Competishun Header

Report Issue

JEE MAIN 2019
09-04-2019 - S1
Question
Let $\sum_{k=1}^{10} f(a+k)=16\left(2^{10}-1\right)$ , where the function f satisfies f(x + y) = f(x) f(y) for all natural numbers x, y and f(1) = 2. Then the natural number ‘a’ is :
Select the correct option:
A
2
B
3
C
16
D
4
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Solution Image
Question Tags
JEE Main
Mathematics
Medium
Start Preparing for JEE with Competishun
Filters 0
JEE Main
JEE Advance
Easy
Medium
Hard
Showing 18 questions
QJEE Advance 20082008
A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance2007
Let $\mathrm{E}^{\mathrm{c}}$ denote the complement of an event E . Let $\mathrm{E}, \mathrm{F}, \mathrm{G}$ be pairwise independent events with $\mathrm{P}(\mathrm{G})>0$...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20112011
Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function such that $f(1)=2$. If $6 \int_1^x f(t) d t=3 x f(x)-x^3$...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20092009
A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho=\mathrm{kr}^{\mathrm{a}}$, where...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance 20112011
Let $f(\theta)=\sin \left(\tan ^{-1}\left(\frac{\sin \theta}{\sqrt{\cos 2 \theta}}\right)\right)$, where $-\frac{\pi}{4}<\theta<\frac{\pi}{4}$. Then the value of $\frac{d}{d(\tan \theta)}(f(\theta))$ is
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance2007
The differential equation $\frac{d y}{d x}=\frac{\sqrt{1-y^2}}{y}$ determines a family of circles with
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20092009
A light inextensible string that goes over a smooth fixed pulley as shown in the figure connects two blocks of...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance 20082008
Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance 20112011
Consider the parabola $y^2=8 x$. Let $\Delta_1$ be the area of the triangle formed by the end points of its...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance2007
Let $\mathrm{O}(0,0), \mathrm{P}(3,4), \mathrm{Q}(6,0)$ be the vertices of the triangle OPQ . The point R inside the triangle OPQ is...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20092009
A steady current I goes through a wire loop PQR having shape of a right angle triangle with $...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance 20112011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advcance 20082008
The balls, having linear momenta $\overrightarrow{\mathrm{p}}_1=\mathrm{p} \hat{\mathrm{i}}$ and $\overrightarrow{\mathrm{p}}_2=-\mathrm{p} \hat{\mathrm{i}}$, undergo a collision in free space. There is no external...
JEE AdvancePhysicsEasy
View Solution
QJEE Advance2007
Let ABCD be a quadrilateral with area 18 , with side AB parallel to the side CD and $\mathrm{AB}=2 \mathrm{CD}$....
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20112011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance2007
If $|z|=1$ and $z \neq \pm 1$, then all the values of $\frac{z}{1-z^2}$ lie on
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance2007
The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in...
JEE AdvanceMathematicsEasy
View Solution
QJEE Advance 20112011
Let $\mathrm{a}, \mathrm{b}$ and c be three real numbers satisfying $...
JEE AdvanceMathematicsEasy
View Solution