WB JEE 2021
JEE 2021 Previous Year
3 hDuration
200Total Marks
155Questions
3Sections
Instructions
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Paper Structure
Chemistry
Chemistry
Q1.
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The products X and Y which are formed in the following sequence of reactions are respectively.
Q2.
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5.75 mg of sodium vapour is converted to sodium ion. If the ionisation energy of sodium is 490 kJ mol^($$-$$1) and atomic weight is 23 units, the amount of energy needed for this conversion will be
Q3.
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Reaction of silver nitrate solution with phosphorus acid produces
Q4.
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Cyclo [18] carbon is an allotrope of carbon with molecular formula C~18~. It is a ring of 18 carbon atoms, connected by single and triple bonds. The total number of triple bonds present in this cyclocarbon are
Q5.
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A solution of NaNO~3~, when treated with a mixture of Zn dust and 'A' yields ammonia. 'A' can be
Q6.
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A given amount of Fe^(2+) is oxidised by x mol of $$MnO_4^ - $$ in acidic medium. The number of moles of $$C{r_2}O_7^{2 - }$$ required to oxidise the same amount of Fe^(2+) in acidic medium is
Q7.
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N~2~H~4~ and H~2~O~2~ show similarity in
Q8.
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The atomic masses of helium and neon are 4.0 and 20.0 amu respectively. The value of the de-Broglie wavelength of helium gas at $$-$$73$$^\circ$$C is M times the de-Broglie wavelength of neon at 727$$^\circ$$C. The value of M is
Q9.
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A saturated solution of BaSO~4~ at 25$$^\circ$$C is 4 $$\times$$ 10^($$-$$5) M. The solubility of BaSO~4~ in 0.1 M Na~2~SO~4~ at this temperature will be
Q10.
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Solubility products (K~sp~) of the salts of types MX, MX~2~ and M~3~X at temperature T are 4.0 $$\times$$ 10^($$-$$8), 3.2 $$\times$$ 10^($$-$$14) and 2.7 $$\times$$ 10^($$-$$15) respectively. Solubilities (in mol dm^($$-$$3)) of the salts at temperature T are in the order.
Q11.
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Aqueous solution of HNO~3~, KOH, CH~3~COOH and CH~3~COONa of identical concentration are provided. The pair(s) of solutions which form a buffer upon mixing is (are)
Q12.
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Extraction of a metal (M) from its sulphide ore (M~2~S) involves the following chemical reactions
$$2{M_2}S + 3{O_2}\buildrel {Heat} \over
\longrightarrow 2{M_2}O + 2S{O_2} \uparrow $$
$${M_2}S + 2{M_2}O\buildrel {Heat} \over
\longrightarrow 6M + S{O_2} \uparrow $$
The metal (M) may be
Q13.
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The exact order of acidity of the compounds p-nitrophenol, acetic acid, acetylene and ethanol is
Q14.
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The dipeptides which may be obtained from the amino acids glycine, and alanine are
The dipeptides which may be obtained from the amino acids glycine, and alanine are
Q15.
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The H~3~O^(+) ions has the following shape
Q16.
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The equilibrium constant for the reaction
N~2~(g) + O~2~(g) $$\rightleftharpoons$$ 2NO(g) is 4 $$\times$$ 10^($$-$$4) at 2000 K. In presence of a catalyst the equilibrium is attained 10 times faster. Therefore, the equilibrium constant, in presence of the catalyst at 2000 K is
Q17.
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2.5 mL 0.4 M weak monoacidic base (K~b~ = 1 $$\times$$ 10^($$-$$12) at 25$$^\circ$$C) is titrated with 2/15 M HCl in water at 25$$^\circ$$C. The concentration of H^(+) at equivalence point is (K~w~ = 1 $$\times$$ 10^($$-$$14), at 25$$^\circ$$C)
Q18.
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Under the same reaction conditions, initial concentration of 1.386 mol dm^($$-$$3) of a substance becomes half in 40 s and 20 s through first-order and zero-order kinetics respectively. Ratio $$\left( {{{{k_1}} \over {{k_0}}}} \right)$$ of the rate constants for first-order (k~1~) and zero-order (k~0~) of the reactions is
Q19.
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The compounds X and Y are respectively
Q20.
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Among the following chlorides the compounds which will be hydrolysed most easily and most slowly in aqueous NaOH solution are respectively:
1. Methoxymethyl chloride
2. Benzyl chloride
3. Neopentyl chloride
4. Propyl chloride
Q21.
