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Let a, b, c be such that b(a+c) ≠ 0. If|[ a a+1 a-1; -b b+1 b-1; c c-1 c+1 ]|+|[ a+1
4:13
Let a, b, c be such that b(a+c) ≠ 0. If|[ a a+1 a-1; -b b+1 b-1; c c-1 c+1 ]|+|[ a+1
Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that
2:20
Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that
If D=| 1 1 1, 1 1+x 1, 1 1 1+x| for x & y is not equal to zero then D is
1:06
If D=| 1 1 1, 1 1+x 1, 1 1 1+x| for x & y is not equal to zero then D is
Let A =[5,5α,α,0,α,5α,0,0,5] , if |A^2| = 25 then |α| equals-
1:20
Let A =[5,5α,α,0,α,5α,0,0,5] , if |A^2| = 25 then |α| equals-
The system of equations αx + y + z = α – 1; x + αy + z = α – 1; x + y + α z = α – 1 has no
1:56
The system of equations αx + y + z = α – 1; x + αy + z = α – 1; x + y + α z = α – 1 has no
If a^2 + b^2 + c^2 = –2 and f(x)= |1+a^2x, (1+b^2)x, (1+c^2)x----(1+a^2)x, 1+b^2x, (1+c^2)x--(1+a^2)
3:24
If a^2 + b^2 + c^2 = –2 and f(x)= |1+a^2x, (1+b^2)x, (1+c^2)x----(1+a^2)x, 1+b^2x, (1+c^2)x--(1+a^2)
If a1, a2,.......an, an+1,...... are in GP and ai is greater than 0 for every i, then
1:58
If a1, a2,.......an, an+1,...... are in GP and ai is greater than 0 for every i, then
If |a a² 1+a³ , b b² 1+b³ , c c² 1+c³| =0 & vectors (1,a,a²), (1,b,b²), (1,c,c²) are non-coplanar
3:24
If |a a² 1+a³ , b b² 1+b³ , c c² 1+c³| =0 & vectors (1,a,a²), (1,b,b²), (1,c,c²) are non-coplanar
If 1, w, w^2 are cube roots of unity and n is not equal to 3p, p belongs to Z, then |{1,w^n, w^2n
1:43
If 1, w, w^2 are cube roots of unity and n is not equal to 3p, p belongs to Z, then |{1,w^n, w^2n
If a, b, c are pth, qth and rth terms of a GP, and all are positive then |{:(loga,p,1),(logb,q,
3:48
If a, b, c are pth, qth and rth terms of a GP, and all are positive then |{:(loga,p,1),(logb,q,
In a game two players A and B take turns in throwing a pair of fair dice starting with player A and
5:12
In a game two players A and B take turns in throwing a pair of fair dice starting with player A and
Let E^c denote the complement of an event E. Let E1, E2 and E3 be any pairwise, independent events
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Let E^c denote the complement of an event E. Let E1, E2 and E3 be any pairwise, independent events
The probability of selecting integers a∈[- 5, 30] such that x^2 + 2(a + 4)x - 5a + 64 greater than 0
2:47
The probability of selecting integers a∈[- 5, 30] such that x^2 + 2(a + 4)x - 5a + 64 greater than 0
If α, β≠ 0, and f(n) = α^n + β^n and 3 1 + f(1) 1+f(2) 1 + f(1) 1 + f(2) 1 + f(3) 1 + f(2) 1
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If α, β≠ 0, and f(n) = α^n + β^n and 3 1 + f(1) 1+f(2) 1 + f(1) 1 + f(2) 1 + f(3) 1 + f(2) 1
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The
2:13
Words with or without meaning are to be formed using all the letters of the word EXAMINATION. The
The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If
4:58
The probabilities of three events A, B and C are given by P(A) = 0.6, P(B) = 0.4 and P(C) = 0.5. If
Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition),
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Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition),
Two families with three members each and one family with four members are to be seated in a row. In
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Two families with three members each and one family with four members are to be seated in a row. In
In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent
3:51
In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent
Four fair dice are thrown independently 27 times. Then the expected number of times, atleast two dic
3:33
Four fair dice are thrown independently 27 times. Then the expected number of times, atleast two dic
The value of [3 + 1/(4+1/(3+1/(4+1/(3 +....∞))))] is equal to
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The value of [3 + 1/(4+1/(3+1/(4+1/(3 +....∞))))] is equal to
The number of solutions of the equation log_4(x - 1) = log_2(x - 3) is
1:41
The number of solutions of the equation log_4(x - 1) = log_2(x - 3) is
Let α and β be two real numbers such that α + β = 1 and αβ = -1. Let p_n = (α)^n + (β)^n, p_(n - 1)
3:11
Let α and β be two real numbers such that α + β = 1 and αβ = -1. Let p_n = (α)^n + (β)^n, p_(n - 1)
Let α and ß be the roots of equation x^2-6x-2=0. If a_n=α^n - ß^n, for n≥1, then the value of
2:51
Let α and ß be the roots of equation x^2-6x-2=0. If a_n=α^n - ß^n, for n≥1, then the value of
If α, β ∈ R are such that 1-2i (here i^2 = - 1 ) is a root of z^2 + α z + β = 0 then (α – β) is equ
2:12
If α, β ∈ R are such that 1-2i (here i^2 = - 1 ) is a root of z^2 + α z + β = 0 then (α – β) is equ
The integer 'k', for which the inequality x^2-2(3k-1)x + 8k^2-7 grater than 0 is valid for every x
2:18
The integer 'k', for which the inequality x^2-2(3k-1)x + 8k^2-7 grater than 0 is valid for every x
Let p and q be two positive numbers such that p + q = 2 and p ^ 4 + q ^ 4 = 272 Then p and q are roo
4:19
Let p and q be two positive numbers such that p + q = 2 and p ^ 4 + q ^ 4 = 272 Then p and q are roo
The number of the real roots of the equation (x + 1)² + |x − 5| = 27/4 is
4:06
The number of the real roots of the equation (x + 1)² + |x − 5| = 27/4 is
cosec18° is a root of the equation : (1) x ^ 2 + 2x - 4 = 0 (2) 4x ^ 2 + 2x - 1 = 0 (3) x ^ 2 -
1:03
cosec18° is a root of the equation : (1) x ^ 2 + 2x - 4 = 0 (2) 4x ^ 2 + 2x - 1 = 0 (3) x ^ 2 -
The set of all values of k is greater than –1, for which the equation (3x^2 + 4x + 3)^2 – (k +1) (3x
5:13
The set of all values of k is greater than –1, for which the equation (3x^2 + 4x + 3)^2 – (k +1) (3x