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The product of the roots of the equation 9x²-18|x|+5 = 0 is

a) 25/81 b) 5/9 c) 5/27 d) 25/9 Solution: Let |x| = t 9t2-18t +5 = 0 9t2 -15t -3t+5 = 0 (3t -5)(3t-1) = 0 |x| = 5/3, 1/3 ⇒ x =... View Article

If the point P on the curve, 4x²+5y² = 20 is farthest from the point Q(0, -4), then PQ² is equal to:

a) 48 b) 29 c) 21 d) 36 Solution: Given ellipse is (x2/5)+(y2/4) = 1 Let point P is (√5 cos θ, 2 sin θ) (PQ)2 = 5cos2... View Article

Let λ∈R. the system of linear equations

Let λ∈R. the system of linear equations 2x1-4x2+λx3 = 1 x1-6x2+x3 = 2 λx1-10x2+4x3 = 3 is inconsistent for: a)... View Article

If the minimum and the maximum values of the function f: [π/4, π/2] → R defined by f(θ) = [latex]\begin{vmatrix} -\sin ^{2}\theta & -1-\sin ^{2}\theta & 1\\ -\cos ^{2}\theta &-1- \cos ^{2}\theta & 1\\ 12 & 10 & -2 \end{vmatrix}[/latex] are m and M respectively, then the ordered pair (m,M) is equal to :

a) (0,4) b) (-4,0) c) (-4,4) d) (0,2√2) Solution: f(θ) = C1 → C1-C2 C3 → C3+C2 = C2 → C2-C3 = =... View Article

If the common tangent to the parabolas, y² = 4x and x² = 4y also touches the circle, x²+y² = c², then c is equal to:

a) 1/2 b) 1/4 c) 1/√2 d) 1/2√2 Solution: y = mx+1/m x2 = 4(mx+1/m) x2 -4mx-4/m = 0 D = 0 16m2+16/m = 0 16(m3+1)/m = 0 m =... View Article

If 3^{2 sin2α-1},14 and 3^{4-2 sin2α} are the first three terms of an A.P. for some α , then the sixth term of this A.P. is

a) 65 b) 81 c) 78 d) 66 Solution: 28 = 32sin2α-1+34-2 sin2α 28 = 9sin2α/3 + 81/9sin2α Let 9sin2α = t 28 =... View Article

If 2¹⁰+2⁹×3¹+2⁸×3²+…..+2×3⁹+3¹⁰= S-2¹¹, then S is equal to

a) 311 b) (311/2)+210 c) 2×311 d) 311-212 Solution: Let S’ = 210+29×31+ 28×32+-----+2×39+310 ..(i)... View Article

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2,4,10,12,14, then the absolute difference of the remaining two observations is

a) 1 b) 4 c) 3 d) 2 Solution: Var(x) = 16 = (x12+ x22+ x42+ x52+ x62+ x72)/7 -64 80×7 = x12+ x22+ x32+…+ x72 Now, x62+ x72... View Article

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

a) 63 b) 54 c) 38 d) 36 Solution: C → Coffee and T → Tea n(C) = 73, n(T) = 65 n(coffee) = 73/100 n(tea) = 65/100 n(T∩C) =... View Article

If the volume of a parallelopiped, whose coterminuous edges are given by the vectors [latex]\vec{a}=\hat{i}+\hat{j}+n\hat{k}[/latex], [latex]\vec{b}=2\hat{i}+4\hat{j}-n\hat{k}[/latex], and [latex]\vec{c}=\hat{i}+n\hat{j}+3\hat{k}[/latex] (n [latex]\geq[/latex] 0), is 158 cu. units, then: a) [latex]\vec{a}.\vec{c}=17[/latex]

a) b) c) n = 9 d) n = 7 Solution: = 158 (12+n2)-(6+n)+n(2n-4) = 158 3n2-5n+6-158 = 0 3n2-5n-152 = 0 3n2-24n+19n-152 = 0... View Article

A galaxy is moving away from the earth at a speed of 286 km/s.

A galaxy is moving away from the earth at a speed of 286 km/s. The shift in the wavelength of a redline at 630 nm is X × 10-10 m. The value... View Article

A TV transmission tower antenna is at a height of 20 m.

A TV transmission tower antenna is at a height of 20 m. Suppose that the receiving antenna is at. (i) Ground level (ii) a height of 5 m The... View Article

An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m

An infinite number of point charges, each carrying 1 μC charge, are placed along the y-axis at y = 1 m, 2 m, 4 m, 8 m... View Article

The projectile motion of a particle of mass 5 g is shown in the figure.

The projectile motion of a particle of mass 5 g is shown in the figure. The initial velocity of the particle is 5√2 ms-1 and the air... View Article

The radius of a sphere is measured to be (7.50 ± 0.85) cm. Suppose the percentage error in its volume is x. The value of x, to the nearest integer x, is

Answer: (34) =34%... View Article

The typical output characteristics curve for a transistor working in the common emitter configuration is shown in the figure

The estimated current gain from the figure is ………….. Answer: (200) For common emitter configuration... View Article

Consider a water tank as shown in the figure.

Consider a water tank as shown in the figure. It's cross-sectional area is 0.4 m2. The tank has an opening B near the bottom whose... View Article

Consider a 72 cm long wire AB as shown in the figure.

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer... View Article

A ball of mass 4 kg, moving with a velocity of 10 ms^-1, collides with a spring of length 8 m and force constant 100 Nm^-1.

A ball of mass 4 kg, moving with a velocity of 10 ms-1, collides with a spring of length 8 m and force constant 100 Nm-1. The length of the... View Article

Two wires of same length and thickness having specific resistances 6 Ω cm and 3 Ω cm respectively are connected in parallel. The effective resistivity is ρ Ω cm. The value of ρ, to the nearest integer, is ___

Answer: (4) In parallel, ⇒ ρ = 2 x 2 = 4... View Article