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The mole fraction of a solute in a binary solution is 0.1 at 298 K, molarity of this solution is same as its molality. Density of this solution at 298 K is 2.0 g cm^($$-$$3). The ratio of molecular weights of the solute and the solvent (M~solute~ / M~solvent~) is
Q22.
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For a spontaneous reaction at all temperatures which of the following is correct?
Q23.
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Indicate the products (X) and (Y) in the following reactions
Na~2~S + nS(n = 1 $$-$$ 8) $$\to$$ (X)
Na~2~SO~3~ + S $$\to$$ (Y)
Q24.
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The white precipitate (Y), obtained on passing colorless and odourless gas (X) through an ammoniacal solution of NaCl, losses about 37% of its weight on heating and a white residue (Z) of basic nature is left. Identify (X), (Y) and (Z) from following sets.
Q25.
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Molecular velocities of two gases at the same temperature (T) are u~1~ and u~2~. Their masses are m~1~ and m~2~ respectively. Which of the following expressions is correct at temperature T?
Q26.
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The maximum number of atoms that can be in one plane in the molecule p-nitrobenzonitrile are
Q27.
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Which structure has delocalised $$\pi$$-electrons?
Q28.
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p-nitro-N, N-dimethylaniline cannot be represented by the resonating structures.
Q29.
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When 20 g of naphthoic acid (C~11~H~8~O~2~) is dissolved in 50 g of benzene, a freezing point depression of 2K is observed. The van't Hoff factor (i) is [K~f~ = 1.72 K kg mol^($$-$$1)]
Q30.
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A solution is made by a concentrated solution of Co(NO~3~)~2~ with a concentrated solution of NaNO~2~ is 50% acetic acid. A solution of a salt containing metal M is added to the mixture, when a yellow precipitate is formed. Metal 'M' is
Q31.
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Indicate the number of unpaired electrons in K~3~[Fe(CN)~6~] and K~4~[Fe(CN)~6~].
Q32.
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Which of the following compounds have magnetic moment identical with [Cr(H~2~O)~6~]^(3+) ?
Q33.
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For the reaction $$_7^{14}N(\alpha ,p)\,{}^{17}O$$, 1.16 MeV (Mass equivalent = 0.00124 amu) of energy is absorbed. Mass on the reactant side is 18.00567 amu and proton mass = 1.00782 amu. The atomic mass of $${}^{17}O$$ will be
Q34.
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The relationship between the pair of compounds shown above are respectively
The relationship between the pair of compounds shown above are respectively
Q35.
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The exact order of boiling points of the compounds n-pentane, isopentane, butanone and 1-butanol is
Q36.
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An element crystallises in a body centered cubic lattice. The edge length of the unit cell is 200 pm and the density of the element is 5.0 g cm^($$-$$3). Calculate the number of atoms in 100 g of this element.
Q37.
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The reduction potential of hydrogen half-cell will be negative if
Q38.
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Which of the following solutions will have highest conductivity?
Q39.
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The product(s) in the following sequence of reactions will be
Q40.
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The compounds A and B above are respectively.
The compounds A and B above are respectively.Mathematics
Mathematics
Q1.
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The mean and variance of a binomial distribution are 4 and 2 respectively. Then the probability of exactly two successes is
Q2.
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Let a, b, c be real numbers, each greater than 1, such that $${2 \over 3}{\log _b}a + {3 \over 5}{\log _c}b + {5 \over 2}{\log _a}c = 3$$. If the value of b is 9, then the value of 'a' must be
Q3.
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Consider the real valued function h : {0, 1, 2, ...... 100} $$\to$$ R such that h(0) = 5, h(100) = 20 and satisfying h(p) = $${1 \over 2}$$ {h(p + 1) + h(p $$-$$ 1)} for every p = 1, 2 ..... 99. Then the value of h(1) is
Q4.
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Three unequal positive numbers a, b, c are such that a, b, c are in G.P. while $$\log \left( {{{5c} \over {2a}}} \right),\log \left( {{{7b} \over {5c}}} \right),\log \left( {{{2a} \over {7b}}} \right)$$ are in A.P. Then a, b, c are the lengths of the sides of
Q5.
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The digit in the unit's place of the number 1! + 2! + 3! + .... + 99! is
Q6.
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let $$\alpha$$, $$\beta$$, $$\gamma$$ be three non-zero vectors which are pairwise non-collinear. if $$\alpha$$ + 3$$\beta$$ is collinear with $$\gamma$$ and $$\beta$$ + 2$$\gamma$$ is collinear with $$\alpha$$ then $$\alpha$$ + 3$$\beta$$ + 6$$\gamma$$ is
Q7.
