Physical independence of force is a consequence of
1) third law of motion 2) second law of motion 3) first law of motion 4) All of the above... View Article
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A man of weight mg is moving up in a rocket with an acceleration of 4g. The apparent weight of the man in the rocket is
1) zero 2) 4 mg 3) 5 mg 4) mg Answer: 2) 5 mg Solution: Apparent weight = m(g + 4g)... View Article
An object of mass 5 kg is attached to the hook of a spring balance and the balance is suspended vertically from the roof of a lift. The reading on the spring balance when the lift is going up with an acceleration of 0.25 ms-2 is taken, (take, g = 10 ms-2)
1) 51.25 N 2) 48.75 N 3) 52.75 N 4) 47.25 N 5) 55 N Answer: 1) 51.25 N Solution: When... View Article
A body of mass 4 kg is accelerated up by a constant force, travels a distance of 5 m in the first second and a distance of 2 m in the third second. The force acting on the body is
1) 2 N 2) 4 N 3) 6 N 4) 8 N Answer: 3) 6 N Solution: Displacement in the nth... View Article
A person is sitting in a lift accelerating upwards. Measured weight of person will be
1) less than actual weight 2) equal to actual weight 3) more than actual weight 4) None of the above... View Article
A wire, which passes through the hole in a small bead, is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from A to B, the force it applies to the wire is
1) always radially outwards 2) always radially inwards 3) radially outwards initially and radially inwards later 4) radially inwards initially... View Article
If ∆ABC is a right-angled triangle with sides a,b and c and smallest angle θ. If 1/a, 1/b and 1/c are also the sides of the right-angle triangle then find sin θ.
a. √((3-√5)/2) b. (3-√5)/2 c. √((3+√5)/2) d. (3+√5)/2 Solution: Answer: a Let a>b>c sin θ = c/a 1/a < 1/b... View Article
Two circles pass through (-1, 4) and their centres lie on x2+y2+2x+4y = 4. If r1 and r2 are maximum and minimum radii and r1/r2 = a+b√2, then the value of a+b is
Answer: 3 Solution: Given circle (x+1)2+(y+2)2 = 32 Any point on the circle is (3 cos θ – 1,3 sin... View Article
If (α, β) is the point on y2 = 6x, that is closest to (3, 3/2) then find 2(α+β)
a. 6 b. 9 c. 7 d. 5 Solution: Answer: (b) Equation of normal at (α, β) is y-β =... View Article
The value of tan (2 tan-1 (3/5) + sin-1(5/13)) is:
a. 220/21 b. 110/21 c. 55/21 d. 20/11 Solution: Answer: (a) tan (tan-1 (6/5)/(1-(9/5)) + tan-1 (5/12)) = tan (tan-1... View Article
In a ∆ABC, if [latex]left | overrightarrow{AB} right |=7[/latex], [latex]left | overrightarrow{BC} right |=5[/latex], and [latex]left | overrightarrow{CA} right |=3[/latex]. If the projection of [latex]overrightarrow{BC}[/latex] on [latex]overrightarrow{CA}[/latex] is n/2, then the value of n is
Answer: 5/2 \(\begin{array}{l}\left | \overrightarrow{AB} \right |=7\end{array} \) \(\begin{array}{l}\left | \overrightarrow{BC} \right |=5\end{array} \) \(\begin{array}{l}\left | \overrightarrow{CA} \right |=3\end{array} \)... View Article
If element of matrix A = [aij](3×3) where [latex]A = \left\{\begin{matrix} (-1)^{j-i} &i<j \\ 2& i=j\\ (-1)^{i+j}& i>j \end{matrix}\right.[/latex], then the value of |3 adj(2A-1)| is:
a. 72 b. 36 c. 108 d. 48 Solution: Answer: (c) A = \(\begin{array}{l}\begin{bmatrix} 2 & -1 & 1\\ -1&... View Article
If A = [latex]\begin{bmatrix} 1 & 0\\ 0& 1 \end{bmatrix}[/latex]1[latex] and B = \sum_{r=1}^{2021}A^{r}[/latex] then value of |B| is
a. 2021 b. 20212 c. -2021 d. 0 Solution: Answer: (b) A = I, B= I+I+I+….,2021 times \(\begin{array}{l}B=2021\begin{bmatrix} 1 &... View Article
Given below are three conditions:A: If 2+4 = 7, then 3+4 = 8 and B: if 3+5 = 8, then earth is flat and C: if A and B are true, then 5+4 = 11. Choose the correct option.
a. A is true, B and C are false b. B is true, A and C are false c. C... View Article
If [latex]g(t)=\begin{Bmatrix} max(t^{3}-6t^{2}+9t-3,0), & t \; belongs\: to\: [0,3] \\ 4-t & t \; belongs\: to\:(3,4) \end{Bmatrix}[/latex] then the number of points at which g(t) is non differentiable is:
a. 1 b. 3 c. 2 d. 4 Solution: Answer: (b) y = t3– 6t2 + 9t – 3 y’... View Article
If f(x) = (5x+3)/(6x+a) and f(f(x) = x then the value of a is:
a. -5 b. 5 c. 6 d. -6 Solution: Answer: (a) f(f(x) = (5f(x)+3)/(6f(x)+a) = x ⇒ 5f(x)+3 = 6xf(x)+ax... View Article
If P(bar(A)cap B)+P(Acap bar(B))= 1-k and P(bar(A)cap C)+P(Acap bar(C))= 1-2k and P(bar(B)cap C)+P( bar(C)cap B)= 1-k and P(A∩B∩C) = k2, k ∈(0, 1)
Question: If \(\begin{array}{l}P(\bar{A}\cap B)+P(A\cap \bar{B})= 1-k\end{array} \), \(\begin{array}{l}P(\bar{A}\cap C)+P(A\cap \bar{C})= 1-2k\end{array} \), \(\begin{array}{l}P(\bar{B}\cap C)+P( \bar{C}\cap B)= 1-k\end{array} \) P(A∩B∩C) =... View Article
If x = ay-1 = z-2, and x = 3y-2 = bz-2 lie in same plane, then the value of a, b is
a. a = 2,b = 3 b. a = 1, b = 1 c. b = 1, a ∈ R-{0}... View Article
If Re [(1+cos θ + 2i sin θ)] = 4, then the value of θ is
a. π/2 b. π/3 c. -π/2 d. π Solution: Answer: (d) [1/(1 + cos2θ + 2i sin θ)] ×(1+cos θ... View Article
Sum of 21 terms of series [latex]log_{9^{frac{1}{2}}}x + log_{9^{frac{1}{3}}}x + log_{9^{frac{1}{4}}}x……….[/latex] is 252, then the value of x is:
a. 7 b. 243 c. 9 d. 81 Solution: Answer: (c) 2 log9 x + 3 log9 x + 4... View Article
