The two femurs each of cross-sectional area \(10 \ \text {cm}^2\) support the upper part of a human body of mass \(40\ \text {kg}\). The average pressure sustained by the femurs is (Take \(\text g = 10 \ \text {m s}^{-2}\) )
(a) \(2 \times 10^3 \ \text {N m}^{-2 }\)
(b) \(2 \times 10^4\ \text {N m}^{-2 }\)
(c) \(2 \times 10^5\ \text {N m}^{-2 }\)
(d) \(2 \times 10^6\ \text {N m}^{-2 }\)
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The number of discontinuous functions \(y(x)\) on \([-2,2]\) satisfying \(x^2+y^2=4\) is
(a) \(0\)
(b) \(1\)
(c) \(2\)
(d) \(\gt 2\)
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The remainder obtained when \((1!)^2+(2!)^2+(3!)^2+.....+(100!)^2\) is divided by \(10^2\) is
a.14
b.17
c. 28
d. 27
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If, for all real values of \(\theta;a=\sin^2\theta+\cos^4\theta\) then
(a) \(a\geq\frac{3}{4}\) (b) \(a\leq\frac{3}{4}\)
(c) a = 1 (d) \(a=\frac{1}{2}\)
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If \(B_E\) represents equatorial magnetic field and \(B_A\) represents axial magnetic field due to a bar magnet.
Which of the following relationships between \(B_E\) and \(B_A\) is correct?
(a) \(B_E=2B_A\)
(b) \(B_A=2B_E\)
(c) \(B_E=4B_A\)
(d) \(B_A=4B_E\)
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If \(9\times 3=36;11\times 7=81 \) then \(5\times 13=?\)
(a) 65
(b) 66
(c) 81
(d) 51
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If a natural number \('\alpha'\) is divided by 7, the remainder is 5. If a natural number \('\beta'\) is divided by 7 , the remainder is 3. The remainder is 'r' if \(\alpha+\beta\) is divided by 7. Find the value of \(\frac{3r+5}{4}.\)
(a) 2 (b) 7
(c) 8 (d) 11
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Find the principal values of \(\cos^{-1}\Bigl(\frac{1}{2}\Bigr)\)
(a) \(-\frac{\pi}{3}\)
(b) \(\frac{\pi}{3}\)
(c) \(\frac{\pi}{2}\)
(d) \(\frac{2\pi}{3}\)
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If \(|a|=8,|b|=3\) and \(|a\times b|=12,\) then find the angle between a and b.
a. \(\frac{\pi}{3}\)
b. \(\frac{\pi}{6}\)
c. \(\frac{\pi}{4}\)
d. None of these
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Two masses \(m_1\) and \(m_2\) connected by a spring of spring constant k rest on a frictionless surface. If the masses are pulled apart and let go, the time period of oscillation is
(a) \(T=2\pi \sqrt{\frac{1}{k}\Big(\frac{m_1m_2}{m_1+m_2}\Big)}\)
(b) \(T=2\pi \sqrt{k\Big(\frac{m_1+m_2}{m_1m_2}\Big)}\)
(c) \(T=2\pi \sqrt{\frac{m_1}{k}}\)
(d) \(T=2\pi \sqrt{\frac{m_2}{k}}\)
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The flux linked with a coil at any instant t given by \(\phi =10t^2-50 t+250\) then, induced emf at \(t=3 s\) is
(a) -10 V
(b) 10 V
(c) 190 V
(d) -190 V
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The flux linked with a coil at any instant t given by \(\phi =10t^2-50 t+250\) then, induced emf at \(t=3 s\) is
(a) -10 V
(b) 10 V
(c) 190 V
(d) -190 V
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The number of commutative binary operations that can be defined on a set of \(2\) elements is
(a) \(8\)
(b) \(6\)
(c) \(4\)
(d) \(2\)
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If \(\log _{10}a+\log _{10}b=\log_{10}(a+b)\) then
(a) \(a=\frac{b^2}{1-b}\)
(b) \(a=\frac{b}{1-b}\)
(c) \(a=\frac{b}{b-1}\)
(d) \(a=\frac{b}{a+b}\)
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The wrong unit conversion among the following is
(a) \(1\) angstrom \(= 10^{-10} \text m \)
(b) \(1\) fermi \(= 10^{-15 }\text m \)
(c) \(1\) light year \(= 9.46 \times 10^{15}\text m \)
(d) \(1\) astronomical unit \(= 1.496 \times 10^{-11} \text m\)
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A railway engine is travelling along a circular railway track of radius 1500 metres with a speed of 66 km/hr. Find the angle turned by the engine in 10 seconds.
(a) \(10^\circ\)
(b) \(7^\circ\)
(c) \(11^\circ\)
(d) \(8^\circ\)
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A railway engine is travelling along a circular railway track of radius 1500 metres with a speed of 66 km/hr. Find the angle turned by the engine in 10 seconds.