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If a($$\alpha$$ $$\times$$ $$\beta$$) + b($$\beta$$ $$\times$$ $$\gamma$$) + c($$\gamma$$ + $$\alpha$$) = 0, where a, b, c are non-zero scalars, then the vectors $$\alpha$$, $$\beta$$, $$\gamma$$ are
Q8.
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The straight the through the origin which divides the area formed by the curves y = 2x $$-$$ x^(2), y = 0 and x = 1 into two equal halves is
Q9.
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The area bounded by the parabolas $$y = 4{x^2},y = {{{x^2}} \over 9}$$ and the straight line y = 2 is
Q10.
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Four persons A, B, C and D throw and unbiased die, turn by turn, in succession till one gets an even number and win the game. What is the probability that A wins the game if A begins?
Q11.
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Let $$\alpha$$, $$\beta$$ be the roots of the equation x^(2) $$-$$ 6x $$-$$ 2 = 0 with $$\alpha$$ > $$\beta$$. If a~n~ = $$\alpha$$^(n) $$-$$ $$\beta$$^(n) for n $$\ge$$ 1, then the value of $${{{a_{10}} - 2{a_8}} \over {2{a_9}}}$$ is
Q12.
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If $$I = \mathop {\lim }\limits_{x \to 0} sin\left( {{{{e^x} - x - 1 - {{{x^2}} \over 2}} \over {{x^2}}}} \right)$$, then limit
Q13.
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$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt n } \over {\sqrt {{n^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 4)}^3}} }} + {{\sqrt n } \over {\sqrt {{{(n + 8)}^3}} }} + .... + {{\sqrt n } \over {\sqrt {{{[n + 4(n - 1)]}^3}} }}} \right\}$$ is
Q14.
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The $$\mathop {\lim }\limits_{x \to \infty } {\left( {{{3x - 1} \over {3x + 1}}} \right)^{4x}}$$ equals
Q15.
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Let f : D $$\to$$ R where D = [$$-$$0, 1] $$\cup$$ [2, 4] be defined by
$$f(x) = \left\{ {\matrix{
{x,} & {if} & {x \in [0,1]} \cr
{4 - x,} & {if} & {x \in [2,4]} \cr
} } \right.$$ Then,
Q16.
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Let $${S_n} = {\cot ^{ - 1}}2 + {\cot ^{ - 1}}8 + {\cot ^{ - 1}}18 + {\cot ^{ - 1}}32 + ....$$ to n^(th) term. Then $$\mathop {\lim }\limits_{n \to \infty } {S_n}$$ is
Q17.
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Two particles A and B move from rest along a straight line with constant accelerations f and f' respectively. If A takes m sec. more than that of B and describes n units more than that of B in acquiring the same velocity, then
Q18.
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The greatest and least value of $$f(x) = {\tan ^{ - 1}} - {1 \over 2}\,ln \,x\,on\,\left[ {{1 \over {\sqrt 3 }},\sqrt 3 } \right]$$ are
Q19.
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Let f : R $$\to$$ R be such that f(0) = 0 and $$\left| {f'(x)} \right| \le 5$$ for all x. Then f(1) is in
Q20.
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If the tangent at the point P with co-ordinates (h, k) on the curve y^(2) = 2x^(3) is perpendicular to the straight line 4x = 3y, then
Q21.
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$$\left| {\matrix{
x & {3x + 2} & {2x - 1} \cr
{2x - 1} & {4x} & {3x + 1} \cr
{7x - 2} & {17x + 6} & {12x - 1} \cr
} } \right| = 0$$ is true for
Q22.
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Let T and U be the set of all orthogonal matrices of order 3 over R and the set of all non-singular matrices of order 3 over R respectively. Let A = {$$-$$1, 0, 1}, then
Q23.
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Let A and B two non singular skew symmetric matrices such that AB = BA, then A^(2)B^(2)(A^(T)B)^($$-$$1)(AB^($$-$$1))^(T) is equal to
Q24.
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Let $$A = \left( {\matrix{
1 & 0 & 0 \cr
0 & {\cos t} & {\sin t} \cr
0 & { - \sin t} & {\cos t} \cr
} } \right)$$
Let $$\lambda$$~1~, $$\lambda$$~2~, $$\lambda$$~3~ be the roots of $$\det (A - \lambda {I_3}) = 0$$, where I~3~ denotes the identity matrix. If $$\lambda$$~1~ + $$\lambda$$~2~ + $$\lambda$$~3~ = $$\sqrt 2 $$ + 1, then the set of possible values of t, $$-$$ $$\pi$$ $$\ge$$ t < $$\pi$$ is
Q25.
