Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.

Differential Equations

Multiple Choice Questions

Let be three unit vectors such that then the angle between is

3π/4
π/2
2π/3
5π/6

185 Views

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

3a²−26a+55=0
3a²−32a+84=0
3a²−34a+91=0
3a²−34a+91=0

206 Views

Let y(x) be the solution of the differential equation $left parenthesis straight x space log space straight x right parenthesis dy over dx space plus straight y space equals space 2 space straight x space log space straight x comma$ (x ≥1). Then, y (e) is equal to

182 Views

If $left parenthesis 2 space sin space straight x right parenthesis space dy over dx space plus space left parenthesis space straight y space plus 1 right parenthesis space cos space straight x space equals space 0 space and space straight y left parenthesis 0 right parenthesis space equals 1 space then space straight y open parentheses straight pi over 2 close parentheses$ is equal to

4/3
1/3
-2/3
-2/3

220 Views

Let In ∫tan x dx,(n> 1) . I⁴ + I⁶ = a tan⁵x + bx⁵ + C, where C is a constant of integration, then the ordered pair (a, b) is equal to

$open parentheses negative 1 fifth comma 0 close parentheses$
$open parentheses negative 1 fifth comma 1 close parentheses$
$open parentheses 1 fifth comma 0 close parentheses$
$open parentheses 1 fifth comma 0 close parentheses$

281 Views

6.
How many real solutions does the equation x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0 have?

7

1

3

3

x⁷+ 14x⁵+ 16x³+ 30x – 560 = 0
Let f(x) = x⁷+ 14x⁵+ 16x³+ 30x
⇒ f′(x) = 7x⁶+ 70x⁴+ 48x²+ 30 > 0 ∀ x.
∴ f (x) is an increasing function ∀ x.

149 Views

Let the orthocentre and centroid of a triangle be A(–3, 5) and B(3, 3) respectively. If C is the circumcentre of this triangle, then the radius of the circle having line segment AC as diameter, is

$\frac{3 \sqrt{5}}{2}$
$\sqrt{10}$
$2 \sqrt{10}$
$3 \sqrt{\frac{5}{2}}$

Consider the non-constant differentiable function f of one variable which obeys the relation $\frac{f (x)}{f (y)}$ f(x - y ). If f'(0)= p and f(y) . f'(5) = q, then f'(- 5) is