DNone of these

Show answer

EnglishTGT 2009

Q243.The cosine of the angle between the vectors ˆ ˆ ˆ a 2i 2j k = + − = + − = + − = + − and ˆ ˆ ˆ b 6i 3j 2k = − + = − + = − + = − + is –

A4/21 B3/4 C2/21 DNone of these

Show answer

EnglishTGT 2009

Q244.If ABCDEF is a quadrlateral and AB AC AD AE AF AD + + + + =λ + + + + =λ + + + + =λ + + + + =λ then what will be the value of λ?

A2 B3 C4 D6

Show answer

EnglishTGT 2009

Q245.A force ˆ ˆ ˆ F 3i 2j 4k = + − = + − = + − = + − is acting on the point (1, –1, 2) so tthe moment about the point (2, –1, 3) will be:

Aˆ ˆ ˆ 2i 7j 2k + − Bˆ ˆ ˆ 2i 7j 2k − + Cˆ ˆ ˆ 2i 7j 2k − − DNone of these

Show answer

EnglishTGT 2009

Q246.If the vertices of a triangle are (1, 1, 2), (2, 3, 5) and (1, 5, 5) respectively then what will be the area of the triangle –

A1 61 2 B1 62 2 C1 60 2 DNone of these

Show answer

EnglishTGT 2005

Q247.Vectors, a b c 4a 7b c − + − − − + − − − + − − − + − − and 3a 6b 6c + + + +; if a,b,c are non-zero and non-coplanar are:

Acollinear Bcoplanar Cboth collinear and coplanar DNone of the above

Show answer

EnglishTGT 2005

Q248.If (((()))) A B B + ⊥ + ⊥ and (((()))) A 2B A, + ⊥ + ⊥ then:

AA 2B = B2 = A B C2A B = DA B =

Show answer

EnglishTGT 2005

Q249.Given two vectors a 2i 3j 6k = − + = − + = − + = − + and b 2i 2j k = − + − = − + − = − + − = − + − and Projection of vector a on vector b λ = Projection of vector b on vector a then what will be the value of λ:

A3/7 B7/3 C3 D7

Show answer

EnglishTGT 2005

Q250.If, a i 2j 3k = − − = − − = − − = − − b i 3j 2k, = + − = + − = + − = + − c 2i j k = + − = + − = + − = + − the what will be the value of (((()))) a. b c × ×:

A-20 B20 C30 DNone of these

Show answer

EnglishTGT 2005

Q251.If pi+3j+4k and qi 5k + + are two vectors, where p,q 0 ≥ are two sealars, then the lengths of both vectors are equal to:

Afor all values of (p, q) Bfor finite value of (p, q) Cfor infinits values of (p, q) DNot for any value of (p, q)

Show answer

EnglishTGT 2005

Q252.If OA i 3j 2k = + − = + − = + − = + −, OB 3i j 2k = + − = + − = + − = + − then what will be the OC which bisects AOB ∠ ∠:

Ai-j-k Bi+j+k C-i+j-k DNone of these

Show answer

EnglishTGT 2005

Q253.If teh angle between the vectors a and b is b, then what will be he angle between the vectors 2a and 3b:

A3/π B2/π C6/π DNone of these

Show answer

EnglishTGT 2004

Q254.If a b b c 0 × = × ≠ × = × ≠ × = × ≠ × = × ≠, then correct relation for a suitable scalar K is:

Aa c kb − = Ba c kb + = Ca b kc + = Db c ka + =

Show answer

EnglishTGT 2004

Q255.If a b 1 =, and a b 1 × = × =, then:

Aa is perpendicular to b Ba is paralled to b Ca. b = 1 Da and b are in opposite direction

Show answer

EnglishTGT 2004

Q256.A vector perpendicular to both the vectors ˆ ˆ ˆ A = 4i - j+3k and ˆ ˆ ˆ B = 3i + j-k is?

Aˆ ˆ ˆ/-2i -13j+ 7k Bˆ ˆ ˆ/2i -13j- 7k Cˆ ˆ ˆ/2i +13j- 7k Dˆ ˆ ˆ/2i -13j+ 7k

Show answer

EnglishTGT 2004

Q257.At what value of x in the vectors ˆ ˆ ˆ ˆ ˆ i + xj + k, j + xk, and ˆ ˆ xi + j. x > 0 the volume of the rectangular parallelogram formed by this vector will be minimum –

A–3 B3 C1/3 D2

Show answer

EnglishTGT 2004

Q258.If the vectors α and γ are perpendicular to each orther then (((()))) α× β×γ α× β×γ α× β×γ α× β×γ and (((()))) ((()) 0 α×β ×γ β ≠ α×β ×γ β ≠ α×β ×γ β ≠ α×β ×γ β ≠ are

AParallel to each other BPerpendicular to each other Cnon coplanar DNull vector

Show answer

EnglishTGT 2004

Q259.If ˆ ˆ ˆ a i j k a.b 1 = + + ⇒ = + + ⇒ = + + ⇒ = + + ⇒ = and ˆ ˆ a b j k × = − × = − × = − × = −, then the vector b is

Aˆ ˆ ˆ/i - j+ k Bˆ ˆ/2j- k Cî Dˆ/2i

Show answer

EnglishTGT 2004

Q260.Let a, b, c be distinct non-negative numbers. If the vectors () () ˆ ˆ ˆ ˆ ˆ, i k ai +aj+ck + and () ˆ ˆ ˆ ci +cj+bk lie in a plane then c is

AArithmatic mean of a and b BGeomtric mean between a and b CHarmonic mean between a and b DEqual to zero

Show answer