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If M is a 3 $$\times$$ 3 matrix such that (0, 1, 2) M = (1 0 0), (3, 4 5) M = (0, 1, 0), then (6 7 8) M is equal to
Q26.
mcq single
+1 / 0.25
If a~n~ (> 0) be the n^(th) term of a G.P. then
$$\left| {\matrix{
{\log {a_n}} & {\log {a_{n + 1}}} & {\log {a_{n + 2}}} \cr
{\log {a_{n + 3}}} & {\log {a_{n + 4}}} & {\log {a_{n + 5}}} \cr
{\log {a_{n + 6}}} & {\log {a_{n + 7}}} & {\log {a_{n + 8}}} \cr
} } \right|$$ is equal to
Q27.
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+2 / 0.5
The determinant $$\left| {\matrix{
{{a^2} + 10} & {ab} & {ac} \cr
{ab} & {{b^2} + 10} & {bc} \cr
{ac} & {bc} & {{c^2} + 10} \cr
} } \right|$$ is
Q28.
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+2 / 0.5
The plane lx + my = 0 is rotated about its line of intersection with the plane z = 0 through an angle $$\alpha$$. The equation changes to
Q29.
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+1 / 0.25
If from a point P(a, b, c), perpendicular PA and PB are drawn to YZ and ZX-planes respectively, then the equation of the plane OAB is
Q30.
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+1 / 0.25
A line with positive direction cosines passes through the point P(2, $$-$$1, 2) and makes equal angle with co-ordinate axes. The line meets the plane 2x + y + z = 9 at point Q. The length of the line segment PQ equals.
Q31.
mcq multi
+2 / 0
A plane meets the co-ordinate axes t the points A, B, C respectively such a way that the centroid of $$\Delta$$ABC is (1, r, r^(2)) for some real r. If the plane passes through the point (5, 5, $$-$$12) then r =
Q32.
mcq single
+1 / 0.25
The equation 6^(x) + 8^(x) = 10^(x) has
Q33.
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+1 / 0.25
If $$\int {{{\sin 2x} \over {{{(a + b\cos x)}^2}}}dx} = \alpha \left[ {{{\log }_e}\left| {a + b\cos x} \right| + {a \over {a + b\cos x}}} \right] + c$$, then $$\alpha$$ is equal to
Q34.
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+1 / 0.25
From a point (d, 0) three normal are drawn to the parabola y^(2) = x, then
Q35.
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+1 / 0.25
The locus of the vertices of the family of parabolas $$6y = 2{a^3}{x^2} + 3{a^2}x - 12a$$ is
Q36.
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+1 / 0.25
For $$y = {\sin ^{ - 1}}\left\{ {{{5x + 12\sqrt {1 - {x^2}} } \over {13}}} \right\};\left| x \right| \le 1$$, if $$a(1 - {x^2}){y_2} + bx{y_1} = 0$$ then (a, b) =
Q37.
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+2 / 0.5
The coefficient of a^(3)b^(4)c^(5) in the expansion of (bc + ca + ab)^(6) is
Q38.
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The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 is
Q39.
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+1 / 0.25
For x$$\in$$R, x $$\ne$$ $$-$$1, if $${(1 + x)^{2016}} + x{(1 + x)^{2015}} + {x^2}{(1 + x)^{2014}} + ..... + {x^{2016}} = \sum\limits_{i = 0}^{2016} {{a_i}\,.\,{x^i}} $$, then a~17~ is equal to
Q40.
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+1 / 0.25
If a > 0, b > 0 then the maximum area of the parallelogram whose three vertices are O(0, 0), A(a cos$$\theta$$, b sin$$\theta$$) and B(a cos$$\theta$$, $$-$$ b sin$$\theta$$) is
Q41.
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+1 / 0.25
Let A be the fixed point (0, 4) and B be a moving point on X-axis. Let M be the midpoint of AB and let the perpendicular bisector of AB meets the Y-axis at R. The locus of the midpoint P of MR is
Q42.
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+1 / 0.25
A moving line intersects the lines x + y = 0 and x $$-$$ y = 0 at the points A, B respectively such that the area of the triangle with vertices (0, 0), A and B has a constant area C. The locus of the mid-point AB is given by the equation
Q43.
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+1 / 0.25
A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching X-axis, the equation of the reflected ray is
Q44.
mcq single
+2 / 0.5
Let R be the real line. Let the relations S and T or R be defined by
$$S = \{ (x,y):y = x + 1,0 < x < 2\} ,T = \{ (x,y):x - y$$ is an integer}. Then
Q45.
