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Using screw gauge of pitch 0.1 cm and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as

1) 2.125 cm2) 2.124 cm3) 2.123 cm4) 2.121 cmSolution:Answer. 2 Least count =(0.1/50) =(1/500) = 0.002when we multiply by division no.'s it must... View Article

When a diode is forward biased, it has a voltage drop of 0.5 V. The safe limit of current through the diode is 10 mA. If a battery of emf 1.5 V is used in the circuit, the value of minimum resistance to be connected in series with the diode so that the current does not exceed the safe limit is:

1) 300 Ω2) 200 Ω3) 50 Ω4) 100 ΩSolution:Answer. 4... View Article

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

1) 122) 33) 94) 6Solution:Answer. 1... View Article

A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown

A block of mass m = 1 kg slides with velocity v = 6 m/s on a frictionless horizontal surface and collides with a uniform vertical rod and sticks... View Article

Let omega not equal 1 be a cube root of unity Then the minimum of the set a + b ohm + c ohm 22 ; Where, a, b, c distinct non-zero integers equals

Solution:| a + bω + cω2|2= (a + bω + cω2) (a + cω + bω2)= (a2 + b2 + c2 - ab – bc – ca)[because, conjugate of (a + bω + cω2) = (a + cω + bω2)]=... View Article

Find the value of (6Δ)² equals

Three lines are given by Let the lines cut the plane x + y + z 1 at the points A, B and C respectively. If the area of the triangle ABC is Δ... View Article

Let S be the sample space of all 3 × 3 matrices with entries from the set…..

Let S be the sample space of all 3 × 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by E1 = {A ϵ S : det A = 0}... View Article

Let AP (a; d) denote the set of all the terms of an infinite arithmetic progression with first term a and common difference d > 0. If AP(1; 3) ∩ AP (2; 5) ∩ AP (3; 7) = AP (a; d) then a + d equals

Solution:I: 1, 4, 7, 10, 13, 16 ….. 32II: 2, 7, 12, 17, 22, 27, 32, 37, 42, 47, 52III: 3, 10, 17, 24, 31, 38, 45, 5252 <-- a + d --> LCM of... View Article

Let the point B be the reflection of the point A(2, 3) with respect to the line 8x – 6y – 23 = 0. Let _A and _B….

Let the point B be the reflection of the point A(2, 3) with respect to the line 8x – 6y – 23 = 0. Let A and B be circle of radii 2 and 1 with... View Article

If [latex]I = \frac{2}{\pi} \int_{-\pi/4}^{\pi/4} \frac{dx}{(1 + e^{sin\ x})(2-cos 2x)}[/latex] then 27I² equals

Solution:27I2 = 4... View Article

Let L₁ and L₂ denotes the lines….

Let L1 and L2 denotes the lines respectively. If L3 is a line which is perpendicular to both L1 and L2 and cuts both of them, then which of... View Article

In a non-right-angle triangle ΔPQR, let p, q, r denote the lengths of the sides opposite to the angles at P, Q, R respectively

In a non-right-angle triangle ΔPQR, let p, q, r denote the lengths of the sides opposite to the angles at P, Q, R respectively. The median from R... View Article

Let denote a curve y = y(x) which is in the first quadrant and let the point (1, 0) lie on it. Let the tangent to at a point P intersect the y-axis at Y_P. If PY_P has length 1 for each point P on , then which of the following is options is/are correct?

a) d) xy' + √[1-x2] = 0Solution: y - y1 = m(x – x1)yp - y1 = -mx1 => 1 = x12 + m2 x12 1 = x2[1 + (dy/dx)2]Or (dy/dx)2 = 1/x2 – 1dy/dx =... View Article

Let α and β be the roots of x² – x – 1 = 0….

Let α and β be the roots of x2 – x – 1 = 0, with α > β. For all positive integers n, define As, b1 = 1 and bn = an-1 + an+1, n ≥ 2 a1 +... View Article

Which of the following options is/are correct?

Then which of the following options is/are correct?a) f’ has a local maximum at x = 1b) f is ontoc) f is increasing on (-∞, 0)d) f’ is NOT... View Article

Let [latex]M = \begin{bmatrix} 0 &1 & a \\ 1& 2 &3 \\ 3 &b &1 \end{bmatrix}[/latex] and adj M = [latex]\begin{bmatrix} -1 &1 & -1 \\ 8& -6 &2 \\ -5 &3 &-1 \end{bmatrix}[/latex] where a and b are real numbers. Which of the following options is/are correct?

a) a + b = 3b) det(adj M2) = 81c) (adj M)-1 + adj M-1 = -Md) If |M| = -2And a + b = 2(b) |adj M2|= |M2|2 = |M|4 = 16(c) (adj M)-1 + adj M-1 = 2... View Article

There are three bags B₁, B₂ and B₃. The bag B₁ contains 5 red and 5 green balls

There are three bags B1, B2 and B3. The bag B1 contains 5 red and 5 green balls, B2 contains 3 red and 5 green balls, and B3 contains 5 red and... View Article

The area of the region {(x, y) : xy ≤ 8, 1 ≤ y ≤ x²} is

The area of the region {(x, y) : xy ≤ 8, 1 ≤ y ≤ x2} isSolution:{(x, y) : xy ≤ 8, 1 ≤ y ≤ x2}8/x = x2 = 16 loge 2 – 14/3... View Article

Let S be the set of all complex numbers z satisfying |z – 2 + i| ≥ √5. If the complex number z₀ is such that 1/|z₀ – 1| is the maximum of the set [latex]begin{Bmatrix} frac{1}{|z-1|}; z in S end{Bmatrix}[/latex] then the principle argument of [latex]frac{4-z_0 – bar{z_0}}{z_0- bar{z_0} +2i}[/latex]

a) π/4b) -π/2c) 3π/4d) π/2Solution:|z - 2 + i| ≥ √5P is along but at √5 distance from C.... View Article

A line y = mx + 1 intersects the circle (x – 3)² + (y + 2)² = 25 at the points P and Q. If the midpoint of the line segment PQ has x-coordinate -3/5, then which one of the following options is correct?

a) 6 ≤ m < 8b) 2 ≤ m < 4c) 4 ≤ m < 6d) -3 ≤ m < -1Solution:y = mx + 1(x - 3)2 + ((mx +1) + 2)2 = 25=> x2 (1+ m2 ) + 6(m -1) x - 7... View Article