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PHYSICS

No of Questions
75
No of Questions
75
No of Questions
75
No of Questions
75
No of Questions
75

PHYSICS

No of Questions
75
No of Questions
75
No of Questions
75
No of Questions
75
No of Questions
75
Q 1.
If the quadratic equation \(\alpha^2(x + 1)^2 + \beta^2(2x^2 – x + 1) – 5x^2 – 3 = 0\) is satisfied for all \(x\in R\), then number of ordered pair \((\alpha, \beta)\) which is possible is/are






Q 2.
n arithmetic means are inserted between two sets of numbers \(a, a^2\) & \(b, b^2\) where\( a, b \in R\). Suppose \(m^{th}\)mean between these two sets of numbers is same, then a + b equals






Q 3.
If the sum of n terms of an A.P. is \(cn^2\), then the sum of cubes of these n terms is






Q 4.
If a, b, c are real and \(x^3–3b^2 x + 2c^3\) is divisible by (x – a) and (x – b), then \(a + b + c \ is (a \neq b)\)






Q 5.
If the equation x – sinx = p has exactly one positive root, then complete set of values of p is






Q 6.
If A is a skew symmetric matrix of odd order, then its inverse is






Q 7.
The eccentricity of conic \(4(2y – x – 3)^2 + 9(2x + y –1)^2 = 80 \)is






Q 8.
A dice is rolled 4 times. The probability of getting a larger number than the previous number each time is






Q 9.
Area bounded by the curve \( y = tan^{–1}x\) and \(y = cot^{–1}x\) between x = 0 and x = 1 is






Q 10.
If p is false and q is true, then






Q 11.
If the function \(f : [0, 27] \to\) R is differentiable and \(0 < \alpha < 1 < \beta < 2 < \gamma < 3\), then \(\int\limits^{27}_0f\ (t)dt \)  is equal to






Q 12.
Least positive root of the equation tan \(x = x^2 + 1 – 2x\) lies in the interval






Q 13.

Given that f satisfies \(|f(x) – f(y)| \leq |x – y|\) for all x and y in [a, b], then








Q 14.
If \( x, y, z, t \in R\) and \( sin^{-1}x+ cos^{-1} y+ cosec^{-1} z\geq t^2,-t\sqrt\pi+\frac{9\pi}4\) , then principal value of \( sin ^{-1}(sin \ t^2)\) is






Q 15.
In a \(\Delta\)ABC, if \(\angle C =30\)º and \(\angle B=22\frac12\)°, then the ratio in which the line joining A and circumcentre O divides BC is






Q 16.
Let \(f_1(x)\) and \(f_2(x)\) be even and odd functions respectively, where \(x^2f_1(x)-2f_1(\frac1x)=f_2(x)\) , then value of \(f_1(3)\) =






Q 17.
If the vectors \(\vec{a}=\hat{i}+2\hat{j}+2\hat{k}\) and \(\vec{b}=3\hat{i}-4\hat{j}\) are the adjacent sides of a parallelogram. Then the vector along the bisector of the angle between \(\vec{a}\) and \(\vec{b}\) having magnitude \(5 \sqrt3\) is






Q 18.
If the function\( f(x) = x^3 + e^{x^/4}\) and \(g(x) = f^{–1}(x)\), then the value of g'(1) =






Q 19.
The distance between the line \(\vec{r}=2\hat{i}-2\hat{j}+3\hat{k}+\lambda (\hat{i}-\hat{j}+4\hat{k})\) and the plane \(\vec{r.}(\hat{i}+5\hat{j}+\hat{k})=5\) is






Q 20.
Equation of common tangent with positive slope to the circle \((x – 4)^2 + y^2 = 4^2\) and hyperbola \(4x^2 – 9y^2 = 36\) is






Q 21.
A curve passing through (1, 2) and satisfying the differential equation \(\int\limits_0^xt^2y(t)dt=x^3y(x)(x>0) \) is \(x^2y=c\). find the value of c.
Q 22.
 For all complex numbers \(z_1, z_2\) satisfying\( |z_1| = 15\) and \(|z_2 – 4 – 3i| = 5 \) then the minimum value of \(|z1 – z2|\) is
Q 23.
If \( f(x)\) is a polynomial function and \(f(a) = f '(a) = 0\) and\( f ''(a) \)is non-zero, then \(\lim\limits_{x \to a} \frac{f(x)}{f'(x)}[\frac{f'(x)}{f(x)}]=\)(where [·] denotes G.I.F.)
Q 24.
Let \( f(x)\) and \(g(x)\) be differentiable for \(– 1 \leq x \leq3\) such that\( f ( -1)= 1, g(- 1)= 2 \) and \(g(3)= 5 \) . Let there exists a real number c in [–1, 3] such that f’ (c) = 2g’ (c) then the value of f (3) is
Q 25.
If \(\vec x,\vec y\) , and \(\vec z\) are unit vectors such that \(|\vec{x}-\vec{y}|^2+|\vec{y}-\vec{z}|^2+|\vec{z}-\vec{x}|^2=9\), then \(|3\vec x+5\vec y+5\vec z |=\)
Q 26.
If for 15 number of observations, \(\sum x =150,\sum x^2=3000\) . But in the above calculation one observation i.e. 10 was taken wrong and was replaced by its correct value 40. Then the correct variance is
Q 27.
Let \(^pC_q\) be the number of ways in which 5 tickets are selected from 20 tickets from 1 to 20 so that no two consecutive numbered tickets are selected, then \( p – q\) may be
Q 28.
The value of \(2^{10}C_0+\frac{2^2}{2} ^{10}C_1+\frac{2^3}3 ^{10}C_2+\frac{2^4}4^{10}C_3+......+\frac{2^{11}}{11} ^{10}C_{10}=\frac {a{^b}-1}{11}\),then \(bc_a\) is,
Q 29.
Let \(I=\int\limits_0^2\frac{15+4x-2x{^2}}{e{^6}^{(x-1)}+1}dx,\)then\(\frac6{49}I=\)
Q 30.
Total number of ways of selecting four letters from the word ‘ELLIPSE’
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