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+1 / 0.25
Let A, B, C be three non-void subsets of set S. Let (A $$\cap$$ C) $$\cup$$ (B $$\cap$$ C') = $$\phi$$ where C' denote the complement of set C in S. Then
Q46.
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Let C denote the set of all complex numbers. Define A = {(z, w) | z, w$$\in$$C and |z| = |w|}, B = {z, w} | z, w$$\in$$C and z^(2) = w^(2)}. Then
Q47.
mcq multi
+2 / 0
If $$\left| {z + i} \right| - \left| {z - 1} \right| = \left| z \right| - 2 = 0$$ for a complex number z, then z is equal to
Q48.
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+1 / 0.25
If |z| = 1 and z $$\ne$$ $$\pm$$ 1, then all the points representing $${z \over {1 - {z^2}}}$$ lie on
Q49.
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+1 / 0.25
The normal to a curve at P(x, y) meets the X-axis at G. If the distance of G from the origin is twice the abscissa of P then the curve is
Q50.
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+1 / 0.25
The locus of the centre of a variable circle which always touches two given circles externally is
Q51.
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+2 / 0
Let f and g be periodic functions with the periods T~1~ and T~2~ respectively. Then f + g is
Q52.
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+1 / 0.25
Consider the functions f~1~(x) = x, f~2~(x) = 2 + log~e~ x, x > 0. The graphs of the functions intersect
Q53.
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+1 / 0.25
Let f : R $$\to$$ R be given by f(x) = | x^(2) $$-$$ 1 |, x$$\in$$R. Then,
Q54.
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+1 / 0.25
f(x) is real valued function such that 2f(x) + 3f($$-$$x) = 15 $$-$$ 4x for all x$$\in$$R. Then f(2) =
Q55.
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+2 / 0.5
Given that f : S $$\to$$ R is said to have a fixed point at c of S if f(c) = c. Let f : [1, $$\infty$$) $$\to$$ R be defined by f(x) = 1 + $$\sqrt x $$. Then
Q56.
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+2 / 0.5
The differential of $$f(x) = {\log _e}(1 + {e^{10x}}) - {\tan ^{ - 1}}({e^{5x}})$$ at x = 0 and for dx = 0.2 is
Q57.
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+1 / 0.25
The differential equation of all the ellipses centred at the origin and have axes as the co-ordinate axes is where $$y^{\prime}\equiv{{{dx}\over {dy}}},y^{\prime\prime}\equiv{{{d^2}y\over {dx^2}}}$$
Q58.
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If $$x{{dy} \over {dx}} + y = {{xf(xy)} \over {f'(xy)'}}$$, then | f(xy) | is equal to (where k is an arbitrary positive constant).
Q59.
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+2 / 0
Let P be a variable point on a circle C and Q be a fixed point outside C. If R is the midpoint of the line segment PQ, then locus of R is
Q60.
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Two tangents to the circle x^(2) + y^(2) = 4 at the points A and B meet at M($$-$$4, 0). The area of the quadrilateral MAOB, where O is the origin is
Q61.
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The co-ordinate of a point on the auxiliary circle of the ellipse x^(2) + 2y^(2) = 4 corresponding to the point on the ellipse whose eccentric angle is 60$$^\circ$$ will be
Q62.
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+2 / 0.5
The points of intersection of two ellipses $${x^2} + 2{y^2} - 6x - 12y + 20 = 0$$ and $$2{x^2} + {y^2} - 10x - 6y + 15 = 0$$ lie on a circle. The centre of the circle is
Q63.
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+1 / 0.25
Let $$g(x) = \int\limits_x^{2x} {{{f(t)} \over t}dt} $$ where x > 0 and f be continuous function and f(2x) = f(x), then
Q64.
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A bulb is placed at the centre of a circular track of radius 10 m. A vertical wall is erected touching the track at a point P. A man is running along the track with a speed of 10 m/sec. Starting from P the speed with which his shadow is running along the wall when he is at an angular distance of 60$$^\circ$$ from P is
Q65.
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What is the number of ways in which an examiner can assign 10 marks to 4 questions, giving not less than 2 marks to any question?
Q66.
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Five letter words, having distinct letters, are to be constructed using the letters of the word 'EQUATION' so that each word contains exactly three vowels and two consonants. How many of them have all the vowels together?
Q67.
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The value of $$\int\limits_0^5 {\max \{ {x^2},6x - 8\} \,dx} $$ is
Q68.
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+1 / 0.25
$$\int\limits_1^3 {{{\left| {x - 1} \right|} \over {\left| {x - 2} \right| + \left| {x - 3} \right|}}dx} $$ is equal to
Q69.
