If the time period of a two meter long simple pendulum is 2 s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:
a. 2π2 ms–2 b. 16 m/s2 c. 9.8 ms–2 d. π2 ms–2 Answer: (a) T = 2π√(l/g) T2 = 4π2l/g... View Article
Latest Posts
The pitch of the screw gauge is 1 mm and there are 100 divisions on the circular scale. When nothing is put in between the jaws, the zero of the circular scale lines 8 divisions below the reference line. When a wire is placed between the jaws, the first linear scale division is clearly visible while 72nd division on circular scale coincides with the reference line. The radius of the wire is
a. 1.64 mm b. 1.80 mm c. 0.82 mm d. 0.90 mm Answer: (c) Least count. = pitch/no. of div.... View Article
Match List-I with List-II:
Match List-I with List-II: List-I List-II (a)h (Planck’s constant) (i) [MLT–1] (b)E (Kinetic energy) (ii) [ML2T–1] (c)V (Electric potential)... View Article
Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half-life of X is half of the half-life of Y. After three half-lives of Y, numbers of nuclei of both are equal. The ratio N1/N2 will be equal to:
Two radioactive substances X and Y originally have N1 and N2 nuclei respectively. Half-life of X is half of the half-life of... View Article
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: When a rod lying freely is heated, no thermal stress is developed in it. Reason R: On heating, the length of the rod increases In the light of the above statements, choose the correct answer from the options given below:
a. A is true but R is false b. Both A and R are true and R is the correct... View Article
A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic field. The ratio of magnetic forces acting on them is _______ and their speeds are in the ratio______.
A proton, a deuteron and an α particle are moving with the same momentum in a uniform magnetic field. The... View Article
An engine of a train, moving with uniform acceleration, passes the signal post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is:
a. √(v2 – u2)/2 b. (v – u)/2 c. √(v2 + u2)/2 d. (u + v)/2 Answer: (c) a =... View Article
Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of TB – TA:
Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of... View Article
The current (i) at time t = 0 and t = ∞ respectively for the given circuit is:
The current (i) at time t = 0 and t = ∞ respectively for the given circuit is: a.... View Article
NISHTHA Scheme
The National Initiative for School Heads’ and Teachers’ Holistic Advancement (NISHTHA) is a capacity building programme for “Improving Quality of... View Article
21 June 2021: PIB Summary & Analysis
June 21st, 2021, PIB:- Download PDF Here TABLE OF CONTENTS 1. International Yoga Day 2. Food security (Assistance to State... View Article
If the Boolean expression is a tautology
If the Boolean expression (p ∧ q) ⍟ (p ⊗ q) is a tautology, then ⍟ and ⊗ are respectively... View Article
If [latex]\vec{a}=\alpha i+\beta j+3k,\vec{b}=-\beta i-\alpha j-k \text \ and \ \vec{c}=i-2j-k,[/latex] such that[latex]\vec{a}.\vec{b}=1[/latex] and [latex]\vec{b}.\vec{c}=-3[/latex], then [latex]\frac{1}{3}((\vec{a}\times\vec{b}).\vec{c})=[/latex] is equal to
Answer: 2 \(\begin{array}{l}\\\vec{a}=(\alpha ,\beta, 3),\vec{b}=(-\beta,-\alpha,-1),\vec{c}=(1,-2,-1)\\ \vec{a}.\vec{b}=1\Rightarrow (-\alpha \beta -\alpha \beta -3)=1\\ -2\alpha \beta =4\\ \alpha \beta =-2\\ \vec{b}.\vec{c}=-3\Rightarrow (-\beta +2\alpha+1)=-3\\... View Article
The maximum value of z in the following equation
The maximum value of z in the following equation z = 6xy + y2, where 3x + 4y ≤ 100... View Article
If the function f (x) = [cos (sinx) – cosx] / x4 is continuous at each point in its domain and f (0) = 1 / k, then k is
Answer: 6 (1 / k) = limx→0 [{2 sin (sinx + x) / 2} sin {x – sinx} / 2]... View Article
If f (x) = sin [cos-1 (1 – 22x) / (1 + 22x)] and its first derivative with respect to x is (- b / a) loge 2 when x = 1, where a and b are integers, then the minimum value of |a2 – b2| is
Answer: 481 cos-1 [1 – 4x] / [1 + 4x] Let 2x = t > 0 cos-1 [(1 – t2)... View Article
If [ . ] represents the greatest integer function, then the value of |∫0√π/2 [[x2] – cosx] dx| is
Answer: 1 ∫0√π/2 [[x2] – cosx] dx = ∫01 [- cosx] dx + ∫1√π/2 [1 – cosx] dx = ∫01... View Article
If (2021)3762 is divided by 17, then the remainder is
Answer: 4 (2021)3762 = (2023 – 2)3762 = multiple of 17 + 23762 = 17λ + 22 (24)940 = 17λ... View Article
The minimum distance between any two points
The minimum distance between any two points P1 and P2 while considering point P1 on one circle and point P2... View Article
If [latex]A=\begin{bmatrix} 2 &3 \\ 0&-1 \end{bmatrix}[/latex], then the value of det (A4) + det (A10 – Adj (2A))10) is equal to
Answer: 16 \(\begin{array}{l}\\|A|=-2\\ |A|^{4}=16\\A^{10}=\begin{bmatrix} 2^{10} & 2^{10}-1\\ 0&1 \end{bmatrix}=\begin{bmatrix} 1024 &1023 \\ 0&1 \end{bmatrix}\\ 2A=\begin{bmatrix} 4 &6 \\ 0&-2 \end{bmatrix}\\... View Article