(a) \(10^\circ\)
(b) \(7^\circ\)
(c) \(11^\circ\)
(d) \(8^\circ\)
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The minimum distance between a point on the curve \(y=e^x\) and a point on the curve \(y=\log _ex\) is
(a) \(\frac{1}{\sqrt{2}}\)
(b) \(\sqrt{2}\)
(c) \(\sqrt{3}\)
(d) \(2\sqrt{2}\)
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Let \(a=\hat{i}+\hat{j}+\hat{k},b=\hat{i}-\hat{j}+\hat{k},a\times b=b+\lambda \ a\ and\ a\cdot c=1,\) then which of the following is true
(a) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=-\frac{1}{3}\)
(b) \([a\ b\ c]=\frac{8}{3}\ and\ \lambda=-\frac{1}{3}\)
(c) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=-\frac{2}{3}\)
(d) \([a\ b\ c]=-\frac{8}{3}\ and\ \lambda=\frac{2}{3}\)
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According to Newton's law of cooling, the rate of cooling of a body is proportional to \((\triangle \theta)^n\), where \(\triangle \theta\) is the difference of the temperature of the body and the surroundings and n is equal to ____
(a) 2 (b) 3
(c) 4 (d) 1
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If \(a>0\) and discriminant of \(ax^2+2bx+c\) is -ve then
\(\begin{vmatrix}
a & b & ax+b\\
b & c & bx+c\\
ax+b &bx+c&0
\end{vmatrix}\) is ______
(a) +ve (b) \((ac-b^2) ( a x^2+2bx+c)\)
(c) -ve (d) 0
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In the real number system, the equation \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=1\) has
(a) no solution
(b) exactly two distinct solutions
(c) exactly four distinct solutions
(d) infinitely many solutions
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The angle \(\alpha,\beta,\gamma\) of a triangle satisfy the equation \(2\sin\alpha + 3\cos\beta =3\sqrt 2\) and \(3\sin\beta+2\cos\alpha=1.\) Then, \(\gamma\) equal
(a) \(150^\circ\)
(b) \(120^\circ\)
(c) \(60^\circ\)
(d) \(30^\circ\)
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Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelength \(\lambda_1:\lambda_2\) emitted in the two cases is
(a) 7/5
(b) 27/20
(c) 27/5
(d) 20/7
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The force F acting on a particle of mass m indicated by force-time graph shown below.
The change in momentum of the particle over the time interval from zero to 8 s is
(a) 24 Ns
(b) 20 Ns
(c) 12 Ns
(d) 6 Ns
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Consider the following statements:
I. \(\lim\limits_{n\to\infty}\frac{2^n+(-2)^n}{2^n}\) does not exist
II. \(\lim\limits_{n\to\infty}\frac{3^n+(-3)^n}{4^n}\) does not exist
Then,
(a) I is true and II is false
(b) I is false and II is true
(c) I and II are true
(d) Neither I nor II is true
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In the figure, galvanometer \(G\) gives maximum deflection when
(a) magnet is pushed into the coil
(b) magnet is rotated into the coil
(c) magnet is stationary at the centre of the coil
(d) number of turns in the coil is reduced
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The order of reactivity in nucleophilic substitution reaction is
(a) \(\text {CH}_3\text F\lt\text {CH}_3\text {Cl} \lt\text {CH}_3\text I\lt\text {CH}_3\text {Br} \) (b) \(\text {CH}_3\text F\lt\text {CH}_3\text {Cl} \lt\text {CH}_3\text {Br}\lt\text {CH}_3\text {I} \)
(c) \(\text {CH}_3\text F\lt\text {CH}_3\text {Br} \lt\text {CH}_3\text {Cl}\lt\text {CH}_3\text {I} \) (d) \(\text {CH}_3\text I\lt\text {CH}_3\text {Br} \lt\text {CH}_3\text {Cl}\lt\text {CH}_3\text {F} \)
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A circular loop of radius \(R\) carrying a current \(l\) is placed in a uniform magnetic field \(B\) perpendicular to the loop. The force on the loop is
(a) \(2\pi RI B\)
(b) \(2\pi R I^2 B^3\)
(c) \(\pi R^2IB\)
(d) zero
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What are the zeroes of \(f(x)=8x^3-2x^2-3x\) ?
(a) \(\{ -\frac 1 2 \:,\frac 3 4\:\}\) (b) \(\{ -\frac 3 4\: ,\frac 1 2\:\}\)
(c) \(\{ -\frac 1 2\: ,\frac 1 2\: ,\frac 3 4\:\}\) (d) \(\{ -\frac 1 2\:,0\:,\frac 3 4\:\}\)
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