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+2 / 0.5
If $$b = \int\limits_0^1 {{{{e^t}} \over {t + 1}}dt} $$, then $$\int\limits_{a - 1}^a {{{{e^{ - t}}} \over {t - a - 1}}} $$ is
Q70.
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+2 / 0.5
Let $$I = \int_{\pi /4}^{\pi /3} {{{\sin x} \over x}dx} $$. Then
Q71.
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If $$\int\limits_{{{\log }_e}2}^x {{{({e^x} - 1)}^{ - 1}}dx = {{\log }_e}{3 \over 2}} $$, then the value of x is
Q72.
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+2 / 0.5
Let f(x) be continuous periodic function with period T. Let $$I = \int\limits_a^{a + T} {f(x)\,dx} $$. Then
Q73.
mcq multi
+2 / 0
Whichever of the following is/are correct?
Q74.
mcq multi
+2 / 0
Let $$f(x) = \left\{ {\matrix{
{0,} & {if} & { - 1 \le x \le 0} \cr
{1,} & {if} & {x = 0} \cr
{2,} & {if} & {0 < x \le 1} \cr
} } \right.$$ and let $$F(x) = \int\limits_{ - 1}^x {f(t)dt} $$, $$-$$1 $$\le$$ x $$\le$$ 1, then
Q75.
mcq single
+1 / 0.25
The value of the integral $$\int\limits_{ - {1 \over 2}}^{{1 \over 2}} {{{\left\{ {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right\}}^{1/2}}} dx$$ is equal to
Physics
Physics
Q1.
mcq multi
+2 / 0
The potential energy of a particle of mass 0.02 kg moving along X-axis is given by V = Ax (x $$-$$ 4) J, where x is in metre and A is a constant. Which of the following statements is/are correct?
Q2.
mcq single
+1 / 0.25
A block of mass m slides with speed v on a frictionless table towards another stationary block of mass m. A massless spring with spring constant k is attached to the second block as shown in figure. The maximum distance, the spring gets compressed through is
A block of mass m slides with speed v on a frictionless table towards another stationary block of mass m. A massless spring with spring constant k is attached to the second block as shown in figure. The maximum distance, the spring gets compressed through is
Q3.
mcq single
+1 / 0.25
What is the value of current through the diode in the circuit given?
What is the value of current through the diode in the circuit given?
Q4.
mcq single
+1 / 0.25
For the given logic circuit, the output Y for inputs (A = 0, B = 1) and (A = 0, B = 0) respectively are
For the given logic circuit, the output Y for inputs (A = 0, B = 1) and (A = 0, B = 0) respectively are
Q5.
mcq single
+1 / 0.25
In Young's double slit experiment, light of wavelength $$\lambda$$ passes through the double slit and forms interference fringes on a screen 1.2 m away. If the difference between 3rd order maximum and 3rd order minimum is 0.18 cm and the slits are 0.02 cm apart, then $$\lambda$$ is
Q6.
mcq single
+1 / 0.25
A simple pendulum, consisting of a small ball of mass m attached to a massless string hanging vertically from the ceiling is oscillating with an amplitude such that T~max~ = 2T~min~, where T~max~ and T~min~ are the maximum and minimum tension in the string, respectively. The value of maximum tension T~max~ in the string is
Q7.
mcq single
+2 / 0.5
A uniform rod of length L pivoted at one end P is freely rotated in a horizontal plane with an angular velocity $$\omega$$ about a vertical axis passing through P. If the temperature of the system is increased by $$\Delta$$T, angular velocity becomes $${\omega \over 2}$$. If coefficient of linear expansion of the rod is $$\alpha$$($$\alpha$$ << 1), then $$\Delta$$T will be
Q8.
mcq single
+1 / 0.25
Centre of mass (CM) of three particles of masses 1 kg, 2 kg and 3 kg lies at the point (1, 2, 3) and CM of another system of particles of 3 kg and 2 kg lies at the point ($$-$$1, 3, $$-$$2). Where should we put a particle of mass 5 kg, so that the CM of entire system lies at the CM of the first system?
Q9.
mcq single
+1 / 0.25
A uniform thin rod of length L, mass m is lying on a smooth horizontal table. A horizontal impulse P is suddenly applied perpendicular to the rod at one end. The total energy of the rod after the impulse is
Q10.
mcq multi
+2 / 0
A particle of mass m and charge q moving with velocity v enters region-b from region-a along the normal to the boundary as shown in the figure. Region-b has a uniform magnetic field B perpendicular to the plane of the paper. Also, region-b has length L.
Choose the correct statement.
A particle of mass m and charge q moving with velocity v enters region-b from region-a along the normal to the boundary as shown in the figure. Region-b has a uniform magnetic field B perpendicular to the plane of the paper. Also, region-b has length L.
Choose the correct statement.
Q11.
mcq single
+2 / 0.5
For a plane electromagnetic wave, the electric field is given by
$$ \overrightarrow{E} = 90\sin (0.5 \times {10^3}x + 1.5 \times {10^{11}}t)\widehat k$$ V/m. The corresponding magnetic field B will be
Q12.
mcq multi
+2 / 0
Consider the p - V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements is/are true?
Consider the p - V diagram for 1 mole of an ideal monatomic gas shown in the figure. Which of the following statements is/are true?
Q13.
mcq single
+1 / 0.25
300 g of water at 25$$^\circ$$C is added to 100 g of ice at 0$$^\circ$$C. The final temperature of the mixture is
Q14.
mcq single
+1 / 0.25
If pressure of real gas O~2~, in a container is given by $$p = {{RT} \over {2V - b}} - {a \over {4{b^2}}}$$, then the mass of the gas in the container is
Q15.
mcq single
+1 / 0.25
In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If $$\Delta$$U~1~, $$\Delta$$U~2~ and $$\Delta$$U~3~ be the changes in internal energy in these processes respectively, then
In the given figure, 1 represents isobaric, 2 represents isothermal and 3 represents adiabatic processes of an ideal gas. If $$\Delta$$U~1~, $$\Delta$$U~2~ and $$\Delta$$U~3~ be the changes in internal energy in these processes respectively, then
Q16.
mcq single
+2 / 0.5
Under isothermal conditions, two soap bubbles of radii a and b coalesce to form a single bubble of radius c. If the external pressure is p, then surface tension of the bubbles is
Q17.
mcq single
+1 / 0.25
A body of density 1.2 $$\times$$ 10^(3) kg/m^(3) is dropped from rest from a height 1 m into a liquid to density 2.4 $$\times$$ 10^(3) kg/m^(3). Neglecting all dissipative effects, the maximum depth to which the body sinks before returning to float on the surface is
Q18.
mcq single
+1 / 0.25
Two solid spheres S~1~ and S~2~ of same uniform density fall from rest under gravity in a viscous medium and after sometime, reach terminal velocities v~1~ and v~2~, respectively. If ratio of masses $${{{m_1}} \over {{m_2}}} = 8$$, then $${{{v_1}} \over {{v_2}}}$$ will be equal to
Q19.
mcq multi
+2 / 0
Electric field component of an EM radiation varies with time as E = a (cos$$\omega$$~0~t + sin$$\omega$$t cos$$\omega$$~0~t), where a is a constant and $$\omega$$ = 10^(15) s^($$-$$1), $$\omega$$~0~ = 5 $$\times$$ 10^(15) s^($$-$$1). This radiation falls on a metal whose stopping potential is $$-$$2 eV. Then, which of the following statements is/are true ? (h = 6.62 $$\times$$ 10^($$-$$34) J-s)
Q20.
mcq single
+1 / 0.25
Two point charges +q~1~ and +q~2~ are placed a finite distance d apart. It is desired to put a third charge q~3~ in between these two charges, so that q~3~ is in equilibrium. This is
Q21.
mcq single
+1 / 0.25
A metal sphere of radius R carrying charge q is surrounded by a thick concentric metal shell of inner and outer radii a and b, respectively. The net charge on the shell is zero. The potential at the centre of the sphere, when the outer surface of the shell is grounded will be
Q22.
mcq single
+1 / 0.25
Three infinite plane sheets carrying uniform charge densities $$-$$ $$\sigma$$, 2$$\sigma$$, 4$$\sigma$$ are placed parallel to XZ-plane at Y = a, 3a, 4a respectively. The electric field at the point (0, 2a, 0) is
Q23.
mcq single
+1 / 0.25
The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as shown in the figure. The value of coordinate M will be
The variation of electric field along the Z-axis due to a uniformly charged circular ring of radius a in XY-plane as shown in the figure. The value of coordinate M will be
Q24.
mcq single
+2 / 0.5
An ideal gas of molar mass M is contained in a very tall vertical cylindrical column in the uniform gravitational field. Assuming the gas temperature to be T, the height at which the centre of gravity of the gas is located is (R$$\to$$universal gas constant)
Q25.
mcq single
+1 / 0.25
In case of projectile motion, which one of the following figures represent variation of horizontal component of velocity (u~x~) with time t? (Assume that air resistance is negligible)
Q26.
mcq single
+1 / 0.25
The acceleration versus distance graph for a particle moving with initial velocity 5 m/s is shown in the figure. The velocity of the particle at x = 35 m will be
The acceleration versus distance graph for a particle moving with initial velocity 5 m/s is shown in the figure. The velocity of the particle at x = 35 m will be
Q27.
mcq single
+1 / 0.25
A spherical convex surface of power 5 D separates object and image space of refractive indices 1.0 and $$4\over3$$ , respectively. The radius of curvature of the surface is
Q28.
mcq single
+1 / 0.25
The cross-section of a reflecting surface is represented by the equation x^(2) + y^(2) = R^(2) as shown in the figure. A ray travelling in the positive x-direction is directed toward positive y-direction after reflection from the surface at point M. The coordinate of the point M on the reflecting surface is
The cross-section of a reflecting surface is represented by the equation x^(2) + y^(2) = R^(2) as shown in the figure. A ray travelling in the positive x-direction is directed toward positive y-direction after reflection from the surface at point M. The coordinate of the point M on the reflecting surface is
Q29.
mcq single
+1 / 0.25
From dimensional analysis, the Rydberg constant can be expressed in terms of electric charge (e), mass (m) and Planck constant (h) as [consider $${1 \over {4\pi {\varepsilon _0}}} \equiv 1$$ unit]
Q30.
mcq single
+1 / 0.25
A 12.5 eV electron beam is used to bombard gaseous hydrogen at ground state. The energy level upto which the hydrogen atoms would be excited is
Q31.
mcq single
+1 / 0.25
Let r, v, E be the radius of orbit, speed of electron and total energy of electron respectively in H-atom. Which of the following quantities according to Bohr theory, is proportional to the quantum number n ?
Q32.
mcq single
+1 / 0.25
Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N~1~ be the contact force between the left two blocks and N~2~ be the contact force between the right two blocks. Then,
Three blocks are pushed with a force F across a frictionless table as shown in figure above. Let N~1~ be the contact force between the left two blocks and N~2~ be the contact force between the right two blocks. Then,
Q33.
mcq single
+1 / 0.25
For two types of magnetic materials A and B, variation of $$1\over\chi$$ ($$\chi$$ : susceptibility) versus temperature T is shown in the figure. Then,
For two types of magnetic materials A and B, variation of $$1\over\chi$$ ($$\chi$$ : susceptibility) versus temperature T is shown in the figure. Then,
Q34.
mcq single
+1 / 0.25
A thin charged rod is bent into the shape of a small circle of radius R, the charge per unit length of the rod being $$\lambda$$. The circle is rotated about its axis with a time period T and it is found the magnetic field at a distance d away (d >> R) from the centre and on the axis, varies as $$R^m \over d^n$$. The values of m and n respectively are
Q35.
mcq multi
+2 / 0
A small bar magnet of dipole moment M is moving with speed v along x-direction towards a small closed circular conducting loop of radius a with its centre O at x = 0 (see figure). Assume x >> a and the coil has a resistance R. Then, which of the following statements is/are true?
A small bar magnet of dipole moment M is moving with speed v along x-direction towards a small closed circular conducting loop of radius a with its centre O at x = 0 (see figure). Assume x >> a and the coil has a resistance R. Then, which of the following statements is/are true?
Q36.
mcq single
+1 / 0.25
Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire passes through the point L at coordinates ($$-$$1, +1) and the other wire passes through the point M at coordinates ($$-$$1, $$-$$1). The resultant magnetic field at the origin O will be
Consider two infinitely long wires parallel to Z-axis carrying same current I in the positive z-direction. One wire passes through the point L at coordinates ($$-$$1, +1) and the other wire passes through the point M at coordinates ($$-$$1, $$-$$1). The resultant magnetic field at the origin O will be
Q37.
mcq single
+2 / 0.5
Two metal wires of identical dimensions are connected in series. If $$\sigma$$~1~ and $$\sigma$$~2~ are the electrical conductivities of the metal wires respectively, the effective conductivity of the combination is
Q38.
mcq single
+1 / 0.25
The carbon resistor with colour code is shown in the figure. There is no fourth band in the resistor. The value of the resistance is
The carbon resistor with colour code is shown in the figure. There is no fourth band in the resistor. The value of the resistance is
Q39.
mcq single
+1 / 0.25
The rms value of potential difference V shown in the figure is
The rms value of potential difference V shown in the figure is
Q40.
mcq single
+1 / 0.25
Consider a pure inductive AC circuit as shown in the figure. If the average power consumed is P, then
Consider a pure inductive AC circuit as shown in the figure. If the average power consumed is P, then